1,1,0,0,0.008052," ","integrate(0,x)","0"," ",0,"0","A",0
2,1,0,0,0.023329," ","integrate(1,x)","x"," ",0,"x","A",0
3,1,2,0,0.015770," ","integrate(5,x)","5 x"," ",0,"5*x","A",0
4,1,3,0,0.015376," ","integrate(-2,x)","- 2 x"," ",0,"-2*x","A",0
5,1,5,0,0.014917," ","integrate(-3/2,x)","- \frac{3 x}{2}"," ",0,"-3*x/2","A",0
6,1,2,0,0.014901," ","integrate(pi,x)","\pi x"," ",0,"pi*x","A",0
7,1,2,0,0.015852," ","integrate(a,x)","a x"," ",0,"a*x","A",0
8,1,3,0,0.016256," ","integrate(3*a,x)","3 a x"," ",0,"3*a*x","A",0
9,1,10,0,0.055023," ","integrate(pi/(16-exp(2))**(1/2),x)","\frac{\pi x}{\sqrt{16 - e^{2}}}"," ",0,"pi*x/sqrt(16 - exp(2))","A",0
10,1,3,0,0.055393," ","integrate(x**100,x)","\frac{x^{101}}{101}"," ",0,"x**101/101","A",0
11,1,3,0,0.054377," ","integrate(x**3,x)","\frac{x^{4}}{4}"," ",0,"x**4/4","A",0
12,1,3,0,0.054521," ","integrate(x**2,x)","\frac{x^{3}}{3}"," ",0,"x**3/3","A",0
13,1,3,0,0.017280," ","integrate(x,x)","\frac{x^{2}}{2}"," ",0,"x**2/2","A",0
14,1,0,0,0.014882," ","integrate(1,x)","x"," ",0,"x","A",0
15,1,2,0,0.059690," ","integrate(1/x,x)","\log{\left(x \right)}"," ",0,"log(x)","A",0
16,1,3,0,0.058352," ","integrate(1/x**2,x)","- \frac{1}{x}"," ",0,"-1/x","A",0
17,1,7,0,0.058160," ","integrate(1/x**3,x)","- \frac{1}{2 x^{2}}"," ",0,"-1/(2*x**2)","A",0
18,1,7,0,0.058667," ","integrate(1/x**4,x)","- \frac{1}{3 x^{3}}"," ",0,"-1/(3*x**3)","A",0
19,1,7,0,0.059987," ","integrate(1/x**100,x)","- \frac{1}{99 x^{99}}"," ",0,"-1/(99*x**99)","A",0
20,1,7,0,0.068156," ","integrate(x**(5/2),x)","\frac{2 x^{\frac{7}{2}}}{7}"," ",0,"2*x**(7/2)/7","A",0
21,1,7,0,0.059055," ","integrate(x**(3/2),x)","\frac{2 x^{\frac{5}{2}}}{5}"," ",0,"2*x**(5/2)/5","A",0
22,1,7,0,0.062350," ","integrate(x**(1/2),x)","\frac{2 x^{\frac{3}{2}}}{3}"," ",0,"2*x**(3/2)/3","A",0
23,1,5,0,0.059037," ","integrate(1/x**(1/2),x)","2 \sqrt{x}"," ",0,"2*sqrt(x)","A",0
24,1,7,0,0.061070," ","integrate(1/x**(3/2),x)","- \frac{2}{\sqrt{x}}"," ",0,"-2/sqrt(x)","A",0
25,1,8,0,0.060824," ","integrate(1/x**(5/2),x)","- \frac{2}{3 x^{\frac{3}{2}}}"," ",0,"-2/(3*x**(3/2))","A",0
26,1,7,0,0.060255," ","integrate(x**(5/3),x)","\frac{3 x^{\frac{8}{3}}}{8}"," ",0,"3*x**(8/3)/8","A",0
27,1,7,0,0.060777," ","integrate(x**(4/3),x)","\frac{3 x^{\frac{7}{3}}}{7}"," ",0,"3*x**(7/3)/7","A",0
28,1,7,0,0.061666," ","integrate(x**(2/3),x)","\frac{3 x^{\frac{5}{3}}}{5}"," ",0,"3*x**(5/3)/5","A",0
29,1,7,0,0.061030," ","integrate(x**(1/3),x)","\frac{3 x^{\frac{4}{3}}}{4}"," ",0,"3*x**(4/3)/4","A",0
30,1,7,0,0.060533," ","integrate(1/x**(1/3),x)","\frac{3 x^{\frac{2}{3}}}{2}"," ",0,"3*x**(2/3)/2","A",0
31,1,5,0,0.059513," ","integrate(1/x**(2/3),x)","3 \sqrt[3]{x}"," ",0,"3*x**(1/3)","A",0
32,1,7,0,0.060031," ","integrate(1/x**(4/3),x)","- \frac{3}{\sqrt[3]{x}}"," ",0,"-3/x**(1/3)","A",0
33,1,8,0,0.060255," ","integrate(1/x**(5/3),x)","- \frac{3}{2 x^{\frac{2}{3}}}"," ",0,"-3/(2*x**(2/3))","A",0
34,1,12,0,0.063332," ","integrate(x**n,x)","\begin{cases} \frac{x^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**(n + 1)/(n + 1), Ne(n, -1)), (log(x), True))","A",0
35,1,17,0,0.064156," ","integrate((b*x)**n,x)","\frac{\begin{cases} \frac{\left(b x\right)^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(b x \right)} & \text{otherwise} \end{cases}}{b}"," ",0,"Piecewise(((b*x)**(n + 1)/(n + 1), Ne(n, -1)), (log(b*x), True))/b","A",0
36,1,19,0,0.086684," ","integrate(1/(e*(d*x+c)+(-a)**(1/2)),x)","\frac{\log{\left(c e + d e x + \sqrt{- a} \right)}}{d e}"," ",0,"log(c*e + d*e*x + sqrt(-a))/(d*e)","A",0
37,1,270,0,71.800555," ","integrate((c+d*(b*x+a))**(5/2),x)","\begin{cases} c^{\frac{5}{2}} x & \text{for}\: b = 0 \wedge d = 0 \\x \left(a d + c\right)^{\frac{5}{2}} & \text{for}\: b = 0 \\c^{\frac{5}{2}} x & \text{for}\: d = 0 \\\frac{2 a^{3} d^{2} \sqrt{a d + b d x + c}}{7 b} + \frac{6 a^{2} d^{2} x \sqrt{a d + b d x + c}}{7} + \frac{6 a^{2} c d \sqrt{a d + b d x + c}}{7 b} + \frac{6 a b d^{2} x^{2} \sqrt{a d + b d x + c}}{7} + \frac{12 a c d x \sqrt{a d + b d x + c}}{7} + \frac{6 a c^{2} \sqrt{a d + b d x + c}}{7 b} + \frac{2 b^{2} d^{2} x^{3} \sqrt{a d + b d x + c}}{7} + \frac{6 b c d x^{2} \sqrt{a d + b d x + c}}{7} + \frac{6 c^{2} x \sqrt{a d + b d x + c}}{7} + \frac{2 c^{3} \sqrt{a d + b d x + c}}{7 b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**(5/2)*x, Eq(b, 0) & Eq(d, 0)), (x*(a*d + c)**(5/2), Eq(b, 0)), (c**(5/2)*x, Eq(d, 0)), (2*a**3*d**2*sqrt(a*d + b*d*x + c)/(7*b) + 6*a**2*d**2*x*sqrt(a*d + b*d*x + c)/7 + 6*a**2*c*d*sqrt(a*d + b*d*x + c)/(7*b) + 6*a*b*d**2*x**2*sqrt(a*d + b*d*x + c)/7 + 12*a*c*d*x*sqrt(a*d + b*d*x + c)/7 + 6*a*c**2*sqrt(a*d + b*d*x + c)/(7*b) + 2*b**2*d**2*x**3*sqrt(a*d + b*d*x + c)/7 + 6*b*c*d*x**2*sqrt(a*d + b*d*x + c)/7 + 6*c**2*x*sqrt(a*d + b*d*x + c)/7 + 2*c**3*sqrt(a*d + b*d*x + c)/(7*b*d), True))","A",0
38,1,156,0,5.270027," ","integrate((c+d*(b*x+a))**(3/2),x)","\begin{cases} c^{\frac{3}{2}} x & \text{for}\: b = 0 \wedge d = 0 \\x \left(a d + c\right)^{\frac{3}{2}} & \text{for}\: b = 0 \\c^{\frac{3}{2}} x & \text{for}\: d = 0 \\\frac{2 a^{2} d \sqrt{a d + b d x + c}}{5 b} + \frac{4 a d x \sqrt{a d + b d x + c}}{5} + \frac{4 a c \sqrt{a d + b d x + c}}{5 b} + \frac{2 b d x^{2} \sqrt{a d + b d x + c}}{5} + \frac{4 c x \sqrt{a d + b d x + c}}{5} + \frac{2 c^{2} \sqrt{a d + b d x + c}}{5 b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**(3/2)*x, Eq(b, 0) & Eq(d, 0)), (x*(a*d + c)**(3/2), Eq(b, 0)), (c**(3/2)*x, Eq(d, 0)), (2*a**2*d*sqrt(a*d + b*d*x + c)/(5*b) + 4*a*d*x*sqrt(a*d + b*d*x + c)/5 + 4*a*c*sqrt(a*d + b*d*x + c)/(5*b) + 2*b*d*x**2*sqrt(a*d + b*d*x + c)/5 + 4*c*x*sqrt(a*d + b*d*x + c)/5 + 2*c**2*sqrt(a*d + b*d*x + c)/(5*b*d), True))","A",0
39,1,82,0,0.444187," ","integrate((c+d*(b*x+a))**(1/2),x)","\begin{cases} \sqrt{c} x & \text{for}\: b = 0 \wedge d = 0 \\x \sqrt{a d + c} & \text{for}\: b = 0 \\\sqrt{c} x & \text{for}\: d = 0 \\\frac{2 a \sqrt{a d + b d x + c}}{3 b} + \frac{2 x \sqrt{a d + b d x + c}}{3} + \frac{2 c \sqrt{a d + b d x + c}}{3 b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c)*x, Eq(b, 0) & Eq(d, 0)), (x*sqrt(a*d + c), Eq(b, 0)), (sqrt(c)*x, Eq(d, 0)), (2*a*sqrt(a*d + b*d*x + c)/(3*b) + 2*x*sqrt(a*d + b*d*x + c)/3 + 2*c*sqrt(a*d + b*d*x + c)/(3*b*d), True))","A",0
40,1,31,0,1.782253," ","integrate(1/(c+d*(b*x+a))**(1/2),x)","\begin{cases} \frac{x}{\sqrt{a d + c}} & \text{for}\: b = 0 \\\frac{x}{\sqrt{c}} & \text{for}\: d = 0 \\\frac{2 \sqrt{c + d \left(a + b x\right)}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/sqrt(a*d + c), Eq(b, 0)), (x/sqrt(c), Eq(d, 0)), (2*sqrt(c + d*(a + b*x))/(b*d), True))","A",0
41,1,58,0,1.794831," ","integrate(1/(c+d*(b*x+a))**(3/2),x)","\begin{cases} \frac{x}{c^{\frac{3}{2}}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x}{\left(a d + c\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \\\frac{x}{c^{\frac{3}{2}}} & \text{for}\: d = 0 \\- \frac{2 \sqrt{a d + b d x + c}}{a b d^{2} + b^{2} d^{2} x + b c d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/c**(3/2), Eq(b, 0) & Eq(d, 0)), (x/(a*d + c)**(3/2), Eq(b, 0)), (x/c**(3/2), Eq(d, 0)), (-2*sqrt(a*d + b*d*x + c)/(a*b*d**2 + b**2*d**2*x + b*c*d), True))","A",0
42,1,102,0,6.786330," ","integrate(1/(c+d*(b*x+a))**(5/2),x)","\begin{cases} \frac{x}{c^{\frac{5}{2}}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x}{\left(a d + c\right)^{\frac{5}{2}}} & \text{for}\: b = 0 \\\frac{x}{c^{\frac{5}{2}}} & \text{for}\: d = 0 \\- \frac{2 \sqrt{a d + b d x + c}}{3 a^{2} b d^{3} + 6 a b^{2} d^{3} x + 6 a b c d^{2} + 3 b^{3} d^{3} x^{2} + 6 b^{2} c d^{2} x + 3 b c^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/c**(5/2), Eq(b, 0) & Eq(d, 0)), (x/(a*d + c)**(5/2), Eq(b, 0)), (x/c**(5/2), Eq(d, 0)), (-2*sqrt(a*d + b*d*x + c)/(3*a**2*b*d**3 + 6*a*b**2*d**3*x + 6*a*b*c*d**2 + 3*b**3*d**3*x**2 + 6*b**2*c*d**2*x + 3*b*c**2*d), True))","A",0
43,1,12,0,0.063302," ","integrate(x**3*(b*x+a),x)","\frac{a x^{4}}{4} + \frac{b x^{5}}{5}"," ",0,"a*x**4/4 + b*x**5/5","A",0
44,1,12,0,0.063240," ","integrate(x**2*(b*x+a),x)","\frac{a x^{3}}{3} + \frac{b x^{4}}{4}"," ",0,"a*x**3/3 + b*x**4/4","A",0
45,1,12,0,0.064328," ","integrate(x*(b*x+a),x)","\frac{a x^{2}}{2} + \frac{b x^{3}}{3}"," ",0,"a*x**2/2 + b*x**3/3","A",0
46,1,8,0,0.060486," ","integrate(b*x+a,x)","a x + \frac{b x^{2}}{2}"," ",0,"a*x + b*x**2/2","A",0
47,1,7,0,0.089982," ","integrate((b*x+a)/x,x)","a \log{\left(x \right)} + b x"," ",0,"a*log(x) + b*x","A",0
48,1,7,0,0.111121," ","integrate((b*x+a)/x**2,x)","- \frac{a}{x} + b \log{\left(x \right)}"," ",0,"-a/x + b*log(x)","A",0
49,1,12,0,0.110302," ","integrate((b*x+a)/x**3,x)","\frac{- a - 2 b x}{2 x^{2}}"," ",0,"(-a - 2*b*x)/(2*x**2)","A",0
50,1,14,0,0.130562," ","integrate((b*x+a)/x**4,x)","\frac{- 2 a - 3 b x}{6 x^{3}}"," ",0,"(-2*a - 3*b*x)/(6*x**3)","A",0
51,1,14,0,0.162989," ","integrate((b*x+a)/x**5,x)","\frac{- 3 a - 4 b x}{12 x^{4}}"," ",0,"(-3*a - 4*b*x)/(12*x**4)","A",0
52,1,26,0,0.072217," ","integrate(x**3*(b*x+a)**2,x)","\frac{a^{2} x^{4}}{4} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{6}}{6}"," ",0,"a**2*x**4/4 + 2*a*b*x**5/5 + b**2*x**6/6","A",0
53,1,24,0,0.073054," ","integrate(x**2*(b*x+a)**2,x)","\frac{a^{2} x^{3}}{3} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{5}}{5}"," ",0,"a**2*x**3/3 + a*b*x**4/2 + b**2*x**5/5","A",0
54,1,26,0,0.066958," ","integrate(x*(b*x+a)**2,x)","\frac{a^{2} x^{2}}{2} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{4}}{4}"," ",0,"a**2*x**2/2 + 2*a*b*x**3/3 + b**2*x**4/4","A",0
55,1,19,0,0.070774," ","integrate((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","B",0
56,1,20,0,0.107831," ","integrate((b*x+a)**2/x,x)","a^{2} \log{\left(x \right)} + 2 a b x + \frac{b^{2} x^{2}}{2}"," ",0,"a**2*log(x) + 2*a*b*x + b**2*x**2/2","A",0
57,1,17,0,0.125788," ","integrate((b*x+a)**2/x**2,x)","- \frac{a^{2}}{x} + 2 a b \log{\left(x \right)} + b^{2} x"," ",0,"-a**2/x + 2*a*b*log(x) + b**2*x","A",0
58,1,22,0,0.166853," ","integrate((b*x+a)**2/x**3,x)","b^{2} \log{\left(x \right)} + \frac{- a^{2} - 4 a b x}{2 x^{2}}"," ",0,"b**2*log(x) + (-a**2 - 4*a*b*x)/(2*x**2)","A",0
59,1,24,0,0.178054," ","integrate((b*x+a)**2/x**4,x)","\frac{- a^{2} - 3 a b x - 3 b^{2} x^{2}}{3 x^{3}}"," ",0,"(-a**2 - 3*a*b*x - 3*b**2*x**2)/(3*x**3)","A",0
60,1,26,0,0.186756," ","integrate((b*x+a)**2/x**5,x)","\frac{- 3 a^{2} - 8 a b x - 6 b^{2} x^{2}}{12 x^{4}}"," ",0,"(-3*a**2 - 8*a*b*x - 6*b**2*x**2)/(12*x**4)","A",0
61,1,26,0,0.189998," ","integrate((b*x+a)**2/x**6,x)","\frac{- 6 a^{2} - 15 a b x - 10 b^{2} x^{2}}{30 x^{5}}"," ",0,"(-6*a**2 - 15*a*b*x - 10*b**2*x**2)/(30*x**5)","A",0
62,1,26,0,0.197580," ","integrate((b*x+a)**2/x**7,x)","\frac{- 10 a^{2} - 24 a b x - 15 b^{2} x^{2}}{60 x^{6}}"," ",0,"(-10*a**2 - 24*a*b*x - 15*b**2*x**2)/(60*x**6)","A",0
63,1,26,0,0.213955," ","integrate((b*x+a)**2/x**8,x)","\frac{- 15 a^{2} - 35 a b x - 21 b^{2} x^{2}}{105 x^{7}}"," ",0,"(-15*a**2 - 35*a*b*x - 21*b**2*x**2)/(105*x**7)","A",0
64,1,37,0,0.077283," ","integrate(x**4*(b*x+a)**3,x)","\frac{a^{3} x^{5}}{5} + \frac{a^{2} b x^{6}}{2} + \frac{3 a b^{2} x^{7}}{7} + \frac{b^{3} x^{8}}{8}"," ",0,"a**3*x**5/5 + a**2*b*x**6/2 + 3*a*b**2*x**7/7 + b**3*x**8/8","A",0
65,1,37,0,0.073507," ","integrate(x**3*(b*x+a)**3,x)","\frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{5}}{5} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{7}}{7}"," ",0,"a**3*x**4/4 + 3*a**2*b*x**5/5 + a*b**2*x**6/2 + b**3*x**7/7","A",0
66,1,39,0,0.072097," ","integrate(x**2*(b*x+a)**3,x)","\frac{a^{3} x^{3}}{3} + \frac{3 a^{2} b x^{4}}{4} + \frac{3 a b^{2} x^{5}}{5} + \frac{b^{3} x^{6}}{6}"," ",0,"a**3*x**3/3 + 3*a**2*b*x**4/4 + 3*a*b**2*x**5/5 + b**3*x**6/6","A",0
67,1,36,0,0.073958," ","integrate(x*(b*x+a)**3,x)","\frac{a^{3} x^{2}}{2} + a^{2} b x^{3} + \frac{3 a b^{2} x^{4}}{4} + \frac{b^{3} x^{5}}{5}"," ",0,"a**3*x**2/2 + a**2*b*x**3 + 3*a*b**2*x**4/4 + b**3*x**5/5","A",0
68,1,32,0,0.073522," ","integrate((b*x+a)**3,x)","a^{3} x + \frac{3 a^{2} b x^{2}}{2} + a b^{2} x^{3} + \frac{b^{3} x^{4}}{4}"," ",0,"a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4","B",0
69,1,34,0,0.121679," ","integrate((b*x+a)**3/x,x)","a^{3} \log{\left(x \right)} + 3 a^{2} b x + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{3}}{3}"," ",0,"a**3*log(x) + 3*a**2*b*x + 3*a*b**2*x**2/2 + b**3*x**3/3","A",0
70,1,31,0,0.130021," ","integrate((b*x+a)**3/x**2,x)","- \frac{a^{3}}{x} + 3 a^{2} b \log{\left(x \right)} + 3 a b^{2} x + \frac{b^{3} x^{2}}{2}"," ",0,"-a**3/x + 3*a**2*b*log(x) + 3*a*b**2*x + b**3*x**2/2","A",0
71,1,32,0,0.187185," ","integrate((b*x+a)**3/x**3,x)","3 a b^{2} \log{\left(x \right)} + b^{3} x + \frac{- a^{3} - 6 a^{2} b x}{2 x^{2}}"," ",0,"3*a*b**2*log(x) + b**3*x + (-a**3 - 6*a**2*b*x)/(2*x**2)","A",0
72,1,36,0,0.235437," ","integrate((b*x+a)**3/x**4,x)","b^{3} \log{\left(x \right)} + \frac{- 2 a^{3} - 9 a^{2} b x - 18 a b^{2} x^{2}}{6 x^{3}}"," ",0,"b**3*log(x) + (-2*a**3 - 9*a**2*b*x - 18*a*b**2*x**2)/(6*x**3)","A",0
73,1,36,0,0.256243," ","integrate((b*x+a)**3/x**5,x)","\frac{- a^{3} - 4 a^{2} b x - 6 a b^{2} x^{2} - 4 b^{3} x^{3}}{4 x^{4}}"," ",0,"(-a**3 - 4*a**2*b*x - 6*a*b**2*x**2 - 4*b**3*x**3)/(4*x**4)","B",0
74,1,37,0,0.247421," ","integrate((b*x+a)**3/x**6,x)","\frac{- 4 a^{3} - 15 a^{2} b x - 20 a b^{2} x^{2} - 10 b^{3} x^{3}}{20 x^{5}}"," ",0,"(-4*a**3 - 15*a**2*b*x - 20*a*b**2*x**2 - 10*b**3*x**3)/(20*x**5)","A",0
75,1,37,0,0.336495," ","integrate((b*x+a)**3/x**7,x)","\frac{- 10 a^{3} - 36 a^{2} b x - 45 a b^{2} x^{2} - 20 b^{3} x^{3}}{60 x^{6}}"," ",0,"(-10*a**3 - 36*a**2*b*x - 45*a*b**2*x**2 - 20*b**3*x**3)/(60*x**6)","A",0
76,1,37,0,0.289828," ","integrate((b*x+a)**3/x**8,x)","\frac{- 20 a^{3} - 70 a^{2} b x - 84 a b^{2} x^{2} - 35 b^{3} x^{3}}{140 x^{7}}"," ",0,"(-20*a**3 - 70*a**2*b*x - 84*a*b**2*x**2 - 35*b**3*x**3)/(140*x**7)","A",0
77,1,63,0,0.089236," ","integrate(x**6*(b*x+a)**5,x)","\frac{a^{5} x^{7}}{7} + \frac{5 a^{4} b x^{8}}{8} + \frac{10 a^{3} b^{2} x^{9}}{9} + a^{2} b^{3} x^{10} + \frac{5 a b^{4} x^{11}}{11} + \frac{b^{5} x^{12}}{12}"," ",0,"a**5*x**7/7 + 5*a**4*b*x**8/8 + 10*a**3*b**2*x**9/9 + a**2*b**3*x**10 + 5*a*b**4*x**11/11 + b**5*x**12/12","A",0
78,1,65,0,0.081576," ","integrate(x**5*(b*x+a)**5,x)","\frac{a^{5} x^{6}}{6} + \frac{5 a^{4} b x^{7}}{7} + \frac{5 a^{3} b^{2} x^{8}}{4} + \frac{10 a^{2} b^{3} x^{9}}{9} + \frac{a b^{4} x^{10}}{2} + \frac{b^{5} x^{11}}{11}"," ",0,"a**5*x**6/6 + 5*a**4*b*x**7/7 + 5*a**3*b**2*x**8/4 + 10*a**2*b**3*x**9/9 + a*b**4*x**10/2 + b**5*x**11/11","A",0
79,1,66,0,0.079385," ","integrate(x**4*(b*x+a)**5,x)","\frac{a^{5} x^{5}}{5} + \frac{5 a^{4} b x^{6}}{6} + \frac{10 a^{3} b^{2} x^{7}}{7} + \frac{5 a^{2} b^{3} x^{8}}{4} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{10}}{10}"," ",0,"a**5*x**5/5 + 5*a**4*b*x**6/6 + 10*a**3*b**2*x**7/7 + 5*a**2*b**3*x**8/4 + 5*a*b**4*x**9/9 + b**5*x**10/10","A",0
80,1,63,0,0.099513," ","integrate(x**3*(b*x+a)**5,x)","\frac{a^{5} x^{4}}{4} + a^{4} b x^{5} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{10 a^{2} b^{3} x^{7}}{7} + \frac{5 a b^{4} x^{8}}{8} + \frac{b^{5} x^{9}}{9}"," ",0,"a**5*x**4/4 + a**4*b*x**5 + 5*a**3*b**2*x**6/3 + 10*a**2*b**3*x**7/7 + 5*a*b**4*x**8/8 + b**5*x**9/9","A",0
81,1,65,0,0.077463," ","integrate(x**2*(b*x+a)**5,x)","\frac{a^{5} x^{3}}{3} + \frac{5 a^{4} b x^{4}}{4} + 2 a^{3} b^{2} x^{5} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{5 a b^{4} x^{7}}{7} + \frac{b^{5} x^{8}}{8}"," ",0,"a**5*x**3/3 + 5*a**4*b*x**4/4 + 2*a**3*b**2*x**5 + 5*a**2*b**3*x**6/3 + 5*a*b**4*x**7/7 + b**5*x**8/8","A",0
82,1,65,0,0.084423," ","integrate(x*(b*x+a)**5,x)","\frac{a^{5} x^{2}}{2} + \frac{5 a^{4} b x^{3}}{3} + \frac{5 a^{3} b^{2} x^{4}}{2} + 2 a^{2} b^{3} x^{5} + \frac{5 a b^{4} x^{6}}{6} + \frac{b^{5} x^{7}}{7}"," ",0,"a**5*x**2/2 + 5*a**4*b*x**3/3 + 5*a**3*b**2*x**4/2 + 2*a**2*b**3*x**5 + 5*a*b**4*x**6/6 + b**5*x**7/7","B",0
83,1,60,0,0.080750," ","integrate((b*x+a)**5,x)","a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6}"," ",0,"a**5*x + 5*a**4*b*x**2/2 + 10*a**3*b**2*x**3/3 + 5*a**2*b**3*x**4/2 + a*b**4*x**5 + b**5*x**6/6","B",0
84,1,60,0,0.154714," ","integrate((b*x+a)**5/x,x)","a^{5} \log{\left(x \right)} + 5 a^{4} b x + 5 a^{3} b^{2} x^{2} + \frac{10 a^{2} b^{3} x^{3}}{3} + \frac{5 a b^{4} x^{4}}{4} + \frac{b^{5} x^{5}}{5}"," ",0,"a**5*log(x) + 5*a**4*b*x + 5*a**3*b**2*x**2 + 10*a**2*b**3*x**3/3 + 5*a*b**4*x**4/4 + b**5*x**5/5","A",0
85,1,56,0,0.175109," ","integrate((b*x+a)**5/x**2,x)","- \frac{a^{5}}{x} + 5 a^{4} b \log{\left(x \right)} + 10 a^{3} b^{2} x + 5 a^{2} b^{3} x^{2} + \frac{5 a b^{4} x^{3}}{3} + \frac{b^{5} x^{4}}{4}"," ",0,"-a**5/x + 5*a**4*b*log(x) + 10*a**3*b**2*x + 5*a**2*b**3*x**2 + 5*a*b**4*x**3/3 + b**5*x**4/4","A",0
86,1,60,0,0.203808," ","integrate((b*x+a)**5/x**3,x)","10 a^{3} b^{2} \log{\left(x \right)} + 10 a^{2} b^{3} x + \frac{5 a b^{4} x^{2}}{2} + \frac{b^{5} x^{3}}{3} + \frac{- a^{5} - 10 a^{4} b x}{2 x^{2}}"," ",0,"10*a**3*b**2*log(x) + 10*a**2*b**3*x + 5*a*b**4*x**2/2 + b**5*x**3/3 + (-a**5 - 10*a**4*b*x)/(2*x**2)","A",0
87,1,60,0,0.257611," ","integrate((b*x+a)**5/x**4,x)","10 a^{2} b^{3} \log{\left(x \right)} + 5 a b^{4} x + \frac{b^{5} x^{2}}{2} + \frac{- 2 a^{5} - 15 a^{4} b x - 60 a^{3} b^{2} x^{2}}{6 x^{3}}"," ",0,"10*a**2*b**3*log(x) + 5*a*b**4*x + b**5*x**2/2 + (-2*a**5 - 15*a**4*b*x - 60*a**3*b**2*x**2)/(6*x**3)","A",0
88,1,58,0,0.289438," ","integrate((b*x+a)**5/x**5,x)","5 a b^{4} \log{\left(x \right)} + b^{5} x + \frac{- 3 a^{5} - 20 a^{4} b x - 60 a^{3} b^{2} x^{2} - 120 a^{2} b^{3} x^{3}}{12 x^{4}}"," ",0,"5*a*b**4*log(x) + b**5*x + (-3*a**5 - 20*a**4*b*x - 60*a**3*b**2*x**2 - 120*a**2*b**3*x**3)/(12*x**4)","A",0
89,1,60,0,0.357226," ","integrate((b*x+a)**5/x**6,x)","b^{5} \log{\left(x \right)} + \frac{- 12 a^{5} - 75 a^{4} b x - 200 a^{3} b^{2} x^{2} - 300 a^{2} b^{3} x^{3} - 300 a b^{4} x^{4}}{60 x^{5}}"," ",0,"b**5*log(x) + (-12*a**5 - 75*a**4*b*x - 200*a**3*b**2*x**2 - 300*a**2*b**3*x**3 - 300*a*b**4*x**4)/(60*x**5)","A",0
90,1,60,0,0.371170," ","integrate((b*x+a)**5/x**7,x)","\frac{- a^{5} - 6 a^{4} b x - 15 a^{3} b^{2} x^{2} - 20 a^{2} b^{3} x^{3} - 15 a b^{4} x^{4} - 6 b^{5} x^{5}}{6 x^{6}}"," ",0,"(-a**5 - 6*a**4*b*x - 15*a**3*b**2*x**2 - 20*a**2*b**3*x**3 - 15*a*b**4*x**4 - 6*b**5*x**5)/(6*x**6)","B",0
91,1,61,0,0.413748," ","integrate((b*x+a)**5/x**8,x)","\frac{- 6 a^{5} - 35 a^{4} b x - 84 a^{3} b^{2} x^{2} - 105 a^{2} b^{3} x^{3} - 70 a b^{4} x^{4} - 21 b^{5} x^{5}}{42 x^{7}}"," ",0,"(-6*a**5 - 35*a**4*b*x - 84*a**3*b**2*x**2 - 105*a**2*b**3*x**3 - 70*a*b**4*x**4 - 21*b**5*x**5)/(42*x**7)","B",0
92,1,61,0,0.431458," ","integrate((b*x+a)**5/x**9,x)","\frac{- 21 a^{5} - 120 a^{4} b x - 280 a^{3} b^{2} x^{2} - 336 a^{2} b^{3} x^{3} - 210 a b^{4} x^{4} - 56 b^{5} x^{5}}{168 x^{8}}"," ",0,"(-21*a**5 - 120*a**4*b*x - 280*a**3*b**2*x**2 - 336*a**2*b**3*x**3 - 210*a*b**4*x**4 - 56*b**5*x**5)/(168*x**8)","A",0
93,1,61,0,0.449980," ","integrate((b*x+a)**5/x**10,x)","\frac{- 56 a^{5} - 315 a^{4} b x - 720 a^{3} b^{2} x^{2} - 840 a^{2} b^{3} x^{3} - 504 a b^{4} x^{4} - 126 b^{5} x^{5}}{504 x^{9}}"," ",0,"(-56*a**5 - 315*a**4*b*x - 720*a**3*b**2*x**2 - 840*a**2*b**3*x**3 - 504*a*b**4*x**4 - 126*b**5*x**5)/(504*x**9)","A",0
94,1,61,0,0.490306," ","integrate((b*x+a)**5/x**11,x)","\frac{- 126 a^{5} - 700 a^{4} b x - 1575 a^{3} b^{2} x^{2} - 1800 a^{2} b^{3} x^{3} - 1050 a b^{4} x^{4} - 252 b^{5} x^{5}}{1260 x^{10}}"," ",0,"(-126*a**5 - 700*a**4*b*x - 1575*a**3*b**2*x**2 - 1800*a**2*b**3*x**3 - 1050*a*b**4*x**4 - 252*b**5*x**5)/(1260*x**10)","A",0
95,1,61,0,0.581808," ","integrate((b*x+a)**5/x**12,x)","\frac{- 252 a^{5} - 1386 a^{4} b x - 3080 a^{3} b^{2} x^{2} - 3465 a^{2} b^{3} x^{3} - 1980 a b^{4} x^{4} - 462 b^{5} x^{5}}{2772 x^{11}}"," ",0,"(-252*a**5 - 1386*a**4*b*x - 3080*a**3*b**2*x**2 - 3465*a**2*b**3*x**3 - 1980*a*b**4*x**4 - 462*b**5*x**5)/(2772*x**11)","A",0
96,1,61,0,0.615519," ","integrate((b*x+a)**5/x**13,x)","\frac{- 462 a^{5} - 2520 a^{4} b x - 5544 a^{3} b^{2} x^{2} - 6160 a^{2} b^{3} x^{3} - 3465 a b^{4} x^{4} - 792 b^{5} x^{5}}{5544 x^{12}}"," ",0,"(-462*a**5 - 2520*a**4*b*x - 5544*a**3*b**2*x**2 - 6160*a**2*b**3*x**3 - 3465*a*b**4*x**4 - 792*b**5*x**5)/(5544*x**12)","A",0
97,1,61,0,0.624603," ","integrate((b*x+a)**5/x**14,x)","\frac{- 792 a^{5} - 4290 a^{4} b x - 9360 a^{3} b^{2} x^{2} - 10296 a^{2} b^{3} x^{3} - 5720 a b^{4} x^{4} - 1287 b^{5} x^{5}}{10296 x^{13}}"," ",0,"(-792*a**5 - 4290*a**4*b*x - 9360*a**3*b**2*x**2 - 10296*a**2*b**3*x**3 - 5720*a*b**4*x**4 - 1287*b**5*x**5)/(10296*x**13)","A",0
98,1,94,0,0.098379," ","integrate(x**8*(b*x+a)**7,x)","\frac{a^{7} x^{9}}{9} + \frac{7 a^{6} b x^{10}}{10} + \frac{21 a^{5} b^{2} x^{11}}{11} + \frac{35 a^{4} b^{3} x^{12}}{12} + \frac{35 a^{3} b^{4} x^{13}}{13} + \frac{3 a^{2} b^{5} x^{14}}{2} + \frac{7 a b^{6} x^{15}}{15} + \frac{b^{7} x^{16}}{16}"," ",0,"a**7*x**9/9 + 7*a**6*b*x**10/10 + 21*a**5*b**2*x**11/11 + 35*a**4*b**3*x**12/12 + 35*a**3*b**4*x**13/13 + 3*a**2*b**5*x**14/2 + 7*a*b**6*x**15/15 + b**7*x**16/16","A",0
99,1,92,0,0.093026," ","integrate(x**7*(b*x+a)**7,x)","\frac{a^{7} x^{8}}{8} + \frac{7 a^{6} b x^{9}}{9} + \frac{21 a^{5} b^{2} x^{10}}{10} + \frac{35 a^{4} b^{3} x^{11}}{11} + \frac{35 a^{3} b^{4} x^{12}}{12} + \frac{21 a^{2} b^{5} x^{13}}{13} + \frac{a b^{6} x^{14}}{2} + \frac{b^{7} x^{15}}{15}"," ",0,"a**7*x**8/8 + 7*a**6*b*x**9/9 + 21*a**5*b**2*x**10/10 + 35*a**4*b**3*x**11/11 + 35*a**3*b**4*x**12/12 + 21*a**2*b**5*x**13/13 + a*b**6*x**14/2 + b**7*x**15/15","A",0
100,1,94,0,0.107131," ","integrate(x**6*(b*x+a)**7,x)","\frac{a^{7} x^{7}}{7} + \frac{7 a^{6} b x^{8}}{8} + \frac{7 a^{5} b^{2} x^{9}}{3} + \frac{7 a^{4} b^{3} x^{10}}{2} + \frac{35 a^{3} b^{4} x^{11}}{11} + \frac{7 a^{2} b^{5} x^{12}}{4} + \frac{7 a b^{6} x^{13}}{13} + \frac{b^{7} x^{14}}{14}"," ",0,"a**7*x**7/7 + 7*a**6*b*x**8/8 + 7*a**5*b**2*x**9/3 + 7*a**4*b**3*x**10/2 + 35*a**3*b**4*x**11/11 + 7*a**2*b**5*x**12/4 + 7*a*b**6*x**13/13 + b**7*x**14/14","A",0
101,1,90,0,0.106289," ","integrate(x**5*(b*x+a)**7,x)","\frac{a^{7} x^{6}}{6} + a^{6} b x^{7} + \frac{21 a^{5} b^{2} x^{8}}{8} + \frac{35 a^{4} b^{3} x^{9}}{9} + \frac{7 a^{3} b^{4} x^{10}}{2} + \frac{21 a^{2} b^{5} x^{11}}{11} + \frac{7 a b^{6} x^{12}}{12} + \frac{b^{7} x^{13}}{13}"," ",0,"a**7*x**6/6 + a**6*b*x**7 + 21*a**5*b**2*x**8/8 + 35*a**4*b**3*x**9/9 + 7*a**3*b**4*x**10/2 + 21*a**2*b**5*x**11/11 + 7*a*b**6*x**12/12 + b**7*x**13/13","A",0
102,1,92,0,0.099235," ","integrate(x**4*(b*x+a)**7,x)","\frac{a^{7} x^{5}}{5} + \frac{7 a^{6} b x^{6}}{6} + 3 a^{5} b^{2} x^{7} + \frac{35 a^{4} b^{3} x^{8}}{8} + \frac{35 a^{3} b^{4} x^{9}}{9} + \frac{21 a^{2} b^{5} x^{10}}{10} + \frac{7 a b^{6} x^{11}}{11} + \frac{b^{7} x^{12}}{12}"," ",0,"a**7*x**5/5 + 7*a**6*b*x**6/6 + 3*a**5*b**2*x**7 + 35*a**4*b**3*x**8/8 + 35*a**3*b**4*x**9/9 + 21*a**2*b**5*x**10/10 + 7*a*b**6*x**11/11 + b**7*x**12/12","A",0
103,1,92,0,0.089490," ","integrate(x**3*(b*x+a)**7,x)","\frac{a^{7} x^{4}}{4} + \frac{7 a^{6} b x^{5}}{5} + \frac{7 a^{5} b^{2} x^{6}}{2} + 5 a^{4} b^{3} x^{7} + \frac{35 a^{3} b^{4} x^{8}}{8} + \frac{7 a^{2} b^{5} x^{9}}{3} + \frac{7 a b^{6} x^{10}}{10} + \frac{b^{7} x^{11}}{11}"," ",0,"a**7*x**4/4 + 7*a**6*b*x**5/5 + 7*a**5*b**2*x**6/2 + 5*a**4*b**3*x**7 + 35*a**3*b**4*x**8/8 + 7*a**2*b**5*x**9/3 + 7*a*b**6*x**10/10 + b**7*x**11/11","A",0
104,1,92,0,0.093306," ","integrate(x**2*(b*x+a)**7,x)","\frac{a^{7} x^{3}}{3} + \frac{7 a^{6} b x^{4}}{4} + \frac{21 a^{5} b^{2} x^{5}}{5} + \frac{35 a^{4} b^{3} x^{6}}{6} + 5 a^{3} b^{4} x^{7} + \frac{21 a^{2} b^{5} x^{8}}{8} + \frac{7 a b^{6} x^{9}}{9} + \frac{b^{7} x^{10}}{10}"," ",0,"a**7*x**3/3 + 7*a**6*b*x**4/4 + 21*a**5*b**2*x**5/5 + 35*a**4*b**3*x**6/6 + 5*a**3*b**4*x**7 + 21*a**2*b**5*x**8/8 + 7*a*b**6*x**9/9 + b**7*x**10/10","B",0
105,1,90,0,0.089938," ","integrate(x*(b*x+a)**7,x)","\frac{a^{7} x^{2}}{2} + \frac{7 a^{6} b x^{3}}{3} + \frac{21 a^{5} b^{2} x^{4}}{4} + 7 a^{4} b^{3} x^{5} + \frac{35 a^{3} b^{4} x^{6}}{6} + 3 a^{2} b^{5} x^{7} + \frac{7 a b^{6} x^{8}}{8} + \frac{b^{7} x^{9}}{9}"," ",0,"a**7*x**2/2 + 7*a**6*b*x**3/3 + 21*a**5*b**2*x**4/4 + 7*a**4*b**3*x**5 + 35*a**3*b**4*x**6/6 + 3*a**2*b**5*x**7 + 7*a*b**6*x**8/8 + b**7*x**9/9","B",0
106,1,83,0,0.082311," ","integrate((b*x+a)**7,x)","a^{7} x + \frac{7 a^{6} b x^{2}}{2} + 7 a^{5} b^{2} x^{3} + \frac{35 a^{4} b^{3} x^{4}}{4} + 7 a^{3} b^{4} x^{5} + \frac{7 a^{2} b^{5} x^{6}}{2} + a b^{6} x^{7} + \frac{b^{7} x^{8}}{8}"," ",0,"a**7*x + 7*a**6*b*x**2/2 + 7*a**5*b**2*x**3 + 35*a**4*b**3*x**4/4 + 7*a**3*b**4*x**5 + 7*a**2*b**5*x**6/2 + a*b**6*x**7 + b**7*x**8/8","B",0
107,1,88,0,0.186827," ","integrate((b*x+a)**7/x,x)","a^{7} \log{\left(x \right)} + 7 a^{6} b x + \frac{21 a^{5} b^{2} x^{2}}{2} + \frac{35 a^{4} b^{3} x^{3}}{3} + \frac{35 a^{3} b^{4} x^{4}}{4} + \frac{21 a^{2} b^{5} x^{5}}{5} + \frac{7 a b^{6} x^{6}}{6} + \frac{b^{7} x^{7}}{7}"," ",0,"a**7*log(x) + 7*a**6*b*x + 21*a**5*b**2*x**2/2 + 35*a**4*b**3*x**3/3 + 35*a**3*b**4*x**4/4 + 21*a**2*b**5*x**5/5 + 7*a*b**6*x**6/6 + b**7*x**7/7","A",0
108,1,85,0,0.200953," ","integrate((b*x+a)**7/x**2,x)","- \frac{a^{7}}{x} + 7 a^{6} b \log{\left(x \right)} + 21 a^{5} b^{2} x + \frac{35 a^{4} b^{3} x^{2}}{2} + \frac{35 a^{3} b^{4} x^{3}}{3} + \frac{21 a^{2} b^{5} x^{4}}{4} + \frac{7 a b^{6} x^{5}}{5} + \frac{b^{7} x^{6}}{6}"," ",0,"-a**7/x + 7*a**6*b*log(x) + 21*a**5*b**2*x + 35*a**4*b**3*x**2/2 + 35*a**3*b**4*x**3/3 + 21*a**2*b**5*x**4/4 + 7*a*b**6*x**5/5 + b**7*x**6/6","A",0
109,1,85,0,0.251901," ","integrate((b*x+a)**7/x**3,x)","21 a^{5} b^{2} \log{\left(x \right)} + 35 a^{4} b^{3} x + \frac{35 a^{3} b^{4} x^{2}}{2} + 7 a^{2} b^{5} x^{3} + \frac{7 a b^{6} x^{4}}{4} + \frac{b^{7} x^{5}}{5} + \frac{- a^{7} - 14 a^{6} b x}{2 x^{2}}"," ",0,"21*a**5*b**2*log(x) + 35*a**4*b**3*x + 35*a**3*b**4*x**2/2 + 7*a**2*b**5*x**3 + 7*a*b**6*x**4/4 + b**7*x**5/5 + (-a**7 - 14*a**6*b*x)/(2*x**2)","A",0
110,1,87,0,0.307729," ","integrate((b*x+a)**7/x**4,x)","35 a^{4} b^{3} \log{\left(x \right)} + 35 a^{3} b^{4} x + \frac{21 a^{2} b^{5} x^{2}}{2} + \frac{7 a b^{6} x^{3}}{3} + \frac{b^{7} x^{4}}{4} + \frac{- 2 a^{7} - 21 a^{6} b x - 126 a^{5} b^{2} x^{2}}{6 x^{3}}"," ",0,"35*a**4*b**3*log(x) + 35*a**3*b**4*x + 21*a**2*b**5*x**2/2 + 7*a*b**6*x**3/3 + b**7*x**4/4 + (-2*a**7 - 21*a**6*b*x - 126*a**5*b**2*x**2)/(6*x**3)","A",0
111,1,85,0,0.328283," ","integrate((b*x+a)**7/x**5,x)","35 a^{3} b^{4} \log{\left(x \right)} + 21 a^{2} b^{5} x + \frac{7 a b^{6} x^{2}}{2} + \frac{b^{7} x^{3}}{3} + \frac{- 3 a^{7} - 28 a^{6} b x - 126 a^{5} b^{2} x^{2} - 420 a^{4} b^{3} x^{3}}{12 x^{4}}"," ",0,"35*a**3*b**4*log(x) + 21*a**2*b**5*x + 7*a*b**6*x**2/2 + b**7*x**3/3 + (-3*a**7 - 28*a**6*b*x - 126*a**5*b**2*x**2 - 420*a**4*b**3*x**3)/(12*x**4)","A",0
112,1,83,0,0.449004," ","integrate((b*x+a)**7/x**6,x)","21 a^{2} b^{5} \log{\left(x \right)} + 7 a b^{6} x + \frac{b^{7} x^{2}}{2} + \frac{- 4 a^{7} - 35 a^{6} b x - 140 a^{5} b^{2} x^{2} - 350 a^{4} b^{3} x^{3} - 700 a^{3} b^{4} x^{4}}{20 x^{5}}"," ",0,"21*a**2*b**5*log(x) + 7*a*b**6*x + b**7*x**2/2 + (-4*a**7 - 35*a**6*b*x - 140*a**5*b**2*x**2 - 350*a**4*b**3*x**3 - 700*a**3*b**4*x**4)/(20*x**5)","A",0
113,1,82,0,0.595477," ","integrate((b*x+a)**7/x**7,x)","7 a b^{6} \log{\left(x \right)} + b^{7} x + \frac{- 10 a^{7} - 84 a^{6} b x - 315 a^{5} b^{2} x^{2} - 700 a^{4} b^{3} x^{3} - 1050 a^{3} b^{4} x^{4} - 1260 a^{2} b^{5} x^{5}}{60 x^{6}}"," ",0,"7*a*b**6*log(x) + b**7*x + (-10*a**7 - 84*a**6*b*x - 315*a**5*b**2*x**2 - 700*a**4*b**3*x**3 - 1050*a**3*b**4*x**4 - 1260*a**2*b**5*x**5)/(60*x**6)","A",0
114,1,83,0,0.627398," ","integrate((b*x+a)**7/x**8,x)","b^{7} \log{\left(x \right)} + \frac{- 60 a^{7} - 490 a^{6} b x - 1764 a^{5} b^{2} x^{2} - 3675 a^{4} b^{3} x^{3} - 4900 a^{3} b^{4} x^{4} - 4410 a^{2} b^{5} x^{5} - 2940 a b^{6} x^{6}}{420 x^{7}}"," ",0,"b**7*log(x) + (-60*a**7 - 490*a**6*b*x - 1764*a**5*b**2*x**2 - 3675*a**4*b**3*x**3 - 4900*a**3*b**4*x**4 - 4410*a**2*b**5*x**5 - 2940*a*b**6*x**6)/(420*x**7)","A",0
115,1,83,0,0.604245," ","integrate((b*x+a)**7/x**9,x)","\frac{- a^{7} - 8 a^{6} b x - 28 a^{5} b^{2} x^{2} - 56 a^{4} b^{3} x^{3} - 70 a^{3} b^{4} x^{4} - 56 a^{2} b^{5} x^{5} - 28 a b^{6} x^{6} - 8 b^{7} x^{7}}{8 x^{8}}"," ",0,"(-a**7 - 8*a**6*b*x - 28*a**5*b**2*x**2 - 56*a**4*b**3*x**3 - 70*a**3*b**4*x**4 - 56*a**2*b**5*x**5 - 28*a*b**6*x**6 - 8*b**7*x**7)/(8*x**8)","B",0
116,1,85,0,0.729479," ","integrate((b*x+a)**7/x**10,x)","\frac{- 8 a^{7} - 63 a^{6} b x - 216 a^{5} b^{2} x^{2} - 420 a^{4} b^{3} x^{3} - 504 a^{3} b^{4} x^{4} - 378 a^{2} b^{5} x^{5} - 168 a b^{6} x^{6} - 36 b^{7} x^{7}}{72 x^{9}}"," ",0,"(-8*a**7 - 63*a**6*b*x - 216*a**5*b**2*x**2 - 420*a**4*b**3*x**3 - 504*a**3*b**4*x**4 - 378*a**2*b**5*x**5 - 168*a*b**6*x**6 - 36*b**7*x**7)/(72*x**9)","B",0
117,1,85,0,0.761713," ","integrate((b*x+a)**7/x**11,x)","\frac{- 36 a^{7} - 280 a^{6} b x - 945 a^{5} b^{2} x^{2} - 1800 a^{4} b^{3} x^{3} - 2100 a^{3} b^{4} x^{4} - 1512 a^{2} b^{5} x^{5} - 630 a b^{6} x^{6} - 120 b^{7} x^{7}}{360 x^{10}}"," ",0,"(-36*a**7 - 280*a**6*b*x - 945*a**5*b**2*x**2 - 1800*a**4*b**3*x**3 - 2100*a**3*b**4*x**4 - 1512*a**2*b**5*x**5 - 630*a*b**6*x**6 - 120*b**7*x**7)/(360*x**10)","A",0
118,1,85,0,0.746611," ","integrate((b*x+a)**7/x**12,x)","\frac{- 120 a^{7} - 924 a^{6} b x - 3080 a^{5} b^{2} x^{2} - 5775 a^{4} b^{3} x^{3} - 6600 a^{3} b^{4} x^{4} - 4620 a^{2} b^{5} x^{5} - 1848 a b^{6} x^{6} - 330 b^{7} x^{7}}{1320 x^{11}}"," ",0,"(-120*a**7 - 924*a**6*b*x - 3080*a**5*b**2*x**2 - 5775*a**4*b**3*x**3 - 6600*a**3*b**4*x**4 - 4620*a**2*b**5*x**5 - 1848*a*b**6*x**6 - 330*b**7*x**7)/(1320*x**11)","A",0
119,1,85,0,0.795163," ","integrate((b*x+a)**7/x**13,x)","\frac{- 330 a^{7} - 2520 a^{6} b x - 8316 a^{5} b^{2} x^{2} - 15400 a^{4} b^{3} x^{3} - 17325 a^{3} b^{4} x^{4} - 11880 a^{2} b^{5} x^{5} - 4620 a b^{6} x^{6} - 792 b^{7} x^{7}}{3960 x^{12}}"," ",0,"(-330*a**7 - 2520*a**6*b*x - 8316*a**5*b**2*x**2 - 15400*a**4*b**3*x**3 - 17325*a**3*b**4*x**4 - 11880*a**2*b**5*x**5 - 4620*a*b**6*x**6 - 792*b**7*x**7)/(3960*x**12)","A",0
120,1,85,0,0.781933," ","integrate((b*x+a)**7/x**14,x)","\frac{- 792 a^{7} - 6006 a^{6} b x - 19656 a^{5} b^{2} x^{2} - 36036 a^{4} b^{3} x^{3} - 40040 a^{3} b^{4} x^{4} - 27027 a^{2} b^{5} x^{5} - 10296 a b^{6} x^{6} - 1716 b^{7} x^{7}}{10296 x^{13}}"," ",0,"(-792*a**7 - 6006*a**6*b*x - 19656*a**5*b**2*x**2 - 36036*a**4*b**3*x**3 - 40040*a**3*b**4*x**4 - 27027*a**2*b**5*x**5 - 10296*a*b**6*x**6 - 1716*b**7*x**7)/(10296*x**13)","A",0
121,1,85,0,0.877759," ","integrate((b*x+a)**7/x**15,x)","\frac{- 1716 a^{7} - 12936 a^{6} b x - 42042 a^{5} b^{2} x^{2} - 76440 a^{4} b^{3} x^{3} - 84084 a^{3} b^{4} x^{4} - 56056 a^{2} b^{5} x^{5} - 21021 a b^{6} x^{6} - 3432 b^{7} x^{7}}{24024 x^{14}}"," ",0,"(-1716*a**7 - 12936*a**6*b*x - 42042*a**5*b**2*x**2 - 76440*a**4*b**3*x**3 - 84084*a**3*b**4*x**4 - 56056*a**2*b**5*x**5 - 21021*a*b**6*x**6 - 3432*b**7*x**7)/(24024*x**14)","A",0
122,1,85,0,0.878359," ","integrate((b*x+a)**7/x**16,x)","\frac{- 3432 a^{7} - 25740 a^{6} b x - 83160 a^{5} b^{2} x^{2} - 150150 a^{4} b^{3} x^{3} - 163800 a^{3} b^{4} x^{4} - 108108 a^{2} b^{5} x^{5} - 40040 a b^{6} x^{6} - 6435 b^{7} x^{7}}{51480 x^{15}}"," ",0,"(-3432*a**7 - 25740*a**6*b*x - 83160*a**5*b**2*x**2 - 150150*a**4*b**3*x**3 - 163800*a**3*b**4*x**4 - 108108*a**2*b**5*x**5 - 40040*a*b**6*x**6 - 6435*b**7*x**7)/(51480*x**15)","A",0
123,1,133,0,0.108202," ","integrate(x**11*(b*x+a)**10,x)","\frac{a^{10} x^{12}}{12} + \frac{10 a^{9} b x^{13}}{13} + \frac{45 a^{8} b^{2} x^{14}}{14} + 8 a^{7} b^{3} x^{15} + \frac{105 a^{6} b^{4} x^{16}}{8} + \frac{252 a^{5} b^{5} x^{17}}{17} + \frac{35 a^{4} b^{6} x^{18}}{3} + \frac{120 a^{3} b^{7} x^{19}}{19} + \frac{9 a^{2} b^{8} x^{20}}{4} + \frac{10 a b^{9} x^{21}}{21} + \frac{b^{10} x^{22}}{22}"," ",0,"a**10*x**12/12 + 10*a**9*b*x**13/13 + 45*a**8*b**2*x**14/14 + 8*a**7*b**3*x**15 + 105*a**6*b**4*x**16/8 + 252*a**5*b**5*x**17/17 + 35*a**4*b**6*x**18/3 + 120*a**3*b**7*x**19/19 + 9*a**2*b**8*x**20/4 + 10*a*b**9*x**21/21 + b**10*x**22/22","A",0
124,1,131,0,0.110997," ","integrate(x**10*(b*x+a)**10,x)","\frac{a^{10} x^{11}}{11} + \frac{5 a^{9} b x^{12}}{6} + \frac{45 a^{8} b^{2} x^{13}}{13} + \frac{60 a^{7} b^{3} x^{14}}{7} + 14 a^{6} b^{4} x^{15} + \frac{63 a^{5} b^{5} x^{16}}{4} + \frac{210 a^{4} b^{6} x^{17}}{17} + \frac{20 a^{3} b^{7} x^{18}}{3} + \frac{45 a^{2} b^{8} x^{19}}{19} + \frac{a b^{9} x^{20}}{2} + \frac{b^{10} x^{21}}{21}"," ",0,"a**10*x**11/11 + 5*a**9*b*x**12/6 + 45*a**8*b**2*x**13/13 + 60*a**7*b**3*x**14/7 + 14*a**6*b**4*x**15 + 63*a**5*b**5*x**16/4 + 210*a**4*b**6*x**17/17 + 20*a**3*b**7*x**18/3 + 45*a**2*b**8*x**19/19 + a*b**9*x**20/2 + b**10*x**21/21","A",0
125,1,133,0,0.103586," ","integrate(x**9*(b*x+a)**10,x)","\frac{a^{10} x^{10}}{10} + \frac{10 a^{9} b x^{11}}{11} + \frac{15 a^{8} b^{2} x^{12}}{4} + \frac{120 a^{7} b^{3} x^{13}}{13} + 15 a^{6} b^{4} x^{14} + \frac{84 a^{5} b^{5} x^{15}}{5} + \frac{105 a^{4} b^{6} x^{16}}{8} + \frac{120 a^{3} b^{7} x^{17}}{17} + \frac{5 a^{2} b^{8} x^{18}}{2} + \frac{10 a b^{9} x^{19}}{19} + \frac{b^{10} x^{20}}{20}"," ",0,"a**10*x**10/10 + 10*a**9*b*x**11/11 + 15*a**8*b**2*x**12/4 + 120*a**7*b**3*x**13/13 + 15*a**6*b**4*x**14 + 84*a**5*b**5*x**15/5 + 105*a**4*b**6*x**16/8 + 120*a**3*b**7*x**17/17 + 5*a**2*b**8*x**18/2 + 10*a*b**9*x**19/19 + b**10*x**20/20","A",0
126,1,126,0,0.112648," ","integrate(x**8*(b*x+a)**10,x)","\frac{a^{10} x^{9}}{9} + a^{9} b x^{10} + \frac{45 a^{8} b^{2} x^{11}}{11} + 10 a^{7} b^{3} x^{12} + \frac{210 a^{6} b^{4} x^{13}}{13} + 18 a^{5} b^{5} x^{14} + 14 a^{4} b^{6} x^{15} + \frac{15 a^{3} b^{7} x^{16}}{2} + \frac{45 a^{2} b^{8} x^{17}}{17} + \frac{5 a b^{9} x^{18}}{9} + \frac{b^{10} x^{19}}{19}"," ",0,"a**10*x**9/9 + a**9*b*x**10 + 45*a**8*b**2*x**11/11 + 10*a**7*b**3*x**12 + 210*a**6*b**4*x**13/13 + 18*a**5*b**5*x**14 + 14*a**4*b**6*x**15 + 15*a**3*b**7*x**16/2 + 45*a**2*b**8*x**17/17 + 5*a*b**9*x**18/9 + b**10*x**19/19","A",0
127,1,131,0,0.105959," ","integrate(x**7*(b*x+a)**10,x)","\frac{a^{10} x^{8}}{8} + \frac{10 a^{9} b x^{9}}{9} + \frac{9 a^{8} b^{2} x^{10}}{2} + \frac{120 a^{7} b^{3} x^{11}}{11} + \frac{35 a^{6} b^{4} x^{12}}{2} + \frac{252 a^{5} b^{5} x^{13}}{13} + 15 a^{4} b^{6} x^{14} + 8 a^{3} b^{7} x^{15} + \frac{45 a^{2} b^{8} x^{16}}{16} + \frac{10 a b^{9} x^{17}}{17} + \frac{b^{10} x^{18}}{18}"," ",0,"a**10*x**8/8 + 10*a**9*b*x**9/9 + 9*a**8*b**2*x**10/2 + 120*a**7*b**3*x**11/11 + 35*a**6*b**4*x**12/2 + 252*a**5*b**5*x**13/13 + 15*a**4*b**6*x**14 + 8*a**3*b**7*x**15 + 45*a**2*b**8*x**16/16 + 10*a*b**9*x**17/17 + b**10*x**18/18","A",0
128,1,128,0,0.102108," ","integrate(x**6*(b*x+a)**10,x)","\frac{a^{10} x^{7}}{7} + \frac{5 a^{9} b x^{8}}{4} + 5 a^{8} b^{2} x^{9} + 12 a^{7} b^{3} x^{10} + \frac{210 a^{6} b^{4} x^{11}}{11} + 21 a^{5} b^{5} x^{12} + \frac{210 a^{4} b^{6} x^{13}}{13} + \frac{60 a^{3} b^{7} x^{14}}{7} + 3 a^{2} b^{8} x^{15} + \frac{5 a b^{9} x^{16}}{8} + \frac{b^{10} x^{17}}{17}"," ",0,"a**10*x**7/7 + 5*a**9*b*x**8/4 + 5*a**8*b**2*x**9 + 12*a**7*b**3*x**10 + 210*a**6*b**4*x**11/11 + 21*a**5*b**5*x**12 + 210*a**4*b**6*x**13/13 + 60*a**3*b**7*x**14/7 + 3*a**2*b**8*x**15 + 5*a*b**9*x**16/8 + b**10*x**17/17","A",0
129,1,133,0,0.101984," ","integrate(x**5*(b*x+a)**10,x)","\frac{a^{10} x^{6}}{6} + \frac{10 a^{9} b x^{7}}{7} + \frac{45 a^{8} b^{2} x^{8}}{8} + \frac{40 a^{7} b^{3} x^{9}}{3} + 21 a^{6} b^{4} x^{10} + \frac{252 a^{5} b^{5} x^{11}}{11} + \frac{35 a^{4} b^{6} x^{12}}{2} + \frac{120 a^{3} b^{7} x^{13}}{13} + \frac{45 a^{2} b^{8} x^{14}}{14} + \frac{2 a b^{9} x^{15}}{3} + \frac{b^{10} x^{16}}{16}"," ",0,"a**10*x**6/6 + 10*a**9*b*x**7/7 + 45*a**8*b**2*x**8/8 + 40*a**7*b**3*x**9/3 + 21*a**6*b**4*x**10 + 252*a**5*b**5*x**11/11 + 35*a**4*b**6*x**12/2 + 120*a**3*b**7*x**13/13 + 45*a**2*b**8*x**14/14 + 2*a*b**9*x**15/3 + b**10*x**16/16","A",0
130,1,131,0,0.109302," ","integrate(x**4*(b*x+a)**10,x)","\frac{a^{10} x^{5}}{5} + \frac{5 a^{9} b x^{6}}{3} + \frac{45 a^{8} b^{2} x^{7}}{7} + 15 a^{7} b^{3} x^{8} + \frac{70 a^{6} b^{4} x^{9}}{3} + \frac{126 a^{5} b^{5} x^{10}}{5} + \frac{210 a^{4} b^{6} x^{11}}{11} + 10 a^{3} b^{7} x^{12} + \frac{45 a^{2} b^{8} x^{13}}{13} + \frac{5 a b^{9} x^{14}}{7} + \frac{b^{10} x^{15}}{15}"," ",0,"a**10*x**5/5 + 5*a**9*b*x**6/3 + 45*a**8*b**2*x**7/7 + 15*a**7*b**3*x**8 + 70*a**6*b**4*x**9/3 + 126*a**5*b**5*x**10/5 + 210*a**4*b**6*x**11/11 + 10*a**3*b**7*x**12 + 45*a**2*b**8*x**13/13 + 5*a*b**9*x**14/7 + b**10*x**15/15","A",0
131,1,129,0,0.117576," ","integrate(x**3*(b*x+a)**10,x)","\frac{a^{10} x^{4}}{4} + 2 a^{9} b x^{5} + \frac{15 a^{8} b^{2} x^{6}}{2} + \frac{120 a^{7} b^{3} x^{7}}{7} + \frac{105 a^{6} b^{4} x^{8}}{4} + 28 a^{5} b^{5} x^{9} + 21 a^{4} b^{6} x^{10} + \frac{120 a^{3} b^{7} x^{11}}{11} + \frac{15 a^{2} b^{8} x^{12}}{4} + \frac{10 a b^{9} x^{13}}{13} + \frac{b^{10} x^{14}}{14}"," ",0,"a**10*x**4/4 + 2*a**9*b*x**5 + 15*a**8*b**2*x**6/2 + 120*a**7*b**3*x**7/7 + 105*a**6*b**4*x**8/4 + 28*a**5*b**5*x**9 + 21*a**4*b**6*x**10 + 120*a**3*b**7*x**11/11 + 15*a**2*b**8*x**12/4 + 10*a*b**9*x**13/13 + b**10*x**14/14","B",0
132,1,128,0,0.106911," ","integrate(x**2*(b*x+a)**10,x)","\frac{a^{10} x^{3}}{3} + \frac{5 a^{9} b x^{4}}{2} + 9 a^{8} b^{2} x^{5} + 20 a^{7} b^{3} x^{6} + 30 a^{6} b^{4} x^{7} + \frac{63 a^{5} b^{5} x^{8}}{2} + \frac{70 a^{4} b^{6} x^{9}}{3} + 12 a^{3} b^{7} x^{10} + \frac{45 a^{2} b^{8} x^{11}}{11} + \frac{5 a b^{9} x^{12}}{6} + \frac{b^{10} x^{13}}{13}"," ",0,"a**10*x**3/3 + 5*a**9*b*x**4/2 + 9*a**8*b**2*x**5 + 20*a**7*b**3*x**6 + 30*a**6*b**4*x**7 + 63*a**5*b**5*x**8/2 + 70*a**4*b**6*x**9/3 + 12*a**3*b**7*x**10 + 45*a**2*b**8*x**11/11 + 5*a*b**9*x**12/6 + b**10*x**13/13","B",0
133,1,129,0,0.110253," ","integrate(x*(b*x+a)**10,x)","\frac{a^{10} x^{2}}{2} + \frac{10 a^{9} b x^{3}}{3} + \frac{45 a^{8} b^{2} x^{4}}{4} + 24 a^{7} b^{3} x^{5} + 35 a^{6} b^{4} x^{6} + 36 a^{5} b^{5} x^{7} + \frac{105 a^{4} b^{6} x^{8}}{4} + \frac{40 a^{3} b^{7} x^{9}}{3} + \frac{9 a^{2} b^{8} x^{10}}{2} + \frac{10 a b^{9} x^{11}}{11} + \frac{b^{10} x^{12}}{12}"," ",0,"a**10*x**2/2 + 10*a**9*b*x**3/3 + 45*a**8*b**2*x**4/4 + 24*a**7*b**3*x**5 + 35*a**6*b**4*x**6 + 36*a**5*b**5*x**7 + 105*a**4*b**6*x**8/4 + 40*a**3*b**7*x**9/3 + 9*a**2*b**8*x**10/2 + 10*a*b**9*x**11/11 + b**10*x**12/12","B",0
134,1,114,0,0.114931," ","integrate((b*x+a)**10,x)","a^{10} x + 5 a^{9} b x^{2} + 15 a^{8} b^{2} x^{3} + 30 a^{7} b^{3} x^{4} + 42 a^{6} b^{4} x^{5} + 42 a^{5} b^{5} x^{6} + 30 a^{4} b^{6} x^{7} + 15 a^{3} b^{7} x^{8} + 5 a^{2} b^{8} x^{9} + a b^{9} x^{10} + \frac{b^{10} x^{11}}{11}"," ",0,"a**10*x + 5*a**9*b*x**2 + 15*a**8*b**2*x**3 + 30*a**7*b**3*x**4 + 42*a**6*b**4*x**5 + 42*a**5*b**5*x**6 + 30*a**4*b**6*x**7 + 15*a**3*b**7*x**8 + 5*a**2*b**8*x**9 + a*b**9*x**10 + b**10*x**11/11","B",0
135,1,126,0,0.257080," ","integrate((b*x+a)**10/x,x)","a^{10} \log{\left(x \right)} + 10 a^{9} b x + \frac{45 a^{8} b^{2} x^{2}}{2} + 40 a^{7} b^{3} x^{3} + \frac{105 a^{6} b^{4} x^{4}}{2} + \frac{252 a^{5} b^{5} x^{5}}{5} + 35 a^{4} b^{6} x^{6} + \frac{120 a^{3} b^{7} x^{7}}{7} + \frac{45 a^{2} b^{8} x^{8}}{8} + \frac{10 a b^{9} x^{9}}{9} + \frac{b^{10} x^{10}}{10}"," ",0,"a**10*log(x) + 10*a**9*b*x + 45*a**8*b**2*x**2/2 + 40*a**7*b**3*x**3 + 105*a**6*b**4*x**4/2 + 252*a**5*b**5*x**5/5 + 35*a**4*b**6*x**6 + 120*a**3*b**7*x**7/7 + 45*a**2*b**8*x**8/8 + 10*a*b**9*x**9/9 + b**10*x**10/10","A",0
136,1,117,0,0.266200," ","integrate((b*x+a)**10/x**2,x)","- \frac{a^{10}}{x} + 10 a^{9} b \log{\left(x \right)} + 45 a^{8} b^{2} x + 60 a^{7} b^{3} x^{2} + 70 a^{6} b^{4} x^{3} + 63 a^{5} b^{5} x^{4} + 42 a^{4} b^{6} x^{5} + 20 a^{3} b^{7} x^{6} + \frac{45 a^{2} b^{8} x^{7}}{7} + \frac{5 a b^{9} x^{8}}{4} + \frac{b^{10} x^{9}}{9}"," ",0,"-a**10/x + 10*a**9*b*log(x) + 45*a**8*b**2*x + 60*a**7*b**3*x**2 + 70*a**6*b**4*x**3 + 63*a**5*b**5*x**4 + 42*a**4*b**6*x**5 + 20*a**3*b**7*x**6 + 45*a**2*b**8*x**7/7 + 5*a*b**9*x**8/4 + b**10*x**9/9","A",0
137,1,122,0,0.310304," ","integrate((b*x+a)**10/x**3,x)","45 a^{8} b^{2} \log{\left(x \right)} + 120 a^{7} b^{3} x + 105 a^{6} b^{4} x^{2} + 84 a^{5} b^{5} x^{3} + \frac{105 a^{4} b^{6} x^{4}}{2} + 24 a^{3} b^{7} x^{5} + \frac{15 a^{2} b^{8} x^{6}}{2} + \frac{10 a b^{9} x^{7}}{7} + \frac{b^{10} x^{8}}{8} + \frac{- a^{10} - 20 a^{9} b x}{2 x^{2}}"," ",0,"45*a**8*b**2*log(x) + 120*a**7*b**3*x + 105*a**6*b**4*x**2 + 84*a**5*b**5*x**3 + 105*a**4*b**6*x**4/2 + 24*a**3*b**7*x**5 + 15*a**2*b**8*x**6/2 + 10*a*b**9*x**7/7 + b**10*x**8/8 + (-a**10 - 20*a**9*b*x)/(2*x**2)","A",0
138,1,119,0,0.338255," ","integrate((b*x+a)**10/x**4,x)","120 a^{7} b^{3} \log{\left(x \right)} + 210 a^{6} b^{4} x + 126 a^{5} b^{5} x^{2} + 70 a^{4} b^{6} x^{3} + 30 a^{3} b^{7} x^{4} + 9 a^{2} b^{8} x^{5} + \frac{5 a b^{9} x^{6}}{3} + \frac{b^{10} x^{7}}{7} + \frac{- a^{10} - 15 a^{9} b x - 135 a^{8} b^{2} x^{2}}{3 x^{3}}"," ",0,"120*a**7*b**3*log(x) + 210*a**6*b**4*x + 126*a**5*b**5*x**2 + 70*a**4*b**6*x**3 + 30*a**3*b**7*x**4 + 9*a**2*b**8*x**5 + 5*a*b**9*x**6/3 + b**10*x**7/7 + (-a**10 - 15*a**9*b*x - 135*a**8*b**2*x**2)/(3*x**3)","A",0
139,1,121,0,0.437112," ","integrate((b*x+a)**10/x**5,x)","210 a^{6} b^{4} \log{\left(x \right)} + 252 a^{5} b^{5} x + 105 a^{4} b^{6} x^{2} + 40 a^{3} b^{7} x^{3} + \frac{45 a^{2} b^{8} x^{4}}{4} + 2 a b^{9} x^{5} + \frac{b^{10} x^{6}}{6} + \frac{- 3 a^{10} - 40 a^{9} b x - 270 a^{8} b^{2} x^{2} - 1440 a^{7} b^{3} x^{3}}{12 x^{4}}"," ",0,"210*a**6*b**4*log(x) + 252*a**5*b**5*x + 105*a**4*b**6*x**2 + 40*a**3*b**7*x**3 + 45*a**2*b**8*x**4/4 + 2*a*b**9*x**5 + b**10*x**6/6 + (-3*a**10 - 40*a**9*b*x - 270*a**8*b**2*x**2 - 1440*a**7*b**3*x**3)/(12*x**4)","A",0
140,1,121,0,0.572748," ","integrate((b*x+a)**10/x**6,x)","252 a^{5} b^{5} \log{\left(x \right)} + 210 a^{4} b^{6} x + 60 a^{3} b^{7} x^{2} + 15 a^{2} b^{8} x^{3} + \frac{5 a b^{9} x^{4}}{2} + \frac{b^{10} x^{5}}{5} + \frac{- 2 a^{10} - 25 a^{9} b x - 150 a^{8} b^{2} x^{2} - 600 a^{7} b^{3} x^{3} - 2100 a^{6} b^{4} x^{4}}{10 x^{5}}"," ",0,"252*a**5*b**5*log(x) + 210*a**4*b**6*x + 60*a**3*b**7*x**2 + 15*a**2*b**8*x**3 + 5*a*b**9*x**4/2 + b**10*x**5/5 + (-2*a**10 - 25*a**9*b*x - 150*a**8*b**2*x**2 - 600*a**7*b**3*x**3 - 2100*a**6*b**4*x**4)/(10*x**5)","A",0
141,1,122,0,0.566379," ","integrate((b*x+a)**10/x**7,x)","210 a^{4} b^{6} \log{\left(x \right)} + 120 a^{3} b^{7} x + \frac{45 a^{2} b^{8} x^{2}}{2} + \frac{10 a b^{9} x^{3}}{3} + \frac{b^{10} x^{4}}{4} + \frac{- 2 a^{10} - 24 a^{9} b x - 135 a^{8} b^{2} x^{2} - 480 a^{7} b^{3} x^{3} - 1260 a^{6} b^{4} x^{4} - 3024 a^{5} b^{5} x^{5}}{12 x^{6}}"," ",0,"210*a**4*b**6*log(x) + 120*a**3*b**7*x + 45*a**2*b**8*x**2/2 + 10*a*b**9*x**3/3 + b**10*x**4/4 + (-2*a**10 - 24*a**9*b*x - 135*a**8*b**2*x**2 - 480*a**7*b**3*x**3 - 1260*a**6*b**4*x**4 - 3024*a**5*b**5*x**5)/(12*x**6)","A",0
142,1,119,0,0.695326," ","integrate((b*x+a)**10/x**8,x)","120 a^{3} b^{7} \log{\left(x \right)} + 45 a^{2} b^{8} x + 5 a b^{9} x^{2} + \frac{b^{10} x^{3}}{3} + \frac{- 3 a^{10} - 35 a^{9} b x - 189 a^{8} b^{2} x^{2} - 630 a^{7} b^{3} x^{3} - 1470 a^{6} b^{4} x^{4} - 2646 a^{5} b^{5} x^{5} - 4410 a^{4} b^{6} x^{6}}{21 x^{7}}"," ",0,"120*a**3*b**7*log(x) + 45*a**2*b**8*x + 5*a*b**9*x**2 + b**10*x**3/3 + (-3*a**10 - 35*a**9*b*x - 189*a**8*b**2*x**2 - 630*a**7*b**3*x**3 - 1470*a**6*b**4*x**4 - 2646*a**5*b**5*x**5 - 4410*a**4*b**6*x**6)/(21*x**7)","A",0
143,1,119,0,0.764937," ","integrate((b*x+a)**10/x**9,x)","45 a^{2} b^{8} \log{\left(x \right)} + 10 a b^{9} x + \frac{b^{10} x^{2}}{2} + \frac{- 7 a^{10} - 80 a^{9} b x - 420 a^{8} b^{2} x^{2} - 1344 a^{7} b^{3} x^{3} - 2940 a^{6} b^{4} x^{4} - 4704 a^{5} b^{5} x^{5} - 5880 a^{4} b^{6} x^{6} - 6720 a^{3} b^{7} x^{7}}{56 x^{8}}"," ",0,"45*a**2*b**8*log(x) + 10*a*b**9*x + b**10*x**2/2 + (-7*a**10 - 80*a**9*b*x - 420*a**8*b**2*x**2 - 1344*a**7*b**3*x**3 - 2940*a**6*b**4*x**4 - 4704*a**5*b**5*x**5 - 5880*a**4*b**6*x**6 - 6720*a**3*b**7*x**7)/(56*x**8)","A",0
144,1,117,0,0.824564," ","integrate((b*x+a)**10/x**10,x)","10 a b^{9} \log{\left(x \right)} + b^{10} x + \frac{- 28 a^{10} - 315 a^{9} b x - 1620 a^{8} b^{2} x^{2} - 5040 a^{7} b^{3} x^{3} - 10584 a^{6} b^{4} x^{4} - 15876 a^{5} b^{5} x^{5} - 17640 a^{4} b^{6} x^{6} - 15120 a^{3} b^{7} x^{7} - 11340 a^{2} b^{8} x^{8}}{252 x^{9}}"," ",0,"10*a*b**9*log(x) + b**10*x + (-28*a**10 - 315*a**9*b*x - 1620*a**8*b**2*x**2 - 5040*a**7*b**3*x**3 - 10584*a**6*b**4*x**4 - 15876*a**5*b**5*x**5 - 17640*a**4*b**6*x**6 - 15120*a**3*b**7*x**7 - 11340*a**2*b**8*x**8)/(252*x**9)","A",0
145,1,119,0,1.013294," ","integrate((b*x+a)**10/x**11,x)","b^{10} \log{\left(x \right)} + \frac{- 252 a^{10} - 2800 a^{9} b x - 14175 a^{8} b^{2} x^{2} - 43200 a^{7} b^{3} x^{3} - 88200 a^{6} b^{4} x^{4} - 127008 a^{5} b^{5} x^{5} - 132300 a^{4} b^{6} x^{6} - 100800 a^{3} b^{7} x^{7} - 56700 a^{2} b^{8} x^{8} - 25200 a b^{9} x^{9}}{2520 x^{10}}"," ",0,"b**10*log(x) + (-252*a**10 - 2800*a**9*b*x - 14175*a**8*b**2*x**2 - 43200*a**7*b**3*x**3 - 88200*a**6*b**4*x**4 - 127008*a**5*b**5*x**5 - 132300*a**4*b**6*x**6 - 100800*a**3*b**7*x**7 - 56700*a**2*b**8*x**8 - 25200*a*b**9*x**9)/(2520*x**10)","A",0
146,1,119,0,1.026383," ","integrate((b*x+a)**10/x**12,x)","\frac{- a^{10} - 11 a^{9} b x - 55 a^{8} b^{2} x^{2} - 165 a^{7} b^{3} x^{3} - 330 a^{6} b^{4} x^{4} - 462 a^{5} b^{5} x^{5} - 462 a^{4} b^{6} x^{6} - 330 a^{3} b^{7} x^{7} - 165 a^{2} b^{8} x^{8} - 55 a b^{9} x^{9} - 11 b^{10} x^{10}}{11 x^{11}}"," ",0,"(-a**10 - 11*a**9*b*x - 55*a**8*b**2*x**2 - 165*a**7*b**3*x**3 - 330*a**6*b**4*x**4 - 462*a**5*b**5*x**5 - 462*a**4*b**6*x**6 - 330*a**3*b**7*x**7 - 165*a**2*b**8*x**8 - 55*a*b**9*x**9 - 11*b**10*x**10)/(11*x**11)","B",0
147,1,121,0,0.991933," ","integrate((b*x+a)**10/x**13,x)","\frac{- 11 a^{10} - 120 a^{9} b x - 594 a^{8} b^{2} x^{2} - 1760 a^{7} b^{3} x^{3} - 3465 a^{6} b^{4} x^{4} - 4752 a^{5} b^{5} x^{5} - 4620 a^{4} b^{6} x^{6} - 3168 a^{3} b^{7} x^{7} - 1485 a^{2} b^{8} x^{8} - 440 a b^{9} x^{9} - 66 b^{10} x^{10}}{132 x^{12}}"," ",0,"(-11*a**10 - 120*a**9*b*x - 594*a**8*b**2*x**2 - 1760*a**7*b**3*x**3 - 3465*a**6*b**4*x**4 - 4752*a**5*b**5*x**5 - 4620*a**4*b**6*x**6 - 3168*a**3*b**7*x**7 - 1485*a**2*b**8*x**8 - 440*a*b**9*x**9 - 66*b**10*x**10)/(132*x**12)","B",0
148,1,121,0,1.222999," ","integrate((b*x+a)**10/x**14,x)","\frac{- 66 a^{10} - 715 a^{9} b x - 3510 a^{8} b^{2} x^{2} - 10296 a^{7} b^{3} x^{3} - 20020 a^{6} b^{4} x^{4} - 27027 a^{5} b^{5} x^{5} - 25740 a^{4} b^{6} x^{6} - 17160 a^{3} b^{7} x^{7} - 7722 a^{2} b^{8} x^{8} - 2145 a b^{9} x^{9} - 286 b^{10} x^{10}}{858 x^{13}}"," ",0,"(-66*a**10 - 715*a**9*b*x - 3510*a**8*b**2*x**2 - 10296*a**7*b**3*x**3 - 20020*a**6*b**4*x**4 - 27027*a**5*b**5*x**5 - 25740*a**4*b**6*x**6 - 17160*a**3*b**7*x**7 - 7722*a**2*b**8*x**8 - 2145*a*b**9*x**9 - 286*b**10*x**10)/(858*x**13)","B",0
149,1,121,0,1.098860," ","integrate((b*x+a)**10/x**15,x)","\frac{- 286 a^{10} - 3080 a^{9} b x - 15015 a^{8} b^{2} x^{2} - 43680 a^{7} b^{3} x^{3} - 84084 a^{6} b^{4} x^{4} - 112112 a^{5} b^{5} x^{5} - 105105 a^{4} b^{6} x^{6} - 68640 a^{3} b^{7} x^{7} - 30030 a^{2} b^{8} x^{8} - 8008 a b^{9} x^{9} - 1001 b^{10} x^{10}}{4004 x^{14}}"," ",0,"(-286*a**10 - 3080*a**9*b*x - 15015*a**8*b**2*x**2 - 43680*a**7*b**3*x**3 - 84084*a**6*b**4*x**4 - 112112*a**5*b**5*x**5 - 105105*a**4*b**6*x**6 - 68640*a**3*b**7*x**7 - 30030*a**2*b**8*x**8 - 8008*a*b**9*x**9 - 1001*b**10*x**10)/(4004*x**14)","A",0
150,1,121,0,1.252752," ","integrate((b*x+a)**10/x**16,x)","\frac{- 1001 a^{10} - 10725 a^{9} b x - 51975 a^{8} b^{2} x^{2} - 150150 a^{7} b^{3} x^{3} - 286650 a^{6} b^{4} x^{4} - 378378 a^{5} b^{5} x^{5} - 350350 a^{4} b^{6} x^{6} - 225225 a^{3} b^{7} x^{7} - 96525 a^{2} b^{8} x^{8} - 25025 a b^{9} x^{9} - 3003 b^{10} x^{10}}{15015 x^{15}}"," ",0,"(-1001*a**10 - 10725*a**9*b*x - 51975*a**8*b**2*x**2 - 150150*a**7*b**3*x**3 - 286650*a**6*b**4*x**4 - 378378*a**5*b**5*x**5 - 350350*a**4*b**6*x**6 - 225225*a**3*b**7*x**7 - 96525*a**2*b**8*x**8 - 25025*a*b**9*x**9 - 3003*b**10*x**10)/(15015*x**15)","A",0
151,1,121,0,1.268491," ","integrate((b*x+a)**10/x**17,x)","\frac{- 3003 a^{10} - 32032 a^{9} b x - 154440 a^{8} b^{2} x^{2} - 443520 a^{7} b^{3} x^{3} - 840840 a^{6} b^{4} x^{4} - 1100736 a^{5} b^{5} x^{5} - 1009008 a^{4} b^{6} x^{6} - 640640 a^{3} b^{7} x^{7} - 270270 a^{2} b^{8} x^{8} - 68640 a b^{9} x^{9} - 8008 b^{10} x^{10}}{48048 x^{16}}"," ",0,"(-3003*a**10 - 32032*a**9*b*x - 154440*a**8*b**2*x**2 - 443520*a**7*b**3*x**3 - 840840*a**6*b**4*x**4 - 1100736*a**5*b**5*x**5 - 1009008*a**4*b**6*x**6 - 640640*a**3*b**7*x**7 - 270270*a**2*b**8*x**8 - 68640*a*b**9*x**9 - 8008*b**10*x**10)/(48048*x**16)","A",0
152,1,121,0,1.327480," ","integrate((b*x+a)**10/x**18,x)","\frac{- 8008 a^{10} - 85085 a^{9} b x - 408408 a^{8} b^{2} x^{2} - 1166880 a^{7} b^{3} x^{3} - 2199120 a^{6} b^{4} x^{4} - 2858856 a^{5} b^{5} x^{5} - 2598960 a^{4} b^{6} x^{6} - 1633632 a^{3} b^{7} x^{7} - 680680 a^{2} b^{8} x^{8} - 170170 a b^{9} x^{9} - 19448 b^{10} x^{10}}{136136 x^{17}}"," ",0,"(-8008*a**10 - 85085*a**9*b*x - 408408*a**8*b**2*x**2 - 1166880*a**7*b**3*x**3 - 2199120*a**6*b**4*x**4 - 2858856*a**5*b**5*x**5 - 2598960*a**4*b**6*x**6 - 1633632*a**3*b**7*x**7 - 680680*a**2*b**8*x**8 - 170170*a*b**9*x**9 - 19448*b**10*x**10)/(136136*x**17)","A",0
153,1,121,0,1.349895," ","integrate((b*x+a)**10/x**19,x)","\frac{- 19448 a^{10} - 205920 a^{9} b x - 984555 a^{8} b^{2} x^{2} - 2800512 a^{7} b^{3} x^{3} - 5250960 a^{6} b^{4} x^{4} - 6785856 a^{5} b^{5} x^{5} - 6126120 a^{4} b^{6} x^{6} - 3818880 a^{3} b^{7} x^{7} - 1575288 a^{2} b^{8} x^{8} - 388960 a b^{9} x^{9} - 43758 b^{10} x^{10}}{350064 x^{18}}"," ",0,"(-19448*a**10 - 205920*a**9*b*x - 984555*a**8*b**2*x**2 - 2800512*a**7*b**3*x**3 - 5250960*a**6*b**4*x**4 - 6785856*a**5*b**5*x**5 - 6126120*a**4*b**6*x**6 - 3818880*a**3*b**7*x**7 - 1575288*a**2*b**8*x**8 - 388960*a*b**9*x**9 - 43758*b**10*x**10)/(350064*x**18)","A",0
154,1,121,0,1.423700," ","integrate((b*x+a)**10/x**20,x)","\frac{- 43758 a^{10} - 461890 a^{9} b x - 2200770 a^{8} b^{2} x^{2} - 6235515 a^{7} b^{3} x^{3} - 11639628 a^{6} b^{4} x^{4} - 14965236 a^{5} b^{5} x^{5} - 13430340 a^{4} b^{6} x^{6} - 8314020 a^{3} b^{7} x^{7} - 3401190 a^{2} b^{8} x^{8} - 831402 a b^{9} x^{9} - 92378 b^{10} x^{10}}{831402 x^{19}}"," ",0,"(-43758*a**10 - 461890*a**9*b*x - 2200770*a**8*b**2*x**2 - 6235515*a**7*b**3*x**3 - 11639628*a**6*b**4*x**4 - 14965236*a**5*b**5*x**5 - 13430340*a**4*b**6*x**6 - 8314020*a**3*b**7*x**7 - 3401190*a**2*b**8*x**8 - 831402*a*b**9*x**9 - 92378*b**10*x**10)/(831402*x**19)","A",0
155,1,12,0,0.067614," ","integrate(c*(b*x+a),x)","a c x + \frac{b c x^{2}}{2}"," ",0,"a*c*x + b*c*x**2/2","A",0
156,1,22,0,0.076820," ","integrate((c+d)*(b*x+a)/e,x)","\frac{x^{2} \left(b c + b d\right)}{2 e} + \frac{x \left(a c + a d\right)}{e}"," ",0,"x**2*(b*c + b*d)/(2*e) + x*(a*c + a*d)/e","A",0
157,1,61,0,0.162746," ","integrate(x**5/(b*x+a),x)","- \frac{a^{5} \log{\left(a + b x \right)}}{b^{6}} + \frac{a^{4} x}{b^{5}} - \frac{a^{3} x^{2}}{2 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{5}}{5 b}"," ",0,"-a**5*log(a + b*x)/b**6 + a**4*x/b**5 - a**3*x**2/(2*b**4) + a**2*x**3/(3*b**3) - a*x**4/(4*b**2) + x**5/(5*b)","A",0
158,1,49,0,0.152006," ","integrate(x**4/(b*x+a),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
159,1,37,0,0.143698," ","integrate(x**3/(b*x+a),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
160,1,26,0,0.129761," ","integrate(x**2/(b*x+a),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
161,1,14,0,0.122493," ","integrate(x/(b*x+a),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
162,1,7,0,0.070200," ","integrate(1/(b*x+a),x)","\frac{\log{\left(a + b x \right)}}{b}"," ",0,"log(a + b*x)/b","A",0
163,1,10,0,0.153158," ","integrate(1/x/(b*x+a),x)","\frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a}"," ",0,"(log(x) - log(a/b + x))/a","A",0
164,1,19,0,0.195474," ","integrate(1/x**2/(b*x+a),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
165,1,31,0,0.216970," ","integrate(1/x**3/(b*x+a),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
166,1,44,0,0.242076," ","integrate(1/x**4/(b*x+a),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
167,1,56,0,0.275374," ","integrate(1/x**5/(b*x+a),x)","\frac{- 3 a^{3} + 4 a^{2} b x - 6 a b^{2} x^{2} + 12 b^{3} x^{3}}{12 a^{4} x^{4}} + \frac{b^{4} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{5}}"," ",0,"(-3*a**3 + 4*a**2*b*x - 6*a*b**2*x**2 + 12*b**3*x**3)/(12*a**4*x**4) + b**4*(log(x) - log(a/b + x))/a**5","A",0
168,1,78,0,0.275154," ","integrate(x**6/(b*x+a)**2,x)","- \frac{a^{6}}{a b^{7} + b^{8} x} - \frac{6 a^{5} \log{\left(a + b x \right)}}{b^{7}} + \frac{5 a^{4} x}{b^{6}} - \frac{2 a^{3} x^{2}}{b^{5}} + \frac{a^{2} x^{3}}{b^{4}} - \frac{a x^{4}}{2 b^{3}} + \frac{x^{5}}{5 b^{2}}"," ",0,"-a**6/(a*b**7 + b**8*x) - 6*a**5*log(a + b*x)/b**7 + 5*a**4*x/b**6 - 2*a**3*x**2/b**5 + a**2*x**3/b**4 - a*x**4/(2*b**3) + x**5/(5*b**2)","A",0
169,1,71,0,0.252363," ","integrate(x**5/(b*x+a)**2,x)","\frac{a^{5}}{a b^{6} + b^{7} x} + \frac{5 a^{4} \log{\left(a + b x \right)}}{b^{6}} - \frac{4 a^{3} x}{b^{5}} + \frac{3 a^{2} x^{2}}{2 b^{4}} - \frac{2 a x^{3}}{3 b^{3}} + \frac{x^{4}}{4 b^{2}}"," ",0,"a**5/(a*b**6 + b**7*x) + 5*a**4*log(a + b*x)/b**6 - 4*a**3*x/b**5 + 3*a**2*x**2/(2*b**4) - 2*a*x**3/(3*b**3) + x**4/(4*b**2)","A",0
170,1,54,0,0.215037," ","integrate(x**4/(b*x+a)**2,x)","- \frac{a^{4}}{a b^{5} + b^{6} x} - \frac{4 a^{3} \log{\left(a + b x \right)}}{b^{5}} + \frac{3 a^{2} x}{b^{4}} - \frac{a x^{2}}{b^{3}} + \frac{x^{3}}{3 b^{2}}"," ",0,"-a**4/(a*b**5 + b**6*x) - 4*a**3*log(a + b*x)/b**5 + 3*a**2*x/b**4 - a*x**2/b**3 + x**3/(3*b**2)","A",0
171,1,44,0,0.203546," ","integrate(x**3/(b*x+a)**2,x)","\frac{a^{3}}{a b^{4} + b^{5} x} + \frac{3 a^{2} \log{\left(a + b x \right)}}{b^{4}} - \frac{2 a x}{b^{3}} + \frac{x^{2}}{2 b^{2}}"," ",0,"a**3/(a*b**4 + b**5*x) + 3*a**2*log(a + b*x)/b**4 - 2*a*x/b**3 + x**2/(2*b**2)","A",0
172,1,31,0,0.173427," ","integrate(x**2/(b*x+a)**2,x)","- \frac{a^{2}}{a b^{3} + b^{4} x} - \frac{2 a \log{\left(a + b x \right)}}{b^{3}} + \frac{x}{b^{2}}"," ",0,"-a**2/(a*b**3 + b**4*x) - 2*a*log(a + b*x)/b**3 + x/b**2","A",0
173,1,20,0,0.168857," ","integrate(x/(b*x+a)**2,x)","\frac{a}{a b^{2} + b^{3} x} + \frac{\log{\left(a + b x \right)}}{b^{2}}"," ",0,"a/(a*b**2 + b**3*x) + log(a + b*x)/b**2","A",0
174,1,10,0,0.148864," ","integrate(1/(b*x+a)**2,x)","- \frac{1}{a b + b^{2} x}"," ",0,"-1/(a*b + b**2*x)","A",0
175,1,22,0,0.222017," ","integrate(1/x/(b*x+a)**2,x)","\frac{1}{a^{2} + a b x} + \frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a^{2}}"," ",0,"1/(a**2 + a*b*x) + (log(x) - log(a/b + x))/a**2","A",0
176,1,37,0,0.302573," ","integrate(1/x**2/(b*x+a)**2,x)","\frac{- a - 2 b x}{a^{3} x + a^{2} b x^{2}} + \frac{2 b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{3}}"," ",0,"(-a - 2*b*x)/(a**3*x + a**2*b*x**2) + 2*b*(-log(x) + log(a/b + x))/a**3","A",0
177,1,54,0,0.311504," ","integrate(1/x**3/(b*x+a)**2,x)","\frac{- a^{2} + 3 a b x + 6 b^{2} x^{2}}{2 a^{4} x^{2} + 2 a^{3} b x^{3}} + \frac{3 b^{2} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{4}}"," ",0,"(-a**2 + 3*a*b*x + 6*b**2*x**2)/(2*a**4*x**2 + 2*a**3*b*x**3) + 3*b**2*(log(x) - log(a/b + x))/a**4","A",0
178,1,66,0,0.336409," ","integrate(1/x**4/(b*x+a)**2,x)","\frac{- a^{3} + 2 a^{2} b x - 6 a b^{2} x^{2} - 12 b^{3} x^{3}}{3 a^{5} x^{3} + 3 a^{4} b x^{4}} + \frac{4 b^{3} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{5}}"," ",0,"(-a**3 + 2*a**2*b*x - 6*a*b**2*x**2 - 12*b**3*x**3)/(3*a**5*x**3 + 3*a**4*b*x**4) + 4*b**3*(-log(x) + log(a/b + x))/a**5","A",0
179,1,80,0,0.393977," ","integrate(1/x**5/(b*x+a)**2,x)","\frac{- 3 a^{4} + 5 a^{3} b x - 10 a^{2} b^{2} x^{2} + 30 a b^{3} x^{3} + 60 b^{4} x^{4}}{12 a^{6} x^{4} + 12 a^{5} b x^{5}} + \frac{5 b^{4} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{6}}"," ",0,"(-3*a**4 + 5*a**3*b*x - 10*a**2*b**2*x**2 + 30*a*b**3*x**3 + 60*b**4*x**4)/(12*a**6*x**4 + 12*a**5*b*x**5) + 5*b**4*(log(x) - log(a/b + x))/a**6","A",0
180,1,109,0,0.531536," ","integrate(x**7/(b*x+a)**3,x)","- \frac{21 a^{5} \log{\left(a + b x \right)}}{b^{8}} + \frac{15 a^{4} x}{b^{7}} - \frac{5 a^{3} x^{2}}{b^{6}} + \frac{2 a^{2} x^{3}}{b^{5}} - \frac{3 a x^{4}}{4 b^{4}} + \frac{- 13 a^{7} - 14 a^{6} b x}{2 a^{2} b^{8} + 4 a b^{9} x + 2 b^{10} x^{2}} + \frac{x^{5}}{5 b^{3}}"," ",0,"-21*a**5*log(a + b*x)/b**8 + 15*a**4*x/b**7 - 5*a**3*x**2/b**6 + 2*a**2*x**3/b**5 - 3*a*x**4/(4*b**4) + (-13*a**7 - 14*a**6*b*x)/(2*a**2*b**8 + 4*a*b**9*x + 2*b**10*x**2) + x**5/(5*b**3)","A",0
181,1,92,0,0.405000," ","integrate(x**6/(b*x+a)**3,x)","\frac{15 a^{4} \log{\left(a + b x \right)}}{b^{7}} - \frac{10 a^{3} x}{b^{6}} + \frac{3 a^{2} x^{2}}{b^{5}} - \frac{a x^{3}}{b^{4}} + \frac{11 a^{6} + 12 a^{5} b x}{2 a^{2} b^{7} + 4 a b^{8} x + 2 b^{9} x^{2}} + \frac{x^{4}}{4 b^{3}}"," ",0,"15*a**4*log(a + b*x)/b**7 - 10*a**3*x/b**6 + 3*a**2*x**2/b**5 - a*x**3/b**4 + (11*a**6 + 12*a**5*b*x)/(2*a**2*b**7 + 4*a*b**8*x + 2*b**9*x**2) + x**4/(4*b**3)","A",0
182,1,85,0,0.358855," ","integrate(x**5/(b*x+a)**3,x)","- \frac{10 a^{3} \log{\left(a + b x \right)}}{b^{6}} + \frac{6 a^{2} x}{b^{5}} - \frac{3 a x^{2}}{2 b^{4}} + \frac{- 9 a^{5} - 10 a^{4} b x}{2 a^{2} b^{6} + 4 a b^{7} x + 2 b^{8} x^{2}} + \frac{x^{3}}{3 b^{3}}"," ",0,"-10*a**3*log(a + b*x)/b**6 + 6*a**2*x/b**5 - 3*a*x**2/(2*b**4) + (-9*a**5 - 10*a**4*b*x)/(2*a**2*b**6 + 4*a*b**7*x + 2*b**8*x**2) + x**3/(3*b**3)","A",0
183,1,70,0,0.339230," ","integrate(x**4/(b*x+a)**3,x)","\frac{6 a^{2} \log{\left(a + b x \right)}}{b^{5}} - \frac{3 a x}{b^{4}} + \frac{7 a^{4} + 8 a^{3} b x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{x^{2}}{2 b^{3}}"," ",0,"6*a**2*log(a + b*x)/b**5 - 3*a*x/b**4 + (7*a**4 + 8*a**3*b*x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + x**2/(2*b**3)","A",0
184,1,58,0,0.310019," ","integrate(x**3/(b*x+a)**3,x)","- \frac{3 a \log{\left(a + b x \right)}}{b^{4}} + \frac{- 5 a^{3} - 6 a^{2} b x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{x}{b^{3}}"," ",0,"-3*a*log(a + b*x)/b**4 + (-5*a**3 - 6*a**2*b*x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + x/b**3","A",0
185,1,46,0,0.249609," ","integrate(x**2/(b*x+a)**3,x)","\frac{3 a^{2} + 4 a b x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{\log{\left(a + b x \right)}}{b^{3}}"," ",0,"(3*a**2 + 4*a*b*x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + log(a + b*x)/b**3","A",0
186,1,32,0,0.200496," ","integrate(x/(b*x+a)**3,x)","\frac{- a - 2 b x}{2 a^{2} b^{2} + 4 a b^{3} x + 2 b^{4} x^{2}}"," ",0,"(-a - 2*b*x)/(2*a**2*b**2 + 4*a*b**3*x + 2*b**4*x**2)","B",0
187,1,26,0,0.208911," ","integrate(1/(b*x+a)**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
188,1,46,0,0.348779," ","integrate(1/x/(b*x+a)**3,x)","\frac{3 a + 2 b x}{2 a^{4} + 4 a^{3} b x + 2 a^{2} b^{2} x^{2}} + \frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a^{3}}"," ",0,"(3*a + 2*b*x)/(2*a**4 + 4*a**3*b*x + 2*a**2*b**2*x**2) + (log(x) - log(a/b + x))/a**3","A",0
189,1,66,0,0.403594," ","integrate(1/x**2/(b*x+a)**3,x)","\frac{- 2 a^{2} - 9 a b x - 6 b^{2} x^{2}}{2 a^{5} x + 4 a^{4} b x^{2} + 2 a^{3} b^{2} x^{3}} + \frac{3 b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{4}}"," ",0,"(-2*a**2 - 9*a*b*x - 6*b**2*x**2)/(2*a**5*x + 4*a**4*b*x**2 + 2*a**3*b**2*x**3) + 3*b*(-log(x) + log(a/b + x))/a**4","A",0
190,1,78,0,0.406316," ","integrate(1/x**3/(b*x+a)**3,x)","\frac{- a^{3} + 4 a^{2} b x + 18 a b^{2} x^{2} + 12 b^{3} x^{3}}{2 a^{6} x^{2} + 4 a^{5} b x^{3} + 2 a^{4} b^{2} x^{4}} + \frac{6 b^{2} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{5}}"," ",0,"(-a**3 + 4*a**2*b*x + 18*a*b**2*x**2 + 12*b**3*x**3)/(2*a**6*x**2 + 4*a**5*b*x**3 + 2*a**4*b**2*x**4) + 6*b**2*(log(x) - log(a/b + x))/a**5","A",0
191,1,92,0,0.479555," ","integrate(1/x**4/(b*x+a)**3,x)","\frac{- 2 a^{4} + 5 a^{3} b x - 20 a^{2} b^{2} x^{2} - 90 a b^{3} x^{3} - 60 b^{4} x^{4}}{6 a^{7} x^{3} + 12 a^{6} b x^{4} + 6 a^{5} b^{2} x^{5}} + \frac{10 b^{3} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{6}}"," ",0,"(-2*a**4 + 5*a**3*b*x - 20*a**2*b**2*x**2 - 90*a*b**3*x**3 - 60*b**4*x**4)/(6*a**7*x**3 + 12*a**6*b*x**4 + 6*a**5*b**2*x**5) + 10*b**3*(-log(x) + log(a/b + x))/a**6","A",0
192,1,102,0,0.476497," ","integrate(1/x**5/(b*x+a)**3,x)","\frac{- a^{5} + 2 a^{4} b x - 5 a^{3} b^{2} x^{2} + 20 a^{2} b^{3} x^{3} + 90 a b^{4} x^{4} + 60 b^{5} x^{5}}{4 a^{8} x^{4} + 8 a^{7} b x^{5} + 4 a^{6} b^{2} x^{6}} + \frac{15 b^{4} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{7}}"," ",0,"(-a**5 + 2*a**4*b*x - 5*a**3*b**2*x**2 + 20*a**2*b**3*x**3 + 90*a*b**4*x**4 + 60*b**5*x**5)/(4*a**8*x**4 + 8*a**7*b*x**5 + 4*a**6*b**2*x**6) + 15*b**4*(log(x) - log(a/b + x))/a**7","A",0
193,1,131,0,0.524163," ","integrate(x**8/(b*x+a)**4,x)","- \frac{56 a^{5} \log{\left(a + b x \right)}}{b^{9}} + \frac{35 a^{4} x}{b^{8}} - \frac{10 a^{3} x^{2}}{b^{7}} + \frac{10 a^{2} x^{3}}{3 b^{6}} - \frac{a x^{4}}{b^{5}} + \frac{- 73 a^{8} - 156 a^{7} b x - 84 a^{6} b^{2} x^{2}}{3 a^{3} b^{9} + 9 a^{2} b^{10} x + 9 a b^{11} x^{2} + 3 b^{12} x^{3}} + \frac{x^{5}}{5 b^{4}}"," ",0,"-56*a**5*log(a + b*x)/b**9 + 35*a**4*x/b**8 - 10*a**3*x**2/b**7 + 10*a**2*x**3/(3*b**6) - a*x**4/b**5 + (-73*a**8 - 156*a**7*b*x - 84*a**6*b**2*x**2)/(3*a**3*b**9 + 9*a**2*b**10*x + 9*a*b**11*x**2 + 3*b**12*x**3) + x**5/(5*b**4)","A",0
194,1,119,0,0.482885," ","integrate(x**7/(b*x+a)**4,x)","\frac{35 a^{4} \log{\left(a + b x \right)}}{b^{8}} - \frac{20 a^{3} x}{b^{7}} + \frac{5 a^{2} x^{2}}{b^{6}} - \frac{4 a x^{3}}{3 b^{5}} + \frac{107 a^{7} + 231 a^{6} b x + 126 a^{5} b^{2} x^{2}}{6 a^{3} b^{8} + 18 a^{2} b^{9} x + 18 a b^{10} x^{2} + 6 b^{11} x^{3}} + \frac{x^{4}}{4 b^{4}}"," ",0,"35*a**4*log(a + b*x)/b**8 - 20*a**3*x/b**7 + 5*a**2*x**2/b**6 - 4*a*x**3/(3*b**5) + (107*a**7 + 231*a**6*b*x + 126*a**5*b**2*x**2)/(6*a**3*b**8 + 18*a**2*b**9*x + 18*a*b**10*x**2 + 6*b**11*x**3) + x**4/(4*b**4)","A",0
195,1,107,0,0.483639," ","integrate(x**6/(b*x+a)**4,x)","- \frac{20 a^{3} \log{\left(a + b x \right)}}{b^{7}} + \frac{10 a^{2} x}{b^{6}} - \frac{2 a x^{2}}{b^{5}} + \frac{- 37 a^{6} - 81 a^{5} b x - 45 a^{4} b^{2} x^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{x^{3}}{3 b^{4}}"," ",0,"-20*a**3*log(a + b*x)/b**7 + 10*a**2*x/b**6 - 2*a*x**2/b**5 + (-37*a**6 - 81*a**5*b*x - 45*a**4*b**2*x**2)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + x**3/(3*b**4)","A",0
196,1,94,0,0.460514," ","integrate(x**5/(b*x+a)**4,x)","\frac{10 a^{2} \log{\left(a + b x \right)}}{b^{6}} - \frac{4 a x}{b^{5}} + \frac{47 a^{5} + 105 a^{4} b x + 60 a^{3} b^{2} x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{x^{2}}{2 b^{4}}"," ",0,"10*a**2*log(a + b*x)/b**6 - 4*a*x/b**5 + (47*a**5 + 105*a**4*b*x + 60*a**3*b**2*x**2)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + x**2/(2*b**4)","A",0
197,1,82,0,0.397653," ","integrate(x**4/(b*x+a)**4,x)","- \frac{4 a \log{\left(a + b x \right)}}{b^{5}} + \frac{- 13 a^{4} - 30 a^{3} b x - 18 a^{2} b^{2} x^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} + \frac{x}{b^{4}}"," ",0,"-4*a*log(a + b*x)/b**5 + (-13*a**4 - 30*a**3*b*x - 18*a**2*b**2*x**2)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) + x/b**4","A",0
198,1,70,0,0.306160," ","integrate(x**3/(b*x+a)**4,x)","\frac{11 a^{3} + 27 a^{2} b x + 18 a b^{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{\log{\left(a + b x \right)}}{b^{4}}"," ",0,"(11*a**3 + 27*a**2*b*x + 18*a*b**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) + log(a + b*x)/b**4","A",0
199,1,56,0,0.296705," ","integrate(x**2/(b*x+a)**4,x)","\frac{- a^{2} - 3 a b x - 3 b^{2} x^{2}}{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 - 3*a*b*x - 3*b**2*x**2)/(3*a**3*b**3 + 9*a**2*b**4*x + 9*a*b**5*x**2 + 3*b**6*x**3)","B",0
200,1,44,0,0.317362," ","integrate(x/(b*x+a)**4,x)","\frac{- a - 3 b 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 - 3*b*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
201,1,37,0,0.265046," ","integrate(1/(b*x+a)**4,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
202,1,70,0,0.444326," ","integrate(1/x/(b*x+a)**4,x)","\frac{11 a^{2} + 15 a b x + 6 b^{2} x^{2}}{6 a^{6} + 18 a^{5} b x + 18 a^{4} b^{2} x^{2} + 6 a^{3} b^{3} x^{3}} + \frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a^{4}}"," ",0,"(11*a**2 + 15*a*b*x + 6*b**2*x**2)/(6*a**6 + 18*a**5*b*x + 18*a**4*b**2*x**2 + 6*a**3*b**3*x**3) + (log(x) - log(a/b + x))/a**4","A",0
203,1,90,0,0.459961," ","integrate(1/x**2/(b*x+a)**4,x)","\frac{- 3 a^{3} - 22 a^{2} b x - 30 a b^{2} x^{2} - 12 b^{3} x^{3}}{3 a^{7} x + 9 a^{6} b x^{2} + 9 a^{5} b^{2} x^{3} + 3 a^{4} b^{3} x^{4}} + \frac{4 b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{5}}"," ",0,"(-3*a**3 - 22*a**2*b*x - 30*a*b**2*x**2 - 12*b**3*x**3)/(3*a**7*x + 9*a**6*b*x**2 + 9*a**5*b**2*x**3 + 3*a**4*b**3*x**4) + 4*b*(-log(x) + log(a/b + x))/a**5","A",0
204,1,104,0,0.557343," ","integrate(1/x**3/(b*x+a)**4,x)","\frac{- 3 a^{4} + 15 a^{3} b x + 110 a^{2} b^{2} x^{2} + 150 a b^{3} x^{3} + 60 b^{4} x^{4}}{6 a^{8} x^{2} + 18 a^{7} b x^{3} + 18 a^{6} b^{2} x^{4} + 6 a^{5} b^{3} x^{5}} + \frac{10 b^{2} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{6}}"," ",0,"(-3*a**4 + 15*a**3*b*x + 110*a**2*b**2*x**2 + 150*a*b**3*x**3 + 60*b**4*x**4)/(6*a**8*x**2 + 18*a**7*b*x**3 + 18*a**6*b**2*x**4 + 6*a**5*b**3*x**5) + 10*b**2*(log(x) - log(a/b + x))/a**6","A",0
205,1,114,0,0.529280," ","integrate(1/x**4/(b*x+a)**4,x)","\frac{- a^{5} + 3 a^{4} b x - 15 a^{3} b^{2} x^{2} - 110 a^{2} b^{3} x^{3} - 150 a b^{4} x^{4} - 60 b^{5} x^{5}}{3 a^{9} x^{3} + 9 a^{8} b x^{4} + 9 a^{7} b^{2} x^{5} + 3 a^{6} b^{3} x^{6}} + \frac{20 b^{3} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{7}}"," ",0,"(-a**5 + 3*a**4*b*x - 15*a**3*b**2*x**2 - 110*a**2*b**3*x**3 - 150*a*b**4*x**4 - 60*b**5*x**5)/(3*a**9*x**3 + 9*a**8*b*x**4 + 9*a**7*b**2*x**5 + 3*a**6*b**3*x**6) + 20*b**3*(-log(x) + log(a/b + x))/a**7","A",0
206,1,128,0,0.581744," ","integrate(1/x**5/(b*x+a)**4,x)","\frac{- 3 a^{6} + 7 a^{5} b x - 21 a^{4} b^{2} x^{2} + 105 a^{3} b^{3} x^{3} + 770 a^{2} b^{4} x^{4} + 1050 a b^{5} x^{5} + 420 b^{6} x^{6}}{12 a^{10} x^{4} + 36 a^{9} b x^{5} + 36 a^{8} b^{2} x^{6} + 12 a^{7} b^{3} x^{7}} + \frac{35 b^{4} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{8}}"," ",0,"(-3*a**6 + 7*a**5*b*x - 21*a**4*b**2*x**2 + 105*a**3*b**3*x**3 + 770*a**2*b**4*x**4 + 1050*a*b**5*x**5 + 420*b**6*x**6)/(12*a**10*x**4 + 36*a**9*b*x**5 + 36*a**8*b**2*x**6 + 12*a**7*b**3*x**7) + 35*b**4*(log(x) - log(a/b + x))/a**8","A",0
207,1,190,0,0.931207," ","integrate(x**10/(b*x+a)**7,x)","\frac{210 a^{4} \log{\left(a + b x \right)}}{b^{11}} - \frac{84 a^{3} x}{b^{10}} + \frac{14 a^{2} x^{2}}{b^{9}} - \frac{7 a x^{3}}{3 b^{8}} + \frac{2131 a^{10} + 11274 a^{9} b x + 23985 a^{8} b^{2} x^{2} + 25680 a^{7} b^{3} x^{3} + 13860 a^{6} b^{4} x^{4} + 3024 a^{5} b^{5} x^{5}}{12 a^{6} b^{11} + 72 a^{5} b^{12} x + 180 a^{4} b^{13} x^{2} + 240 a^{3} b^{14} x^{3} + 180 a^{2} b^{15} x^{4} + 72 a b^{16} x^{5} + 12 b^{17} x^{6}} + \frac{x^{4}}{4 b^{7}}"," ",0,"210*a**4*log(a + b*x)/b**11 - 84*a**3*x/b**10 + 14*a**2*x**2/b**9 - 7*a*x**3/(3*b**8) + (2131*a**10 + 11274*a**9*b*x + 23985*a**8*b**2*x**2 + 25680*a**7*b**3*x**3 + 13860*a**6*b**4*x**4 + 3024*a**5*b**5*x**5)/(12*a**6*b**11 + 72*a**5*b**12*x + 180*a**4*b**13*x**2 + 240*a**3*b**14*x**3 + 180*a**2*b**15*x**4 + 72*a*b**16*x**5 + 12*b**17*x**6) + x**4/(4*b**7)","A",0
208,1,180,0,0.913929," ","integrate(x**9/(b*x+a)**7,x)","- \frac{84 a^{3} \log{\left(a + b x \right)}}{b^{10}} + \frac{28 a^{2} x}{b^{9}} - \frac{7 a x^{2}}{2 b^{8}} + \frac{- 2509 a^{9} - 13374 a^{8} b x - 28710 a^{7} b^{2} x^{2} - 31080 a^{6} b^{3} x^{3} - 17010 a^{5} b^{4} x^{4} - 3780 a^{4} b^{5} x^{5}}{30 a^{6} b^{10} + 180 a^{5} b^{11} x + 450 a^{4} b^{12} x^{2} + 600 a^{3} b^{13} x^{3} + 450 a^{2} b^{14} x^{4} + 180 a b^{15} x^{5} + 30 b^{16} x^{6}} + \frac{x^{3}}{3 b^{7}}"," ",0,"-84*a**3*log(a + b*x)/b**10 + 28*a**2*x/b**9 - 7*a*x**2/(2*b**8) + (-2509*a**9 - 13374*a**8*b*x - 28710*a**7*b**2*x**2 - 31080*a**6*b**3*x**3 - 17010*a**5*b**4*x**4 - 3780*a**4*b**5*x**5)/(30*a**6*b**10 + 180*a**5*b**11*x + 450*a**4*b**12*x**2 + 600*a**3*b**13*x**3 + 450*a**2*b**14*x**4 + 180*a*b**15*x**5 + 30*b**16*x**6) + x**3/(3*b**7)","A",0
209,1,165,0,0.842753," ","integrate(x**8/(b*x+a)**7,x)","\frac{28 a^{2} \log{\left(a + b x \right)}}{b^{9}} - \frac{7 a x}{b^{8}} + \frac{1023 a^{8} + 5508 a^{7} b x + 11970 a^{6} b^{2} x^{2} + 13160 a^{5} b^{3} x^{3} + 7350 a^{4} b^{4} x^{4} + 1680 a^{3} b^{5} x^{5}}{30 a^{6} b^{9} + 180 a^{5} b^{10} x + 450 a^{4} b^{11} x^{2} + 600 a^{3} b^{12} x^{3} + 450 a^{2} b^{13} x^{4} + 180 a b^{14} x^{5} + 30 b^{15} x^{6}} + \frac{x^{2}}{2 b^{7}}"," ",0,"28*a**2*log(a + b*x)/b**9 - 7*a*x/b**8 + (1023*a**8 + 5508*a**7*b*x + 11970*a**6*b**2*x**2 + 13160*a**5*b**3*x**3 + 7350*a**4*b**4*x**4 + 1680*a**3*b**5*x**5)/(30*a**6*b**9 + 180*a**5*b**10*x + 450*a**4*b**11*x**2 + 600*a**3*b**12*x**3 + 450*a**2*b**13*x**4 + 180*a*b**14*x**5 + 30*b**15*x**6) + x**2/(2*b**7)","A",0
210,1,153,0,0.820322," ","integrate(x**7/(b*x+a)**7,x)","- \frac{7 a \log{\left(a + b x \right)}}{b^{8}} + \frac{- 669 a^{7} - 3654 a^{6} b x - 8085 a^{5} b^{2} x^{2} - 9100 a^{4} b^{3} x^{3} - 5250 a^{3} b^{4} x^{4} - 1260 a^{2} b^{5} x^{5}}{60 a^{6} b^{8} + 360 a^{5} b^{9} x + 900 a^{4} b^{10} x^{2} + 1200 a^{3} b^{11} x^{3} + 900 a^{2} b^{12} x^{4} + 360 a b^{13} x^{5} + 60 b^{14} x^{6}} + \frac{x}{b^{7}}"," ",0,"-7*a*log(a + b*x)/b**8 + (-669*a**7 - 3654*a**6*b*x - 8085*a**5*b**2*x**2 - 9100*a**4*b**3*x**3 - 5250*a**3*b**4*x**4 - 1260*a**2*b**5*x**5)/(60*a**6*b**8 + 360*a**5*b**9*x + 900*a**4*b**10*x**2 + 1200*a**3*b**11*x**3 + 900*a**2*b**12*x**4 + 360*a*b**13*x**5 + 60*b**14*x**6) + x/b**7","A",0
211,1,141,0,0.642042," ","integrate(x**6/(b*x+a)**7,x)","\frac{147 a^{6} + 822 a^{5} b x + 1875 a^{4} b^{2} x^{2} + 2200 a^{3} b^{3} x^{3} + 1350 a^{2} b^{4} x^{4} + 360 a b^{5} x^{5}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{\log{\left(a + b x \right)}}{b^{7}}"," ",0,"(147*a**6 + 822*a**5*b*x + 1875*a**4*b**2*x**2 + 2200*a**3*b**3*x**3 + 1350*a**2*b**4*x**4 + 360*a*b**5*x**5)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + log(a + b*x)/b**7","A",0
212,1,128,0,0.583094," ","integrate(x**5/(b*x+a)**7,x)","\frac{- a^{5} - 6 a^{4} b x - 15 a^{3} b^{2} x^{2} - 20 a^{2} b^{3} x^{3} - 15 a b^{4} x^{4} - 6 b^{5} x^{5}}{6 a^{6} b^{6} + 36 a^{5} b^{7} x + 90 a^{4} b^{8} x^{2} + 120 a^{3} b^{9} x^{3} + 90 a^{2} b^{10} x^{4} + 36 a b^{11} x^{5} + 6 b^{12} x^{6}}"," ",0,"(-a**5 - 6*a**4*b*x - 15*a**3*b**2*x**2 - 20*a**2*b**3*x**3 - 15*a*b**4*x**4 - 6*b**5*x**5)/(6*a**6*b**6 + 36*a**5*b**7*x + 90*a**4*b**8*x**2 + 120*a**3*b**9*x**3 + 90*a**2*b**10*x**4 + 36*a*b**11*x**5 + 6*b**12*x**6)","B",0
213,1,116,0,0.572502," ","integrate(x**4/(b*x+a)**7,x)","\frac{- a^{4} - 6 a^{3} b x - 15 a^{2} b^{2} x^{2} - 20 a b^{3} x^{3} - 15 b^{4} x^{4}}{30 a^{6} b^{5} + 180 a^{5} b^{6} x + 450 a^{4} b^{7} x^{2} + 600 a^{3} b^{8} x^{3} + 450 a^{2} b^{9} x^{4} + 180 a b^{10} x^{5} + 30 b^{11} x^{6}}"," ",0,"(-a**4 - 6*a**3*b*x - 15*a**2*b**2*x**2 - 20*a*b**3*x**3 - 15*b**4*x**4)/(30*a**6*b**5 + 180*a**5*b**6*x + 450*a**4*b**7*x**2 + 600*a**3*b**8*x**3 + 450*a**2*b**9*x**4 + 180*a*b**10*x**5 + 30*b**11*x**6)","B",0
214,1,104,0,0.558918," ","integrate(x**3/(b*x+a)**7,x)","\frac{- a^{3} - 6 a^{2} b x - 15 a b^{2} x^{2} - 20 b^{3} x^{3}}{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 - 6*a**2*b*x - 15*a*b**2*x**2 - 20*b**3*x**3)/(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
215,1,92,0,0.547096," ","integrate(x**2/(b*x+a)**7,x)","\frac{- a^{2} - 6 a b x - 15 b^{2} x^{2}}{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 - 6*a*b*x - 15*b**2*x**2)/(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
216,1,80,0,0.503343," ","integrate(x/(b*x+a)**7,x)","\frac{- a - 6 b x}{30 a^{6} b^{2} + 180 a^{5} b^{3} x + 450 a^{4} b^{4} x^{2} + 600 a^{3} b^{5} x^{3} + 450 a^{2} b^{6} x^{4} + 180 a b^{7} x^{5} + 30 b^{8} x^{6}}"," ",0,"(-a - 6*b*x)/(30*a**6*b**2 + 180*a**5*b**3*x + 450*a**4*b**4*x**2 + 600*a**3*b**5*x**3 + 450*a**2*b**6*x**4 + 180*a*b**7*x**5 + 30*b**8*x**6)","B",0
217,1,73,0,0.464360," ","integrate(1/(b*x+a)**7,x)","- \frac{1}{6 a^{6} b + 36 a^{5} b^{2} x + 90 a^{4} b^{3} x^{2} + 120 a^{3} b^{4} x^{3} + 90 a^{2} b^{5} x^{4} + 36 a b^{6} x^{5} + 6 b^{7} x^{6}}"," ",0,"-1/(6*a**6*b + 36*a**5*b**2*x + 90*a**4*b**3*x**2 + 120*a**3*b**4*x**3 + 90*a**2*b**5*x**4 + 36*a*b**6*x**5 + 6*b**7*x**6)","B",0
218,1,141,0,0.681327," ","integrate(1/x/(b*x+a)**7,x)","\frac{147 a^{5} + 522 a^{4} b x + 855 a^{3} b^{2} x^{2} + 740 a^{2} b^{3} x^{3} + 330 a b^{4} x^{4} + 60 b^{5} x^{5}}{60 a^{12} + 360 a^{11} b x + 900 a^{10} b^{2} x^{2} + 1200 a^{9} b^{3} x^{3} + 900 a^{8} b^{4} x^{4} + 360 a^{7} b^{5} x^{5} + 60 a^{6} b^{6} x^{6}} + \frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a^{7}}"," ",0,"(147*a**5 + 522*a**4*b*x + 855*a**3*b**2*x**2 + 740*a**2*b**3*x**3 + 330*a*b**4*x**4 + 60*b**5*x**5)/(60*a**12 + 360*a**11*b*x + 900*a**10*b**2*x**2 + 1200*a**9*b**3*x**3 + 900*a**8*b**4*x**4 + 360*a**7*b**5*x**5 + 60*a**6*b**6*x**6) + (log(x) - log(a/b + x))/a**7","A",0
219,1,162,0,0.796884," ","integrate(1/x**2/(b*x+a)**7,x)","\frac{- 60 a^{6} - 1029 a^{5} b x - 3654 a^{4} b^{2} x^{2} - 5985 a^{3} b^{3} x^{3} - 5180 a^{2} b^{4} x^{4} - 2310 a b^{5} x^{5} - 420 b^{6} x^{6}}{60 a^{13} x + 360 a^{12} b x^{2} + 900 a^{11} b^{2} x^{3} + 1200 a^{10} b^{3} x^{4} + 900 a^{9} b^{4} x^{5} + 360 a^{8} b^{5} x^{6} + 60 a^{7} b^{6} x^{7}} + \frac{7 b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{8}}"," ",0,"(-60*a**6 - 1029*a**5*b*x - 3654*a**4*b**2*x**2 - 5985*a**3*b**3*x**3 - 5180*a**2*b**4*x**4 - 2310*a*b**5*x**5 - 420*b**6*x**6)/(60*a**13*x + 360*a**12*b*x**2 + 900*a**11*b**2*x**3 + 1200*a**10*b**3*x**4 + 900*a**9*b**4*x**5 + 360*a**8*b**5*x**6 + 60*a**7*b**6*x**7) + 7*b*(-log(x) + log(a/b + x))/a**8","A",0
220,1,175,0,0.842975," ","integrate(1/x**3/(b*x+a)**7,x)","\frac{- 15 a^{7} + 120 a^{6} b x + 2058 a^{5} b^{2} x^{2} + 7308 a^{4} b^{3} x^{3} + 11970 a^{3} b^{4} x^{4} + 10360 a^{2} b^{5} x^{5} + 4620 a b^{6} x^{6} + 840 b^{7} x^{7}}{30 a^{14} x^{2} + 180 a^{13} b x^{3} + 450 a^{12} b^{2} x^{4} + 600 a^{11} b^{3} x^{5} + 450 a^{10} b^{4} x^{6} + 180 a^{9} b^{5} x^{7} + 30 a^{8} b^{6} x^{8}} + \frac{28 b^{2} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{9}}"," ",0,"(-15*a**7 + 120*a**6*b*x + 2058*a**5*b**2*x**2 + 7308*a**4*b**3*x**3 + 11970*a**3*b**4*x**4 + 10360*a**2*b**5*x**5 + 4620*a*b**6*x**6 + 840*b**7*x**7)/(30*a**14*x**2 + 180*a**13*b*x**3 + 450*a**12*b**2*x**4 + 600*a**11*b**3*x**5 + 450*a**10*b**4*x**6 + 180*a**9*b**5*x**7 + 30*a**8*b**6*x**8) + 28*b**2*(log(x) - log(a/b + x))/a**9","A",0
221,1,187,0,0.992383," ","integrate(1/x**4/(b*x+a)**7,x)","\frac{- 10 a^{8} + 45 a^{7} b x - 360 a^{6} b^{2} x^{2} - 6174 a^{5} b^{3} x^{3} - 21924 a^{4} b^{4} x^{4} - 35910 a^{3} b^{5} x^{5} - 31080 a^{2} b^{6} x^{6} - 13860 a b^{7} x^{7} - 2520 b^{8} x^{8}}{30 a^{15} x^{3} + 180 a^{14} b x^{4} + 450 a^{13} b^{2} x^{5} + 600 a^{12} b^{3} x^{6} + 450 a^{11} b^{4} x^{7} + 180 a^{10} b^{5} x^{8} + 30 a^{9} b^{6} x^{9}} + \frac{84 b^{3} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{10}}"," ",0,"(-10*a**8 + 45*a**7*b*x - 360*a**6*b**2*x**2 - 6174*a**5*b**3*x**3 - 21924*a**4*b**4*x**4 - 35910*a**3*b**5*x**5 - 31080*a**2*b**6*x**6 - 13860*a*b**7*x**7 - 2520*b**8*x**8)/(30*a**15*x**3 + 180*a**14*b*x**4 + 450*a**13*b**2*x**5 + 600*a**12*b**3*x**6 + 450*a**11*b**4*x**7 + 180*a**10*b**5*x**8 + 30*a**9*b**6*x**9) + 84*b**3*(-log(x) + log(a/b + x))/a**10","A",0
222,1,250,0,1.544878," ","integrate(x**12/(b*x+a)**10,x)","- \frac{220 a^{3} \log{\left(a + b x \right)}}{b^{13}} + \frac{55 a^{2} x}{b^{12}} - \frac{5 a x^{2}}{b^{11}} + \frac{- 35201 a^{12} - 296019 a^{11} b x - 1093356 a^{10} b^{2} x^{2} - 2318316 a^{9} b^{3} x^{3} - 3089394 a^{8} b^{4} x^{4} - 2652804 a^{7} b^{5} x^{5} - 1435896 a^{6} b^{6} x^{6} - 449064 a^{5} b^{7} x^{7} - 62370 a^{4} b^{8} x^{8}}{126 a^{9} b^{13} + 1134 a^{8} b^{14} x + 4536 a^{7} b^{15} x^{2} + 10584 a^{6} b^{16} x^{3} + 15876 a^{5} b^{17} x^{4} + 15876 a^{4} b^{18} x^{5} + 10584 a^{3} b^{19} x^{6} + 4536 a^{2} b^{20} x^{7} + 1134 a b^{21} x^{8} + 126 b^{22} x^{9}} + \frac{x^{3}}{3 b^{10}}"," ",0,"-220*a**3*log(a + b*x)/b**13 + 55*a**2*x/b**12 - 5*a*x**2/b**11 + (-35201*a**12 - 296019*a**11*b*x - 1093356*a**10*b**2*x**2 - 2318316*a**9*b**3*x**3 - 3089394*a**8*b**4*x**4 - 2652804*a**7*b**5*x**5 - 1435896*a**6*b**6*x**6 - 449064*a**5*b**7*x**7 - 62370*a**4*b**8*x**8)/(126*a**9*b**13 + 1134*a**8*b**14*x + 4536*a**7*b**15*x**2 + 10584*a**6*b**16*x**3 + 15876*a**5*b**17*x**4 + 15876*a**4*b**18*x**5 + 10584*a**3*b**19*x**6 + 4536*a**2*b**20*x**7 + 1134*a*b**21*x**8 + 126*b**22*x**9) + x**3/(3*b**10)","A",0
223,1,236,0,1.476906," ","integrate(x**11/(b*x+a)**10,x)","\frac{55 a^{2} \log{\left(a + b x \right)}}{b^{12}} - \frac{10 a x}{b^{11}} + \frac{42131 a^{11} + 356499 a^{10} b x + 1326204 a^{9} b^{2} x^{2} + 2835756 a^{8} b^{3} x^{3} + 3817044 a^{7} b^{4} x^{4} + 3318084 a^{6} b^{5} x^{5} + 1823976 a^{5} b^{6} x^{6} + 582120 a^{4} b^{7} x^{7} + 83160 a^{3} b^{8} x^{8}}{504 a^{9} b^{12} + 4536 a^{8} b^{13} x + 18144 a^{7} b^{14} x^{2} + 42336 a^{6} b^{15} x^{3} + 63504 a^{5} b^{16} x^{4} + 63504 a^{4} b^{17} x^{5} + 42336 a^{3} b^{18} x^{6} + 18144 a^{2} b^{19} x^{7} + 4536 a b^{20} x^{8} + 504 b^{21} x^{9}} + \frac{x^{2}}{2 b^{10}}"," ",0,"55*a**2*log(a + b*x)/b**12 - 10*a*x/b**11 + (42131*a**11 + 356499*a**10*b*x + 1326204*a**9*b**2*x**2 + 2835756*a**8*b**3*x**3 + 3817044*a**7*b**4*x**4 + 3318084*a**6*b**5*x**5 + 1823976*a**5*b**6*x**6 + 582120*a**4*b**7*x**7 + 83160*a**3*b**8*x**8)/(504*a**9*b**12 + 4536*a**8*b**13*x + 18144*a**7*b**14*x**2 + 42336*a**6*b**15*x**3 + 63504*a**5*b**16*x**4 + 63504*a**4*b**17*x**5 + 42336*a**3*b**18*x**6 + 18144*a**2*b**19*x**7 + 4536*a*b**20*x**8 + 504*b**21*x**9) + x**2/(2*b**10)","A",0
224,1,224,0,1.325850," ","integrate(x**10/(b*x+a)**10,x)","- \frac{10 a \log{\left(a + b x \right)}}{b^{11}} + \frac{- 4861 a^{10} - 41481 a^{9} b x - 155844 a^{8} b^{2} x^{2} - 337176 a^{7} b^{3} x^{3} - 460404 a^{6} b^{4} x^{4} - 407484 a^{5} b^{5} x^{5} - 229320 a^{4} b^{6} x^{6} - 75600 a^{3} b^{7} x^{7} - 11340 a^{2} b^{8} x^{8}}{252 a^{9} b^{11} + 2268 a^{8} b^{12} x + 9072 a^{7} b^{13} x^{2} + 21168 a^{6} b^{14} x^{3} + 31752 a^{5} b^{15} x^{4} + 31752 a^{4} b^{16} x^{5} + 21168 a^{3} b^{17} x^{6} + 9072 a^{2} b^{18} x^{7} + 2268 a b^{19} x^{8} + 252 b^{20} x^{9}} + \frac{x}{b^{10}}"," ",0,"-10*a*log(a + b*x)/b**11 + (-4861*a**10 - 41481*a**9*b*x - 155844*a**8*b**2*x**2 - 337176*a**7*b**3*x**3 - 460404*a**6*b**4*x**4 - 407484*a**5*b**5*x**5 - 229320*a**4*b**6*x**6 - 75600*a**3*b**7*x**7 - 11340*a**2*b**8*x**8)/(252*a**9*b**11 + 2268*a**8*b**12*x + 9072*a**7*b**13*x**2 + 21168*a**6*b**14*x**3 + 31752*a**5*b**15*x**4 + 31752*a**4*b**16*x**5 + 21168*a**3*b**17*x**6 + 9072*a**2*b**18*x**7 + 2268*a*b**19*x**8 + 252*b**20*x**9) + x/b**10","A",0
225,1,212,0,1.105018," ","integrate(x**9/(b*x+a)**10,x)","\frac{7129 a^{9} + 61641 a^{8} b x + 235224 a^{7} b^{2} x^{2} + 518616 a^{6} b^{3} x^{3} + 725004 a^{5} b^{4} x^{4} + 661500 a^{4} b^{5} x^{5} + 388080 a^{3} b^{6} x^{6} + 136080 a^{2} b^{7} x^{7} + 22680 a b^{8} x^{8}}{2520 a^{9} b^{10} + 22680 a^{8} b^{11} x + 90720 a^{7} b^{12} x^{2} + 211680 a^{6} b^{13} x^{3} + 317520 a^{5} b^{14} x^{4} + 317520 a^{4} b^{15} x^{5} + 211680 a^{3} b^{16} x^{6} + 90720 a^{2} b^{17} x^{7} + 22680 a b^{18} x^{8} + 2520 b^{19} x^{9}} + \frac{\log{\left(a + b x \right)}}{b^{10}}"," ",0,"(7129*a**9 + 61641*a**8*b*x + 235224*a**7*b**2*x**2 + 518616*a**6*b**3*x**3 + 725004*a**5*b**4*x**4 + 661500*a**4*b**5*x**5 + 388080*a**3*b**6*x**6 + 136080*a**2*b**7*x**7 + 22680*a*b**8*x**8)/(2520*a**9*b**10 + 22680*a**8*b**11*x + 90720*a**7*b**12*x**2 + 211680*a**6*b**13*x**3 + 317520*a**5*b**14*x**4 + 317520*a**4*b**15*x**5 + 211680*a**3*b**16*x**6 + 90720*a**2*b**17*x**7 + 22680*a*b**18*x**8 + 2520*b**19*x**9) + log(a + b*x)/b**10","A",0
226,1,199,0,0.979952," ","integrate(x**8/(b*x+a)**10,x)","\frac{- a^{8} - 9 a^{7} b x - 36 a^{6} b^{2} x^{2} - 84 a^{5} b^{3} x^{3} - 126 a^{4} b^{4} x^{4} - 126 a^{3} b^{5} x^{5} - 84 a^{2} b^{6} x^{6} - 36 a b^{7} x^{7} - 9 b^{8} x^{8}}{9 a^{9} b^{9} + 81 a^{8} b^{10} x + 324 a^{7} b^{11} x^{2} + 756 a^{6} b^{12} x^{3} + 1134 a^{5} b^{13} x^{4} + 1134 a^{4} b^{14} x^{5} + 756 a^{3} b^{15} x^{6} + 324 a^{2} b^{16} x^{7} + 81 a b^{17} x^{8} + 9 b^{18} x^{9}}"," ",0,"(-a**8 - 9*a**7*b*x - 36*a**6*b**2*x**2 - 84*a**5*b**3*x**3 - 126*a**4*b**4*x**4 - 126*a**3*b**5*x**5 - 84*a**2*b**6*x**6 - 36*a*b**7*x**7 - 9*b**8*x**8)/(9*a**9*b**9 + 81*a**8*b**10*x + 324*a**7*b**11*x**2 + 756*a**6*b**12*x**3 + 1134*a**5*b**13*x**4 + 1134*a**4*b**14*x**5 + 756*a**3*b**15*x**6 + 324*a**2*b**16*x**7 + 81*a*b**17*x**8 + 9*b**18*x**9)","B",0
227,1,187,0,0.998643," ","integrate(x**7/(b*x+a)**10,x)","\frac{- a^{7} - 9 a^{6} b x - 36 a^{5} b^{2} x^{2} - 84 a^{4} b^{3} x^{3} - 126 a^{3} b^{4} x^{4} - 126 a^{2} b^{5} x^{5} - 84 a b^{6} x^{6} - 36 b^{7} x^{7}}{72 a^{9} b^{8} + 648 a^{8} b^{9} x + 2592 a^{7} b^{10} x^{2} + 6048 a^{6} b^{11} x^{3} + 9072 a^{5} b^{12} x^{4} + 9072 a^{4} b^{13} x^{5} + 6048 a^{3} b^{14} x^{6} + 2592 a^{2} b^{15} x^{7} + 648 a b^{16} x^{8} + 72 b^{17} x^{9}}"," ",0,"(-a**7 - 9*a**6*b*x - 36*a**5*b**2*x**2 - 84*a**4*b**3*x**3 - 126*a**3*b**4*x**4 - 126*a**2*b**5*x**5 - 84*a*b**6*x**6 - 36*b**7*x**7)/(72*a**9*b**8 + 648*a**8*b**9*x + 2592*a**7*b**10*x**2 + 6048*a**6*b**11*x**3 + 9072*a**5*b**12*x**4 + 9072*a**4*b**13*x**5 + 6048*a**3*b**14*x**6 + 2592*a**2*b**15*x**7 + 648*a*b**16*x**8 + 72*b**17*x**9)","B",0
228,1,175,0,0.913486," ","integrate(x**6/(b*x+a)**10,x)","\frac{- a^{6} - 9 a^{5} b x - 36 a^{4} b^{2} x^{2} - 84 a^{3} b^{3} x^{3} - 126 a^{2} b^{4} x^{4} - 126 a b^{5} x^{5} - 84 b^{6} x^{6}}{252 a^{9} b^{7} + 2268 a^{8} b^{8} x + 9072 a^{7} b^{9} x^{2} + 21168 a^{6} b^{10} x^{3} + 31752 a^{5} b^{11} x^{4} + 31752 a^{4} b^{12} x^{5} + 21168 a^{3} b^{13} x^{6} + 9072 a^{2} b^{14} x^{7} + 2268 a b^{15} x^{8} + 252 b^{16} x^{9}}"," ",0,"(-a**6 - 9*a**5*b*x - 36*a**4*b**2*x**2 - 84*a**3*b**3*x**3 - 126*a**2*b**4*x**4 - 126*a*b**5*x**5 - 84*b**6*x**6)/(252*a**9*b**7 + 2268*a**8*b**8*x + 9072*a**7*b**9*x**2 + 21168*a**6*b**10*x**3 + 31752*a**5*b**11*x**4 + 31752*a**4*b**12*x**5 + 21168*a**3*b**13*x**6 + 9072*a**2*b**14*x**7 + 2268*a*b**15*x**8 + 252*b**16*x**9)","B",0
229,1,163,0,0.840176," ","integrate(x**5/(b*x+a)**10,x)","\frac{- a^{5} - 9 a^{4} b x - 36 a^{3} b^{2} x^{2} - 84 a^{2} b^{3} x^{3} - 126 a b^{4} x^{4} - 126 b^{5} x^{5}}{504 a^{9} b^{6} + 4536 a^{8} b^{7} x + 18144 a^{7} b^{8} x^{2} + 42336 a^{6} b^{9} x^{3} + 63504 a^{5} b^{10} x^{4} + 63504 a^{4} b^{11} x^{5} + 42336 a^{3} b^{12} x^{6} + 18144 a^{2} b^{13} x^{7} + 4536 a b^{14} x^{8} + 504 b^{15} x^{9}}"," ",0,"(-a**5 - 9*a**4*b*x - 36*a**3*b**2*x**2 - 84*a**2*b**3*x**3 - 126*a*b**4*x**4 - 126*b**5*x**5)/(504*a**9*b**6 + 4536*a**8*b**7*x + 18144*a**7*b**8*x**2 + 42336*a**6*b**9*x**3 + 63504*a**5*b**10*x**4 + 63504*a**4*b**11*x**5 + 42336*a**3*b**12*x**6 + 18144*a**2*b**13*x**7 + 4536*a*b**14*x**8 + 504*b**15*x**9)","B",0
230,1,151,0,0.793907," ","integrate(x**4/(b*x+a)**10,x)","\frac{- a^{4} - 9 a^{3} b x - 36 a^{2} b^{2} x^{2} - 84 a b^{3} x^{3} - 126 b^{4} x^{4}}{630 a^{9} b^{5} + 5670 a^{8} b^{6} x + 22680 a^{7} b^{7} x^{2} + 52920 a^{6} b^{8} x^{3} + 79380 a^{5} b^{9} x^{4} + 79380 a^{4} b^{10} x^{5} + 52920 a^{3} b^{11} x^{6} + 22680 a^{2} b^{12} x^{7} + 5670 a b^{13} x^{8} + 630 b^{14} x^{9}}"," ",0,"(-a**4 - 9*a**3*b*x - 36*a**2*b**2*x**2 - 84*a*b**3*x**3 - 126*b**4*x**4)/(630*a**9*b**5 + 5670*a**8*b**6*x + 22680*a**7*b**7*x**2 + 52920*a**6*b**8*x**3 + 79380*a**5*b**9*x**4 + 79380*a**4*b**10*x**5 + 52920*a**3*b**11*x**6 + 22680*a**2*b**12*x**7 + 5670*a*b**13*x**8 + 630*b**14*x**9)","B",0
231,1,139,0,0.697661," ","integrate(x**3/(b*x+a)**10,x)","\frac{- a^{3} - 9 a^{2} b x - 36 a b^{2} x^{2} - 84 b^{3} x^{3}}{504 a^{9} b^{4} + 4536 a^{8} b^{5} x + 18144 a^{7} b^{6} x^{2} + 42336 a^{6} b^{7} x^{3} + 63504 a^{5} b^{8} x^{4} + 63504 a^{4} b^{9} x^{5} + 42336 a^{3} b^{10} x^{6} + 18144 a^{2} b^{11} x^{7} + 4536 a b^{12} x^{8} + 504 b^{13} x^{9}}"," ",0,"(-a**3 - 9*a**2*b*x - 36*a*b**2*x**2 - 84*b**3*x**3)/(504*a**9*b**4 + 4536*a**8*b**5*x + 18144*a**7*b**6*x**2 + 42336*a**6*b**7*x**3 + 63504*a**5*b**8*x**4 + 63504*a**4*b**9*x**5 + 42336*a**3*b**10*x**6 + 18144*a**2*b**11*x**7 + 4536*a*b**12*x**8 + 504*b**13*x**9)","B",0
232,1,128,0,0.679193," ","integrate(x**2/(b*x+a)**10,x)","\frac{- a^{2} - 9 a b x - 36 b^{2} x^{2}}{252 a^{9} b^{3} + 2268 a^{8} b^{4} x + 9072 a^{7} b^{5} x^{2} + 21168 a^{6} b^{6} x^{3} + 31752 a^{5} b^{7} x^{4} + 31752 a^{4} b^{8} x^{5} + 21168 a^{3} b^{9} x^{6} + 9072 a^{2} b^{10} x^{7} + 2268 a b^{11} x^{8} + 252 b^{12} x^{9}}"," ",0,"(-a**2 - 9*a*b*x - 36*b**2*x**2)/(252*a**9*b**3 + 2268*a**8*b**4*x + 9072*a**7*b**5*x**2 + 21168*a**6*b**6*x**3 + 31752*a**5*b**7*x**4 + 31752*a**4*b**8*x**5 + 21168*a**3*b**9*x**6 + 9072*a**2*b**10*x**7 + 2268*a*b**11*x**8 + 252*b**12*x**9)","B",0
233,1,116,0,0.722917," ","integrate(x/(b*x+a)**10,x)","\frac{- a - 9 b x}{72 a^{9} b^{2} + 648 a^{8} b^{3} x + 2592 a^{7} b^{4} x^{2} + 6048 a^{6} b^{5} x^{3} + 9072 a^{5} b^{6} x^{4} + 9072 a^{4} b^{7} x^{5} + 6048 a^{3} b^{8} x^{6} + 2592 a^{2} b^{9} x^{7} + 648 a b^{10} x^{8} + 72 b^{11} x^{9}}"," ",0,"(-a - 9*b*x)/(72*a**9*b**2 + 648*a**8*b**3*x + 2592*a**7*b**4*x**2 + 6048*a**6*b**5*x**3 + 9072*a**5*b**6*x**4 + 9072*a**4*b**7*x**5 + 6048*a**3*b**8*x**6 + 2592*a**2*b**9*x**7 + 648*a*b**10*x**8 + 72*b**11*x**9)","B",0
234,1,109,0,0.671338," ","integrate(1/(b*x+a)**10,x)","- \frac{1}{9 a^{9} b + 81 a^{8} b^{2} x + 324 a^{7} b^{3} x^{2} + 756 a^{6} b^{4} x^{3} + 1134 a^{5} b^{5} x^{4} + 1134 a^{4} b^{6} x^{5} + 756 a^{3} b^{7} x^{6} + 324 a^{2} b^{8} x^{7} + 81 a b^{9} x^{8} + 9 b^{10} x^{9}}"," ",0,"-1/(9*a**9*b + 81*a**8*b**2*x + 324*a**7*b**3*x**2 + 756*a**6*b**4*x**3 + 1134*a**5*b**5*x**4 + 1134*a**4*b**6*x**5 + 756*a**3*b**7*x**6 + 324*a**2*b**8*x**7 + 81*a*b**9*x**8 + 9*b**10*x**9)","B",0
235,1,212,0,1.022644," ","integrate(1/x/(b*x+a)**10,x)","\frac{7129 a^{8} + 41481 a^{7} b x + 120564 a^{6} b^{2} x^{2} + 210756 a^{5} b^{3} x^{3} + 236754 a^{4} b^{4} x^{4} + 173250 a^{3} b^{5} x^{5} + 80220 a^{2} b^{6} x^{6} + 21420 a b^{7} x^{7} + 2520 b^{8} x^{8}}{2520 a^{18} + 22680 a^{17} b x + 90720 a^{16} b^{2} x^{2} + 211680 a^{15} b^{3} x^{3} + 317520 a^{14} b^{4} x^{4} + 317520 a^{13} b^{5} x^{5} + 211680 a^{12} b^{6} x^{6} + 90720 a^{11} b^{7} x^{7} + 22680 a^{10} b^{8} x^{8} + 2520 a^{9} b^{9} x^{9}} + \frac{\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}}{a^{10}}"," ",0,"(7129*a**8 + 41481*a**7*b*x + 120564*a**6*b**2*x**2 + 210756*a**5*b**3*x**3 + 236754*a**4*b**4*x**4 + 173250*a**3*b**5*x**5 + 80220*a**2*b**6*x**6 + 21420*a*b**7*x**7 + 2520*b**8*x**8)/(2520*a**18 + 22680*a**17*b*x + 90720*a**16*b**2*x**2 + 211680*a**15*b**3*x**3 + 317520*a**14*b**4*x**4 + 317520*a**13*b**5*x**5 + 211680*a**12*b**6*x**6 + 90720*a**11*b**7*x**7 + 22680*a**10*b**8*x**8 + 2520*a**9*b**9*x**9) + (log(x) - log(a/b + x))/a**10","A",0
236,1,233,0,1.148418," ","integrate(1/x**2/(b*x+a)**10,x)","\frac{- 252 a^{9} - 7129 a^{8} b x - 41481 a^{7} b^{2} x^{2} - 120564 a^{6} b^{3} x^{3} - 210756 a^{5} b^{4} x^{4} - 236754 a^{4} b^{5} x^{5} - 173250 a^{3} b^{6} x^{6} - 80220 a^{2} b^{7} x^{7} - 21420 a b^{8} x^{8} - 2520 b^{9} x^{9}}{252 a^{19} x + 2268 a^{18} b x^{2} + 9072 a^{17} b^{2} x^{3} + 21168 a^{16} b^{3} x^{4} + 31752 a^{15} b^{4} x^{5} + 31752 a^{14} b^{5} x^{6} + 21168 a^{13} b^{6} x^{7} + 9072 a^{12} b^{7} x^{8} + 2268 a^{11} b^{8} x^{9} + 252 a^{10} b^{9} x^{10}} + \frac{10 b \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{11}}"," ",0,"(-252*a**9 - 7129*a**8*b*x - 41481*a**7*b**2*x**2 - 120564*a**6*b**3*x**3 - 210756*a**5*b**4*x**4 - 236754*a**4*b**5*x**5 - 173250*a**3*b**6*x**6 - 80220*a**2*b**7*x**7 - 21420*a*b**8*x**8 - 2520*b**9*x**9)/(252*a**19*x + 2268*a**18*b*x**2 + 9072*a**17*b**2*x**3 + 21168*a**16*b**3*x**4 + 31752*a**15*b**4*x**5 + 31752*a**14*b**5*x**6 + 21168*a**13*b**6*x**7 + 9072*a**12*b**7*x**8 + 2268*a**11*b**8*x**9 + 252*a**10*b**9*x**10) + 10*b*(-log(x) + log(a/b + x))/a**11","A",0
237,1,246,0,1.176022," ","integrate(1/x**3/(b*x+a)**10,x)","\frac{- 252 a^{10} + 2772 a^{9} b x + 78419 a^{8} b^{2} x^{2} + 456291 a^{7} b^{3} x^{3} + 1326204 a^{6} b^{4} x^{4} + 2318316 a^{5} b^{5} x^{5} + 2604294 a^{4} b^{6} x^{6} + 1905750 a^{3} b^{7} x^{7} + 882420 a^{2} b^{8} x^{8} + 235620 a b^{9} x^{9} + 27720 b^{10} x^{10}}{504 a^{20} x^{2} + 4536 a^{19} b x^{3} + 18144 a^{18} b^{2} x^{4} + 42336 a^{17} b^{3} x^{5} + 63504 a^{16} b^{4} x^{6} + 63504 a^{15} b^{5} x^{7} + 42336 a^{14} b^{6} x^{8} + 18144 a^{13} b^{7} x^{9} + 4536 a^{12} b^{8} x^{10} + 504 a^{11} b^{9} x^{11}} + \frac{55 b^{2} \left(\log{\left(x \right)} - \log{\left(\frac{a}{b} + x \right)}\right)}{a^{12}}"," ",0,"(-252*a**10 + 2772*a**9*b*x + 78419*a**8*b**2*x**2 + 456291*a**7*b**3*x**3 + 1326204*a**6*b**4*x**4 + 2318316*a**5*b**5*x**5 + 2604294*a**4*b**6*x**6 + 1905750*a**3*b**7*x**7 + 882420*a**2*b**8*x**8 + 235620*a*b**9*x**9 + 27720*b**10*x**10)/(504*a**20*x**2 + 4536*a**19*b*x**3 + 18144*a**18*b**2*x**4 + 42336*a**17*b**3*x**5 + 63504*a**16*b**4*x**6 + 63504*a**15*b**5*x**7 + 42336*a**14*b**6*x**8 + 18144*a**13*b**7*x**9 + 4536*a**12*b**8*x**10 + 504*a**11*b**9*x**11) + 55*b**2*(log(x) - log(a/b + x))/a**12","A",0
238,1,258,0,1.241342," ","integrate(1/x**4/(b*x+a)**10,x)","\frac{- 42 a^{11} + 252 a^{10} b x - 2772 a^{9} b^{2} x^{2} - 78419 a^{8} b^{3} x^{3} - 456291 a^{7} b^{4} x^{4} - 1326204 a^{6} b^{5} x^{5} - 2318316 a^{5} b^{6} x^{6} - 2604294 a^{4} b^{7} x^{7} - 1905750 a^{3} b^{8} x^{8} - 882420 a^{2} b^{9} x^{9} - 235620 a b^{10} x^{10} - 27720 b^{11} x^{11}}{126 a^{21} x^{3} + 1134 a^{20} b x^{4} + 4536 a^{19} b^{2} x^{5} + 10584 a^{18} b^{3} x^{6} + 15876 a^{17} b^{4} x^{7} + 15876 a^{16} b^{5} x^{8} + 10584 a^{15} b^{6} x^{9} + 4536 a^{14} b^{7} x^{10} + 1134 a^{13} b^{8} x^{11} + 126 a^{12} b^{9} x^{12}} + \frac{220 b^{3} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{13}}"," ",0,"(-42*a**11 + 252*a**10*b*x - 2772*a**9*b**2*x**2 - 78419*a**8*b**3*x**3 - 456291*a**7*b**4*x**4 - 1326204*a**6*b**5*x**5 - 2318316*a**5*b**6*x**6 - 2604294*a**4*b**7*x**7 - 1905750*a**3*b**8*x**8 - 882420*a**2*b**9*x**9 - 235620*a*b**10*x**10 - 27720*b**11*x**11)/(126*a**21*x**3 + 1134*a**20*b*x**4 + 4536*a**19*b**2*x**5 + 10584*a**18*b**3*x**6 + 15876*a**17*b**4*x**7 + 15876*a**16*b**5*x**8 + 10584*a**15*b**6*x**9 + 4536*a**14*b**7*x**10 + 1134*a**13*b**8*x**11 + 126*a**12*b**9*x**12) + 220*b**3*(-log(x) + log(a/b + x))/a**13","A",0
239,1,143,0,0.914094," ","integrate((b*x+a)**12/x**10,x)","220 a^{3} b^{9} \log{\left(x \right)} + 66 a^{2} b^{10} x + 6 a b^{11} x^{2} + \frac{b^{12} x^{3}}{3} + \frac{- 14 a^{12} - 189 a^{11} b x - 1188 a^{10} b^{2} x^{2} - 4620 a^{9} b^{3} x^{3} - 12474 a^{8} b^{4} x^{4} - 24948 a^{7} b^{5} x^{5} - 38808 a^{6} b^{6} x^{6} - 49896 a^{5} b^{7} x^{7} - 62370 a^{4} b^{8} x^{8}}{126 x^{9}}"," ",0,"220*a**3*b**9*log(x) + 66*a**2*b**10*x + 6*a*b**11*x**2 + b**12*x**3/3 + (-14*a**12 - 189*a**11*b*x - 1188*a**10*b**2*x**2 - 4620*a**9*b**3*x**3 - 12474*a**8*b**4*x**4 - 24948*a**7*b**5*x**5 - 38808*a**6*b**6*x**6 - 49896*a**5*b**7*x**7 - 62370*a**4*b**8*x**8)/(126*x**9)","A",0
240,1,131,0,0.848479," ","integrate((b*x+a)**11/x**10,x)","55 a^{2} b^{9} \log{\left(x \right)} + 11 a b^{10} x + \frac{b^{11} x^{2}}{2} + \frac{- 56 a^{11} - 693 a^{10} b x - 3960 a^{9} b^{2} x^{2} - 13860 a^{8} b^{3} x^{3} - 33264 a^{7} b^{4} x^{4} - 58212 a^{6} b^{5} x^{5} - 77616 a^{5} b^{6} x^{6} - 83160 a^{4} b^{7} x^{7} - 83160 a^{3} b^{8} x^{8}}{504 x^{9}}"," ",0,"55*a**2*b**9*log(x) + 11*a*b**10*x + b**11*x**2/2 + (-56*a**11 - 693*a**10*b*x - 3960*a**9*b**2*x**2 - 13860*a**8*b**3*x**3 - 33264*a**7*b**4*x**4 - 58212*a**6*b**5*x**5 - 77616*a**5*b**6*x**6 - 83160*a**4*b**7*x**7 - 83160*a**3*b**8*x**8)/(504*x**9)","A",0
241,1,117,0,0.864811," ","integrate((b*x+a)**10/x**10,x)","10 a b^{9} \log{\left(x \right)} + b^{10} x + \frac{- 28 a^{10} - 315 a^{9} b x - 1620 a^{8} b^{2} x^{2} - 5040 a^{7} b^{3} x^{3} - 10584 a^{6} b^{4} x^{4} - 15876 a^{5} b^{5} x^{5} - 17640 a^{4} b^{6} x^{6} - 15120 a^{3} b^{7} x^{7} - 11340 a^{2} b^{8} x^{8}}{252 x^{9}}"," ",0,"10*a*b**9*log(x) + b**10*x + (-28*a**10 - 315*a**9*b*x - 1620*a**8*b**2*x**2 - 5040*a**7*b**3*x**3 - 10584*a**6*b**4*x**4 - 15876*a**5*b**5*x**5 - 17640*a**4*b**6*x**6 - 15120*a**3*b**7*x**7 - 11340*a**2*b**8*x**8)/(252*x**9)","A",0
242,1,107,0,0.785795," ","integrate((b*x+a)**9/x**10,x)","b^{9} \log{\left(x \right)} + \frac{- 280 a^{9} - 2835 a^{8} b x - 12960 a^{7} b^{2} x^{2} - 35280 a^{6} b^{3} x^{3} - 63504 a^{5} b^{4} x^{4} - 79380 a^{4} b^{5} x^{5} - 70560 a^{3} b^{6} x^{6} - 45360 a^{2} b^{7} x^{7} - 22680 a b^{8} x^{8}}{2520 x^{9}}"," ",0,"b**9*log(x) + (-280*a**9 - 2835*a**8*b*x - 12960*a**7*b**2*x**2 - 35280*a**6*b**3*x**3 - 63504*a**5*b**4*x**4 - 79380*a**4*b**5*x**5 - 70560*a**3*b**6*x**6 - 45360*a**2*b**7*x**7 - 22680*a*b**8*x**8)/(2520*x**9)","A",0
243,1,95,0,0.727238," ","integrate((b*x+a)**8/x**10,x)","\frac{- a^{8} - 9 a^{7} b x - 36 a^{6} b^{2} x^{2} - 84 a^{5} b^{3} x^{3} - 126 a^{4} b^{4} x^{4} - 126 a^{3} b^{5} x^{5} - 84 a^{2} b^{6} x^{6} - 36 a b^{7} x^{7} - 9 b^{8} x^{8}}{9 x^{9}}"," ",0,"(-a**8 - 9*a**7*b*x - 36*a**6*b**2*x**2 - 84*a**5*b**3*x**3 - 126*a**4*b**4*x**4 - 126*a**3*b**5*x**5 - 84*a**2*b**6*x**6 - 36*a*b**7*x**7 - 9*b**8*x**8)/(9*x**9)","B",0
244,1,85,0,0.704748," ","integrate((b*x+a)**7/x**10,x)","\frac{- 8 a^{7} - 63 a^{6} b x - 216 a^{5} b^{2} x^{2} - 420 a^{4} b^{3} x^{3} - 504 a^{3} b^{4} x^{4} - 378 a^{2} b^{5} x^{5} - 168 a b^{6} x^{6} - 36 b^{7} x^{7}}{72 x^{9}}"," ",0,"(-8*a**7 - 63*a**6*b*x - 216*a**5*b**2*x**2 - 420*a**4*b**3*x**3 - 504*a**3*b**4*x**4 - 378*a**2*b**5*x**5 - 168*a*b**6*x**6 - 36*b**7*x**7)/(72*x**9)","B",0
245,1,73,0,0.562912," ","integrate((b*x+a)**6/x**10,x)","\frac{- 28 a^{6} - 189 a^{5} b x - 540 a^{4} b^{2} x^{2} - 840 a^{3} b^{3} x^{3} - 756 a^{2} b^{4} x^{4} - 378 a b^{5} x^{5} - 84 b^{6} x^{6}}{252 x^{9}}"," ",0,"(-28*a**6 - 189*a**5*b*x - 540*a**4*b**2*x**2 - 840*a**3*b**3*x**3 - 756*a**2*b**4*x**4 - 378*a*b**5*x**5 - 84*b**6*x**6)/(252*x**9)","A",0
246,1,61,0,0.493352," ","integrate((b*x+a)**5/x**10,x)","\frac{- 56 a^{5} - 315 a^{4} b x - 720 a^{3} b^{2} x^{2} - 840 a^{2} b^{3} x^{3} - 504 a b^{4} x^{4} - 126 b^{5} x^{5}}{504 x^{9}}"," ",0,"(-56*a**5 - 315*a**4*b*x - 720*a**3*b**2*x**2 - 840*a**2*b**3*x**3 - 504*a*b**4*x**4 - 126*b**5*x**5)/(504*x**9)","A",0
247,1,49,0,0.497167," ","integrate((b*x+a)**4/x**10,x)","\frac{- 70 a^{4} - 315 a^{3} b x - 540 a^{2} b^{2} x^{2} - 420 a b^{3} x^{3} - 126 b^{4} x^{4}}{630 x^{9}}"," ",0,"(-70*a**4 - 315*a**3*b*x - 540*a**2*b**2*x**2 - 420*a*b**3*x**3 - 126*b**4*x**4)/(630*x**9)","A",0
248,1,37,0,0.379190," ","integrate((b*x+a)**3/x**10,x)","\frac{- 56 a^{3} - 189 a^{2} b x - 216 a b^{2} x^{2} - 84 b^{3} x^{3}}{504 x^{9}}"," ",0,"(-56*a**3 - 189*a**2*b*x - 216*a*b**2*x**2 - 84*b**3*x**3)/(504*x**9)","A",0
249,1,26,0,0.269517," ","integrate((b*x+a)**2/x**10,x)","\frac{- 28 a^{2} - 63 a b x - 36 b^{2} x^{2}}{252 x^{9}}"," ",0,"(-28*a**2 - 63*a*b*x - 36*b**2*x**2)/(252*x**9)","A",0
250,1,14,0,0.210418," ","integrate((b*x+a)/x**10,x)","\frac{- 8 a - 9 b x}{72 x^{9}}"," ",0,"(-8*a - 9*b*x)/(72*x**9)","A",0
251,1,7,0,0.073886," ","integrate(1/x**10,x)","- \frac{1}{9 x^{9}}"," ",0,"-1/(9*x**9)","A",0
252,1,116,0,0.409757," ","integrate(1/x**10/(b*x+a),x)","\frac{- 280 a^{8} + 315 a^{7} b x - 360 a^{6} b^{2} x^{2} + 420 a^{5} b^{3} x^{3} - 504 a^{4} b^{4} x^{4} + 630 a^{3} b^{5} x^{5} - 840 a^{2} b^{6} x^{6} + 1260 a b^{7} x^{7} - 2520 b^{8} x^{8}}{2520 a^{9} x^{9}} + \frac{b^{9} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{10}}"," ",0,"(-280*a**8 + 315*a**7*b*x - 360*a**6*b**2*x**2 + 420*a**5*b**3*x**3 - 504*a**4*b**4*x**4 + 630*a**3*b**5*x**5 - 840*a**2*b**6*x**6 + 1260*a*b**7*x**7 - 2520*b**8*x**8)/(2520*a**9*x**9) + b**9*(-log(x) + log(a/b + x))/a**10","A",0
253,1,139,0,0.613090," ","integrate(1/x**10/(b*x+a)**2,x)","\frac{- 28 a^{9} + 35 a^{8} b x - 45 a^{7} b^{2} x^{2} + 60 a^{6} b^{3} x^{3} - 84 a^{5} b^{4} x^{4} + 126 a^{4} b^{5} x^{5} - 210 a^{3} b^{6} x^{6} + 420 a^{2} b^{7} x^{7} - 1260 a b^{8} x^{8} - 2520 b^{9} x^{9}}{252 a^{11} x^{9} + 252 a^{10} b x^{10}} + \frac{10 b^{9} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{11}}"," ",0,"(-28*a**9 + 35*a**8*b*x - 45*a**7*b**2*x**2 + 60*a**6*b**3*x**3 - 84*a**5*b**4*x**4 + 126*a**4*b**5*x**5 - 210*a**3*b**6*x**6 + 420*a**2*b**7*x**7 - 1260*a*b**8*x**8 - 2520*b**9*x**9)/(252*a**11*x**9 + 252*a**10*b*x**10) + 10*b**9*(-log(x) + log(a/b + x))/a**11","A",0
254,1,163,0,0.677888," ","integrate(1/x**10/(b*x+a)**3,x)","\frac{- 56 a^{10} + 77 a^{9} b x - 110 a^{8} b^{2} x^{2} + 165 a^{7} b^{3} x^{3} - 264 a^{6} b^{4} x^{4} + 462 a^{5} b^{5} x^{5} - 924 a^{4} b^{6} x^{6} + 2310 a^{3} b^{7} x^{7} - 9240 a^{2} b^{8} x^{8} - 41580 a b^{9} x^{9} - 27720 b^{10} x^{10}}{504 a^{13} x^{9} + 1008 a^{12} b x^{10} + 504 a^{11} b^{2} x^{11}} + \frac{55 b^{9} \left(- \log{\left(x \right)} + \log{\left(\frac{a}{b} + x \right)}\right)}{a^{12}}"," ",0,"(-56*a**10 + 77*a**9*b*x - 110*a**8*b**2*x**2 + 165*a**7*b**3*x**3 - 264*a**6*b**4*x**4 + 462*a**5*b**5*x**5 - 924*a**4*b**6*x**6 + 2310*a**3*b**7*x**7 - 9240*a**2*b**8*x**8 - 41580*a*b**9*x**9 - 27720*b**10*x**10)/(504*a**13*x**9 + 1008*a**12*b*x**10 + 504*a**11*b**2*x**11) + 55*b**9*(-log(x) + log(a/b + x))/a**12","A",0
255,1,12,0,0.117342," ","integrate(1/x/(2+3*x),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
256,1,12,0,0.120471," ","integrate(1/x/(4+6*x),x)","\frac{\log{\left(x \right)}}{4} - \frac{\log{\left(x + \frac{2}{3} \right)}}{4}"," ",0,"log(x)/4 - log(x + 2/3)/4","A",0
257,1,20,0,0.139116," ","integrate(1/x**2/(4+6*x),x)","- \frac{3 \log{\left(x \right)}}{8} + \frac{3 \log{\left(x + \frac{2}{3} \right)}}{8} - \frac{1}{4 x}"," ",0,"-3*log(x)/8 + 3*log(x + 2/3)/8 - 1/(4*x)","A",0
258,1,26,0,0.146967," ","integrate(1/x**3/(4+6*x),x)","\frac{9 \log{\left(x \right)}}{16} - \frac{9 \log{\left(x + \frac{2}{3} \right)}}{16} + \frac{3 x - 1}{8 x^{2}}"," ",0,"9*log(x)/16 - 9*log(x + 2/3)/16 + (3*x - 1)/(8*x**2)","A",0
259,1,31,0,0.162288," ","integrate(1/x**4/(4+6*x),x)","- \frac{27 \log{\left(x \right)}}{32} + \frac{27 \log{\left(x + \frac{2}{3} \right)}}{32} + \frac{- 27 x^{2} + 9 x - 4}{48 x^{3}}"," ",0,"-27*log(x)/32 + 27*log(x + 2/3)/32 + (-27*x**2 + 9*x - 4)/(48*x**3)","A",0
260,1,36,0,0.165611," ","integrate(1/x**5/(4+6*x),x)","\frac{81 \log{\left(x \right)}}{64} - \frac{81 \log{\left(x + \frac{2}{3} \right)}}{64} + \frac{27 x^{3} - 9 x^{2} + 4 x - 2}{32 x^{4}}"," ",0,"81*log(x)/64 - 81*log(x + 2/3)/64 + (27*x**3 - 9*x**2 + 4*x - 2)/(32*x**4)","A",0
261,1,19,0,0.136491," ","integrate(1/x/(4+6*x)**2,x)","\frac{\log{\left(x \right)}}{16} - \frac{\log{\left(x + \frac{2}{3} \right)}}{16} + \frac{1}{24 x + 16}"," ",0,"log(x)/16 - log(x + 2/3)/16 + 1/(24*x + 16)","A",0
262,1,31,0,0.148142," ","integrate(1/x**2/(4+6*x)**2,x)","\frac{- 3 x - 1}{24 x^{2} + 16 x} - \frac{3 \log{\left(x \right)}}{16} + \frac{3 \log{\left(x + \frac{2}{3} \right)}}{16}"," ",0,"(-3*x - 1)/(24*x**2 + 16*x) - 3*log(x)/16 + 3*log(x + 2/3)/16","A",0
263,1,36,0,0.156640," ","integrate(1/x**3/(4+6*x)**2,x)","\frac{27 \log{\left(x \right)}}{64} - \frac{27 \log{\left(x + \frac{2}{3} \right)}}{64} + \frac{27 x^{2} + 9 x - 2}{96 x^{3} + 64 x^{2}}"," ",0,"27*log(x)/64 - 27*log(x + 2/3)/64 + (27*x**2 + 9*x - 2)/(96*x**3 + 64*x**2)","A",0
264,1,41,0,0.169009," ","integrate(1/x**4/(4+6*x)**2,x)","- \frac{27 \log{\left(x \right)}}{32} + \frac{27 \log{\left(x + \frac{2}{3} \right)}}{32} + \frac{- 81 x^{3} - 27 x^{2} + 6 x - 2}{144 x^{4} + 96 x^{3}}"," ",0,"-27*log(x)/32 + 27*log(x + 2/3)/32 + (-81*x**3 - 27*x**2 + 6*x - 2)/(144*x**4 + 96*x**3)","A",0
265,1,46,0,0.175004," ","integrate(1/x**5/(4+6*x)**2,x)","\frac{405 \log{\left(x \right)}}{256} - \frac{405 \log{\left(x + \frac{2}{3} \right)}}{256} + \frac{405 x^{4} + 135 x^{3} - 30 x^{2} + 10 x - 4}{384 x^{5} + 256 x^{4}}"," ",0,"405*log(x)/256 - 405*log(x + 2/3)/256 + (405*x**4 + 135*x**3 - 30*x**2 + 10*x - 4)/(384*x**5 + 256*x**4)","A",0
266,1,27,0,0.170204," ","integrate(1/x/(4+6*x)**3,x)","\frac{3 x + 3}{288 x^{2} + 384 x + 128} + \frac{\log{\left(x \right)}}{64} - \frac{\log{\left(x + \frac{2}{3} \right)}}{64}"," ",0,"(3*x + 3)/(288*x**2 + 384*x + 128) + log(x)/64 - log(x + 2/3)/64","A",0
267,1,41,0,0.179845," ","integrate(1/x**2/(4+6*x)**3,x)","\frac{- 27 x^{2} - 27 x - 4}{576 x^{3} + 768 x^{2} + 256 x} - \frac{9 \log{\left(x \right)}}{128} + \frac{9 \log{\left(x + \frac{2}{3} \right)}}{128}"," ",0,"(-27*x**2 - 27*x - 4)/(576*x**3 + 768*x**2 + 256*x) - 9*log(x)/128 + 9*log(x + 2/3)/128","A",0
268,1,46,0,0.181043," ","integrate(1/x**3/(4+6*x)**3,x)","\frac{27 \log{\left(x \right)}}{128} - \frac{27 \log{\left(x + \frac{2}{3} \right)}}{128} + \frac{81 x^{3} + 81 x^{2} + 12 x - 2}{576 x^{4} + 768 x^{3} + 256 x^{2}}"," ",0,"27*log(x)/128 - 27*log(x + 2/3)/128 + (81*x**3 + 81*x**2 + 12*x - 2)/(576*x**4 + 768*x**3 + 256*x**2)","A",0
269,1,51,0,0.206718," ","integrate(1/x**4/(4+6*x)**3,x)","- \frac{135 \log{\left(x \right)}}{256} + \frac{135 \log{\left(x + \frac{2}{3} \right)}}{256} + \frac{- 1215 x^{4} - 1215 x^{3} - 180 x^{2} + 30 x - 8}{3456 x^{5} + 4608 x^{4} + 1536 x^{3}}"," ",0,"-135*log(x)/256 + 135*log(x + 2/3)/256 + (-1215*x**4 - 1215*x**3 - 180*x**2 + 30*x - 8)/(3456*x**5 + 4608*x**4 + 1536*x**3)","A",0
270,1,56,0,0.215885," ","integrate(1/x**5/(4+6*x)**3,x)","\frac{1215 \log{\left(x \right)}}{1024} - \frac{1215 \log{\left(x + \frac{2}{3} \right)}}{1024} + \frac{3645 x^{5} + 3645 x^{4} + 540 x^{3} - 90 x^{2} + 24 x - 8}{4608 x^{6} + 6144 x^{5} + 2048 x^{4}}"," ",0,"1215*log(x)/1024 - 1215*log(x + 2/3)/1024 + (3645*x**5 + 3645*x**4 + 540*x**3 - 90*x**2 + 24*x - 8)/(4608*x**6 + 6144*x**5 + 2048*x**4)","A",0
271,1,7,0,0.074150," ","integrate(1/(2*x+2),x)","\frac{\log{\left(2 x + 2 \right)}}{2}"," ",0,"log(2*x + 2)/2","A",0
272,1,8,0,0.071136," ","integrate(1/(4-6*x),x)","- \frac{\log{\left(6 x - 4 \right)}}{6}"," ",0,"-log(6*x - 4)/6","A",0
273,1,14,0,0.079220," ","integrate(1/(a+x*a**(1/2)),x)","\frac{\log{\left(\sqrt{a} x + a \right)}}{\sqrt{a}}"," ",0,"log(sqrt(a)*x + a)/sqrt(a)","A",0
274,1,17,0,0.080527," ","integrate(1/(a+x*(-a)**(1/2)),x)","\frac{\log{\left(a + x \sqrt{- a} \right)}}{\sqrt{- a}}"," ",0,"log(a + x*sqrt(-a))/sqrt(-a)","A",0
275,1,19,0,0.078542," ","integrate(1/(a**2+x*(-a)**(1/2)),x)","\frac{\log{\left(a^{2} + x \sqrt{- a} \right)}}{\sqrt{- a}}"," ",0,"log(a**2 + x*sqrt(-a))/sqrt(-a)","A",0
276,1,19,0,0.079608," ","integrate(1/(a**3+x*(-a)**(1/2)),x)","\frac{\log{\left(a^{3} + x \sqrt{- a} \right)}}{\sqrt{- a}}"," ",0,"log(a**3 + x*sqrt(-a))/sqrt(-a)","A",0
277,1,19,0,0.092281," ","integrate(1/(1/a+x*(-a)**(1/2)),x)","\frac{\log{\left(a x \sqrt{- a} + 1 \right)}}{\sqrt{- a}}"," ",0,"log(a*x*sqrt(-a) + 1)/sqrt(-a)","A",0
278,1,20,0,0.088311," ","integrate(1/(1/a**2+x*(-a)**(1/2)),x)","\frac{\log{\left(a^{2} x \sqrt{- a} + 1 \right)}}{\sqrt{- a}}"," ",0,"log(a**2*x*sqrt(-a) + 1)/sqrt(-a)","A",0
279,1,8,0,0.135335," ","integrate(1/x/(b*x+1),x)","\log{\left(x \right)} - \log{\left(x + \frac{1}{b} \right)}"," ",0,"log(x) - log(x + 1/b)","A",0
280,1,8,0,0.125326," ","integrate(1/x/(b*x-1),x)","- \log{\left(x \right)} + \log{\left(x - \frac{1}{b} \right)}"," ",0,"-log(x) + log(x - 1/b)","A",0
281,1,14,0,0.176921," ","integrate(1/x**2/(b*x+1),x)","b \left(- \log{\left(x \right)} + \log{\left(x + \frac{1}{b} \right)}\right) - \frac{1}{x}"," ",0,"b*(-log(x) + log(x + 1/b)) - 1/x","A",0
282,1,14,0,0.191312," ","integrate(1/x**2/(b*x-1),x)","b \left(- \log{\left(x \right)} + \log{\left(x - \frac{1}{b} \right)}\right) + \frac{1}{x}"," ",0,"b*(-log(x) + log(x - 1/b)) + 1/x","A",0
283,1,10,0,0.148298," ","integrate(b/x+1/x**2/(b*x+1),x)","b \log{\left(b x + 1 \right)} - \frac{1}{x}"," ",0,"b*log(b*x + 1) - 1/x","A",0
284,1,1742,0,2.909681," ","integrate(x**3*(b*x+a)**(1/2),x)","- \frac{32 a^{\frac{49}{2}} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{32 a^{\frac{49}{2}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} - \frac{176 a^{\frac{47}{2}} b x \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{192 a^{\frac{47}{2}} b x}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} - \frac{396 a^{\frac{45}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{480 a^{\frac{45}{2}} b^{2} x^{2}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} - \frac{462 a^{\frac{43}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{640 a^{\frac{43}{2}} b^{3} x^{3}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} - \frac{210 a^{\frac{41}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{480 a^{\frac{41}{2}} b^{4} x^{4}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{378 a^{\frac{39}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{192 a^{\frac{39}{2}} b^{5} x^{5}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{1134 a^{\frac{37}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{32 a^{\frac{37}{2}} b^{6} x^{6}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{1494 a^{\frac{35}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{1098 a^{\frac{33}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{430 a^{\frac{31}{2}} b^{9} x^{9} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}} + \frac{70 a^{\frac{29}{2}} b^{10} x^{10} \sqrt{1 + \frac{b x}{a}}}{315 a^{20} b^{4} + 1890 a^{19} b^{5} x + 4725 a^{18} b^{6} x^{2} + 6300 a^{17} b^{7} x^{3} + 4725 a^{16} b^{8} x^{4} + 1890 a^{15} b^{9} x^{5} + 315 a^{14} b^{10} x^{6}}"," ",0,"-32*a**(49/2)*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 32*a**(49/2)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) - 176*a**(47/2)*b*x*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 192*a**(47/2)*b*x/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) - 396*a**(45/2)*b**2*x**2*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 480*a**(45/2)*b**2*x**2/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) - 462*a**(43/2)*b**3*x**3*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 640*a**(43/2)*b**3*x**3/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) - 210*a**(41/2)*b**4*x**4*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 480*a**(41/2)*b**4*x**4/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 378*a**(39/2)*b**5*x**5*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 192*a**(39/2)*b**5*x**5/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 1134*a**(37/2)*b**6*x**6*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 32*a**(37/2)*b**6*x**6/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 1494*a**(35/2)*b**7*x**7*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 1098*a**(33/2)*b**8*x**8*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 430*a**(31/2)*b**9*x**9*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6) + 70*a**(29/2)*b**10*x**10*sqrt(1 + b*x/a)/(315*a**20*b**4 + 1890*a**19*b**5*x + 4725*a**18*b**6*x**2 + 6300*a**17*b**7*x**3 + 4725*a**16*b**8*x**4 + 1890*a**15*b**9*x**5 + 315*a**14*b**10*x**6)","B",0
285,1,666,0,2.039418," ","integrate(x**2*(b*x+a)**(1/2),x)","\frac{16 a^{\frac{23}{2}} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{23}{2}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{21}{2}} b x \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{21}{2}} b x}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{19}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{19}{2}} b^{2} x^{2}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{17}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{17}{2}} b^{3} x^{3}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{100 a^{\frac{15}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{96 a^{\frac{13}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{11}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{105 a^{8} b^{3} + 315 a^{7} b^{4} x + 315 a^{6} b^{5} x^{2} + 105 a^{5} b^{6} x^{3}}"," ",0,"16*a**(23/2)*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 16*a**(23/2)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 40*a**(21/2)*b*x*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 48*a**(21/2)*b*x/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 30*a**(19/2)*b**2*x**2*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 48*a**(19/2)*b**2*x**2/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 40*a**(17/2)*b**3*x**3*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) - 16*a**(17/2)*b**3*x**3/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 100*a**(15/2)*b**4*x**4*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 96*a**(13/2)*b**5*x**5*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3) + 30*a**(11/2)*b**6*x**6*sqrt(1 + b*x/a)/(105*a**8*b**3 + 315*a**7*b**4*x + 315*a**6*b**5*x**2 + 105*a**5*b**6*x**3)","B",0
286,1,202,0,1.392900," ","integrate(x*(b*x+a)**(1/2),x)","- \frac{4 a^{\frac{9}{2}} \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{4 a^{\frac{9}{2}}}{15 a^{2} b^{2} + 15 a b^{3} x} - \frac{2 a^{\frac{7}{2}} b x \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{4 a^{\frac{7}{2}} b x}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{8 a^{\frac{5}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x} + \frac{6 a^{\frac{3}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{15 a^{2} b^{2} + 15 a b^{3} x}"," ",0,"-4*a**(9/2)*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x) + 4*a**(9/2)/(15*a**2*b**2 + 15*a*b**3*x) - 2*a**(7/2)*b*x*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x) + 4*a**(7/2)*b*x/(15*a**2*b**2 + 15*a*b**3*x) + 8*a**(5/2)*b**2*x**2*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x) + 6*a**(3/2)*b**3*x**3*sqrt(1 + b*x/a)/(15*a**2*b**2 + 15*a*b**3*x)","B",0
287,1,12,0,0.074443," ","integrate((b*x+a)**(1/2),x)","\frac{2 \left(a + b x\right)^{\frac{3}{2}}}{3 b}"," ",0,"2*(a + b*x)**(3/2)/(3*b)","A",0
288,1,68,0,1.602276," ","integrate((b*x+a)**(1/2)/x,x)","- 2 \sqrt{a} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{2 a}{\sqrt{b} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{2 \sqrt{b} \sqrt{x}}{\sqrt{\frac{a}{b x} + 1}}"," ",0,"-2*sqrt(a)*asinh(sqrt(a)/(sqrt(b)*sqrt(x))) + 2*a/(sqrt(b)*sqrt(x)*sqrt(a/(b*x) + 1)) + 2*sqrt(b)*sqrt(x)/sqrt(a/(b*x) + 1)","B",0
289,1,44,0,2.221145," ","integrate((b*x+a)**(1/2)/x**2,x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x} + 1}}{\sqrt{x}} - \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}}"," ",0,"-sqrt(b)*sqrt(a/(b*x) + 1)/sqrt(x) - b*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a)","A",0
290,1,97,0,4.015150," ","integrate((b*x+a)**(1/2)/x**3,x)","- \frac{a}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{3 \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{b^{\frac{3}{2}}}{4 a \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{3}{2}}}"," ",0,"-a/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) + 1)) - 3*sqrt(b)/(4*x**(3/2)*sqrt(a/(b*x) + 1)) - b**(3/2)/(4*a*sqrt(x)*sqrt(a/(b*x) + 1)) + b**2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(3/2))","A",0
291,1,122,0,6.678386," ","integrate((b*x+a)**(1/2)/x**4,x)","- \frac{a}{3 \sqrt{b} x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{5 \sqrt{b}}{12 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{b^{\frac{3}{2}}}{24 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{b^{\frac{5}{2}}}{8 a^{2} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} - \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{8 a^{\frac{5}{2}}}"," ",0,"-a/(3*sqrt(b)*x**(7/2)*sqrt(a/(b*x) + 1)) - 5*sqrt(b)/(12*x**(5/2)*sqrt(a/(b*x) + 1)) + b**(3/2)/(24*a*x**(3/2)*sqrt(a/(b*x) + 1)) + b**(5/2)/(8*a**2*sqrt(x)*sqrt(a/(b*x) + 1)) - b**3*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(8*a**(5/2))","A",0
292,1,1742,0,3.199049," ","integrate(x**3*(b*x+a)**(3/2),x)","- \frac{32 a^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{32 a^{\frac{51}{2}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} - \frac{176 a^{\frac{49}{2}} b x \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{192 a^{\frac{49}{2}} b x}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} - \frac{396 a^{\frac{47}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{480 a^{\frac{47}{2}} b^{2} x^{2}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} - \frac{462 a^{\frac{45}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{640 a^{\frac{45}{2}} b^{3} x^{3}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{480 a^{\frac{43}{2}} b^{4} x^{4}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{1848 a^{\frac{41}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{192 a^{\frac{41}{2}} b^{5} x^{5}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{5544 a^{\frac{39}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{32 a^{\frac{39}{2}} b^{6} x^{6}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{8844 a^{\frac{37}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{8448 a^{\frac{35}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{4840 a^{\frac{33}{2}} b^{9} x^{9} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{1540 a^{\frac{31}{2}} b^{10} x^{10} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}} + \frac{210 a^{\frac{29}{2}} b^{11} x^{11} \sqrt{1 + \frac{b x}{a}}}{1155 a^{20} b^{4} + 6930 a^{19} b^{5} x + 17325 a^{18} b^{6} x^{2} + 23100 a^{17} b^{7} x^{3} + 17325 a^{16} b^{8} x^{4} + 6930 a^{15} b^{9} x^{5} + 1155 a^{14} b^{10} x^{6}}"," ",0,"-32*a**(51/2)*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 32*a**(51/2)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) - 176*a**(49/2)*b*x*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 192*a**(49/2)*b*x/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) - 396*a**(47/2)*b**2*x**2*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 480*a**(47/2)*b**2*x**2/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) - 462*a**(45/2)*b**3*x**3*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 640*a**(45/2)*b**3*x**3/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 480*a**(43/2)*b**4*x**4/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 1848*a**(41/2)*b**5*x**5*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 192*a**(41/2)*b**5*x**5/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 5544*a**(39/2)*b**6*x**6*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 32*a**(39/2)*b**6*x**6/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 8844*a**(37/2)*b**7*x**7*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 8448*a**(35/2)*b**8*x**8*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 4840*a**(33/2)*b**9*x**9*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 1540*a**(31/2)*b**10*x**10*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6) + 210*a**(29/2)*b**11*x**11*sqrt(1 + b*x/a)/(1155*a**20*b**4 + 6930*a**19*b**5*x + 17325*a**18*b**6*x**2 + 23100*a**17*b**7*x**3 + 17325*a**16*b**8*x**4 + 6930*a**15*b**9*x**5 + 1155*a**14*b**10*x**6)","B",0
293,1,733,0,2.174590," ","integrate(x**2*(b*x+a)**(3/2),x)","\frac{16 a^{\frac{25}{2}} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{25}{2}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{23}{2}} b x \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{23}{2}} b x}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{21}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{21}{2}} b^{2} x^{2}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{110 a^{\frac{19}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{19}{2}} b^{3} x^{3}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{380 a^{\frac{17}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{516 a^{\frac{15}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{310 a^{\frac{13}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}} + \frac{70 a^{\frac{11}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{315 a^{8} b^{3} + 945 a^{7} b^{4} x + 945 a^{6} b^{5} x^{2} + 315 a^{5} b^{6} x^{3}}"," ",0,"16*a**(25/2)*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) - 16*a**(25/2)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 40*a**(23/2)*b*x*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) - 48*a**(23/2)*b*x/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 30*a**(21/2)*b**2*x**2*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) - 48*a**(21/2)*b**2*x**2/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 110*a**(19/2)*b**3*x**3*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) - 16*a**(19/2)*b**3*x**3/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 380*a**(17/2)*b**4*x**4*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 516*a**(15/2)*b**5*x**5*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 310*a**(13/2)*b**6*x**6*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3) + 70*a**(11/2)*b**7*x**7*sqrt(1 + b*x/a)/(315*a**8*b**3 + 945*a**7*b**4*x + 945*a**6*b**5*x**2 + 315*a**5*b**6*x**3)","B",0
294,1,80,0,0.740185," ","integrate(x*(b*x+a)**(3/2),x)","\begin{cases} - \frac{4 a^{3} \sqrt{a + b x}}{35 b^{2}} + \frac{2 a^{2} x \sqrt{a + b x}}{35 b} + \frac{16 a x^{2} \sqrt{a + b x}}{35} + \frac{2 b x^{3} \sqrt{a + b x}}{7} & \text{for}\: b \neq 0 \\\frac{a^{\frac{3}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**3*sqrt(a + b*x)/(35*b**2) + 2*a**2*x*sqrt(a + b*x)/(35*b) + 16*a*x**2*sqrt(a + b*x)/35 + 2*b*x**3*sqrt(a + b*x)/7, Ne(b, 0)), (a**(3/2)*x**2/2, True))","A",0
295,1,12,0,0.072024," ","integrate((b*x+a)**(3/2),x)","\frac{2 \left(a + b x\right)^{\frac{5}{2}}}{5 b}"," ",0,"2*(a + b*x)**(5/2)/(5*b)","A",0
296,1,71,0,2.294849," ","integrate((b*x+a)**(3/2)/x,x)","\frac{8 a^{\frac{3}{2}} \sqrt{1 + \frac{b x}{a}}}{3} + a^{\frac{3}{2}} \log{\left(\frac{b x}{a} \right)} - 2 a^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)} + \frac{2 \sqrt{a} b x \sqrt{1 + \frac{b x}{a}}}{3}"," ",0,"8*a**(3/2)*sqrt(1 + b*x/a)/3 + a**(3/2)*log(b*x/a) - 2*a**(3/2)*log(sqrt(1 + b*x/a) + 1) + 2*sqrt(a)*b*x*sqrt(1 + b*x/a)/3","A",0
297,1,92,0,2.664107," ","integrate((b*x+a)**(3/2)/x**2,x)","- 3 \sqrt{a} b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} - \frac{a^{2}}{\sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{a \sqrt{b}}{\sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{2 b^{\frac{3}{2}} \sqrt{x}}{\sqrt{\frac{a}{b x} + 1}}"," ",0,"-3*sqrt(a)*b*asinh(sqrt(a)/(sqrt(b)*sqrt(x))) - a**2/(sqrt(b)*x**(3/2)*sqrt(a/(b*x) + 1)) + a*sqrt(b)/(sqrt(x)*sqrt(a/(b*x) + 1)) + 2*b**(3/2)*sqrt(x)/sqrt(a/(b*x) + 1)","B",0
298,1,76,0,3.283158," ","integrate((b*x+a)**(3/2)/x**3,x)","- \frac{a \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{2 x^{\frac{3}{2}}} - \frac{5 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{4 \sqrt{x}} - \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 \sqrt{a}}"," ",0,"-a*sqrt(b)*sqrt(a/(b*x) + 1)/(2*x**(3/2)) - 5*b**(3/2)*sqrt(a/(b*x) + 1)/(4*sqrt(x)) - 3*b**2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*sqrt(a))","A",0
299,1,124,0,5.836646," ","integrate((b*x+a)**(3/2)/x**4,x)","- \frac{a^{2}}{3 \sqrt{b} x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{11 a \sqrt{b}}{12 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{17 b^{\frac{3}{2}}}{24 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{b^{\frac{5}{2}}}{8 a \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{8 a^{\frac{3}{2}}}"," ",0,"-a**2/(3*sqrt(b)*x**(7/2)*sqrt(a/(b*x) + 1)) - 11*a*sqrt(b)/(12*x**(5/2)*sqrt(a/(b*x) + 1)) - 17*b**(3/2)/(24*x**(3/2)*sqrt(a/(b*x) + 1)) - b**(5/2)/(8*a*sqrt(x)*sqrt(a/(b*x) + 1)) + b**3*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(8*a**(3/2))","A",0
300,1,146,0,4.469077," ","integrate(x**3*(b*x+a)**(5/2),x)","\begin{cases} - \frac{32 a^{6} \sqrt{a + b x}}{3003 b^{4}} + \frac{16 a^{5} x \sqrt{a + b x}}{3003 b^{3}} - \frac{4 a^{4} x^{2} \sqrt{a + b x}}{1001 b^{2}} + \frac{10 a^{3} x^{3} \sqrt{a + b x}}{3003 b} + \frac{106 a^{2} x^{4} \sqrt{a + b x}}{429} + \frac{54 a b x^{5} \sqrt{a + b x}}{143} + \frac{2 b^{2} x^{6} \sqrt{a + b x}}{13} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**6*sqrt(a + b*x)/(3003*b**4) + 16*a**5*x*sqrt(a + b*x)/(3003*b**3) - 4*a**4*x**2*sqrt(a + b*x)/(1001*b**2) + 10*a**3*x**3*sqrt(a + b*x)/(3003*b) + 106*a**2*x**4*sqrt(a + b*x)/429 + 54*a*b*x**5*sqrt(a + b*x)/143 + 2*b**2*x**6*sqrt(a + b*x)/13, Ne(b, 0)), (a**(5/2)*x**4/4, True))","A",0
301,1,124,0,3.769546," ","integrate(x**2*(b*x+a)**(5/2),x)","\begin{cases} \frac{16 a^{5} \sqrt{a + b x}}{693 b^{3}} - \frac{8 a^{4} x \sqrt{a + b x}}{693 b^{2}} + \frac{2 a^{3} x^{2} \sqrt{a + b x}}{231 b} + \frac{226 a^{2} x^{3} \sqrt{a + b x}}{693} + \frac{46 a b x^{4} \sqrt{a + b x}}{99} + \frac{2 b^{2} x^{5} \sqrt{a + b x}}{11} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**5*sqrt(a + b*x)/(693*b**3) - 8*a**4*x*sqrt(a + b*x)/(693*b**2) + 2*a**3*x**2*sqrt(a + b*x)/(231*b) + 226*a**2*x**3*sqrt(a + b*x)/693 + 46*a*b*x**4*sqrt(a + b*x)/99 + 2*b**2*x**5*sqrt(a + b*x)/11, Ne(b, 0)), (a**(5/2)*x**3/3, True))","A",0
302,1,102,0,2.598880," ","integrate(x*(b*x+a)**(5/2),x)","\begin{cases} - \frac{4 a^{4} \sqrt{a + b x}}{63 b^{2}} + \frac{2 a^{3} x \sqrt{a + b x}}{63 b} + \frac{10 a^{2} x^{2} \sqrt{a + b x}}{21} + \frac{38 a b x^{3} \sqrt{a + b x}}{63} + \frac{2 b^{2} x^{4} \sqrt{a + b x}}{9} & \text{for}\: b \neq 0 \\\frac{a^{\frac{5}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**4*sqrt(a + b*x)/(63*b**2) + 2*a**3*x*sqrt(a + b*x)/(63*b) + 10*a**2*x**2*sqrt(a + b*x)/21 + 38*a*b*x**3*sqrt(a + b*x)/63 + 2*b**2*x**4*sqrt(a + b*x)/9, Ne(b, 0)), (a**(5/2)*x**2/2, True))","A",0
303,1,12,0,0.077402," ","integrate((b*x+a)**(5/2),x)","\frac{2 \left(a + b x\right)^{\frac{7}{2}}}{7 b}"," ",0,"2*(a + b*x)**(7/2)/(7*b)","A",0
304,1,97,0,4.117203," ","integrate((b*x+a)**(5/2)/x,x)","\frac{46 a^{\frac{5}{2}} \sqrt{1 + \frac{b x}{a}}}{15} + a^{\frac{5}{2}} \log{\left(\frac{b x}{a} \right)} - 2 a^{\frac{5}{2}} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)} + \frac{22 a^{\frac{3}{2}} b x \sqrt{1 + \frac{b x}{a}}}{15} + \frac{2 \sqrt{a} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{5}"," ",0,"46*a**(5/2)*sqrt(1 + b*x/a)/15 + a**(5/2)*log(b*x/a) - 2*a**(5/2)*log(sqrt(1 + b*x/a) + 1) + 22*a**(3/2)*b*x*sqrt(1 + b*x/a)/15 + 2*sqrt(a)*b**2*x**2*sqrt(1 + b*x/a)/5","A",0
305,1,99,0,3.746758," ","integrate((b*x+a)**(5/2)/x**2,x)","- \frac{a^{\frac{5}{2}} \sqrt{1 + \frac{b x}{a}}}{x} + \frac{14 a^{\frac{3}{2}} b \sqrt{1 + \frac{b x}{a}}}{3} + \frac{5 a^{\frac{3}{2}} b \log{\left(\frac{b x}{a} \right)}}{2} - 5 a^{\frac{3}{2}} b \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)} + \frac{2 \sqrt{a} b^{2} x \sqrt{1 + \frac{b x}{a}}}{3}"," ",0,"-a**(5/2)*sqrt(1 + b*x/a)/x + 14*a**(3/2)*b*sqrt(1 + b*x/a)/3 + 5*a**(3/2)*b*log(b*x/a)/2 - 5*a**(3/2)*b*log(sqrt(1 + b*x/a) + 1) + 2*sqrt(a)*b**2*x*sqrt(1 + b*x/a)/3","A",0
306,1,126,0,4.299545," ","integrate((b*x+a)**(5/2)/x**3,x)","- \frac{15 \sqrt{a} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4} - \frac{a^{3}}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{11 a^{2} \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{a b^{\frac{3}{2}}}{4 \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{2 b^{\frac{5}{2}} \sqrt{x}}{\sqrt{\frac{a}{b x} + 1}}"," ",0,"-15*sqrt(a)*b**2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/4 - a**3/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) + 1)) - 11*a**2*sqrt(b)/(4*x**(3/2)*sqrt(a/(b*x) + 1)) - a*b**(3/2)/(4*sqrt(x)*sqrt(a/(b*x) + 1)) + 2*b**(5/2)*sqrt(x)/sqrt(a/(b*x) + 1)","A",0
307,1,104,0,5.157197," ","integrate((b*x+a)**(5/2)/x**4,x)","- \frac{a^{2} \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 x^{\frac{5}{2}}} - \frac{13 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{12 x^{\frac{3}{2}}} - \frac{11 b^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}}{8 \sqrt{x}} - \frac{5 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{8 \sqrt{a}}"," ",0,"-a**2*sqrt(b)*sqrt(a/(b*x) + 1)/(3*x**(5/2)) - 13*a*b**(3/2)*sqrt(a/(b*x) + 1)/(12*x**(3/2)) - 11*b**(5/2)*sqrt(a/(b*x) + 1)/(8*sqrt(x)) - 5*b**3*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(8*sqrt(a))","A",0
308,1,155,0,8.359054," ","integrate((b*x+a)**(5/2)/x**5,x)","- \frac{a^{3}}{4 \sqrt{b} x^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{23 a^{2} \sqrt{b}}{24 x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{127 a b^{\frac{3}{2}}}{96 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{133 b^{\frac{5}{2}}}{192 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{5 b^{\frac{7}{2}}}{64 a \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{5 b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{64 a^{\frac{3}{2}}}"," ",0,"-a**3/(4*sqrt(b)*x**(9/2)*sqrt(a/(b*x) + 1)) - 23*a**2*sqrt(b)/(24*x**(7/2)*sqrt(a/(b*x) + 1)) - 127*a*b**(3/2)/(96*x**(5/2)*sqrt(a/(b*x) + 1)) - 133*b**(5/2)/(192*x**(3/2)*sqrt(a/(b*x) + 1)) - 5*b**(7/2)/(64*a*sqrt(x)*sqrt(a/(b*x) + 1)) + 5*b**4*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(64*a**(3/2))","A",0
309,1,279,0,40.295895," ","integrate(x**7*(b*x+a)**(9/2),x)","\begin{cases} - \frac{4096 a^{12} \sqrt{a + b x}}{26558675 b^{8}} + \frac{2048 a^{11} x \sqrt{a + b x}}{26558675 b^{7}} - \frac{1536 a^{10} x^{2} \sqrt{a + b x}}{26558675 b^{6}} + \frac{256 a^{9} x^{3} \sqrt{a + b x}}{5311735 b^{5}} - \frac{224 a^{8} x^{4} \sqrt{a + b x}}{5311735 b^{4}} + \frac{1008 a^{7} x^{5} \sqrt{a + b x}}{26558675 b^{3}} - \frac{84 a^{6} x^{6} \sqrt{a + b x}}{2414425 b^{2}} + \frac{6 a^{5} x^{7} \sqrt{a + b x}}{185725 b} + \frac{4642 a^{4} x^{8} \sqrt{a + b x}}{37145} + \frac{956 a^{3} b x^{9} \sqrt{a + b x}}{2185} + \frac{336 a^{2} b^{2} x^{10} \sqrt{a + b x}}{575} + \frac{202 a b^{3} x^{11} \sqrt{a + b x}}{575} + \frac{2 b^{4} x^{12} \sqrt{a + b x}}{25} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4096*a**12*sqrt(a + b*x)/(26558675*b**8) + 2048*a**11*x*sqrt(a + b*x)/(26558675*b**7) - 1536*a**10*x**2*sqrt(a + b*x)/(26558675*b**6) + 256*a**9*x**3*sqrt(a + b*x)/(5311735*b**5) - 224*a**8*x**4*sqrt(a + b*x)/(5311735*b**4) + 1008*a**7*x**5*sqrt(a + b*x)/(26558675*b**3) - 84*a**6*x**6*sqrt(a + b*x)/(2414425*b**2) + 6*a**5*x**7*sqrt(a + b*x)/(185725*b) + 4642*a**4*x**8*sqrt(a + b*x)/37145 + 956*a**3*b*x**9*sqrt(a + b*x)/2185 + 336*a**2*b**2*x**10*sqrt(a + b*x)/575 + 202*a*b**3*x**11*sqrt(a + b*x)/575 + 2*b**4*x**12*sqrt(a + b*x)/25, Ne(b, 0)), (a**(9/2)*x**8/8, True))","A",0
310,1,257,0,36.609428," ","integrate(x**6*(b*x+a)**(9/2),x)","\begin{cases} \frac{2048 a^{11} \sqrt{a + b x}}{7436429 b^{7}} - \frac{1024 a^{10} x \sqrt{a + b x}}{7436429 b^{6}} + \frac{768 a^{9} x^{2} \sqrt{a + b x}}{7436429 b^{5}} - \frac{640 a^{8} x^{3} \sqrt{a + b x}}{7436429 b^{4}} + \frac{80 a^{7} x^{4} \sqrt{a + b x}}{1062347 b^{3}} - \frac{72 a^{6} x^{5} \sqrt{a + b x}}{1062347 b^{2}} + \frac{6 a^{5} x^{6} \sqrt{a + b x}}{96577 b} + \frac{7426 a^{4} x^{7} \sqrt{a + b x}}{52003} + \frac{25540 a^{3} b x^{8} \sqrt{a + b x}}{52003} + \frac{1980 a^{2} b^{2} x^{9} \sqrt{a + b x}}{3059} + \frac{62 a b^{3} x^{10} \sqrt{a + b x}}{161} + \frac{2 b^{4} x^{11} \sqrt{a + b x}}{23} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{7}}{7} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2048*a**11*sqrt(a + b*x)/(7436429*b**7) - 1024*a**10*x*sqrt(a + b*x)/(7436429*b**6) + 768*a**9*x**2*sqrt(a + b*x)/(7436429*b**5) - 640*a**8*x**3*sqrt(a + b*x)/(7436429*b**4) + 80*a**7*x**4*sqrt(a + b*x)/(1062347*b**3) - 72*a**6*x**5*sqrt(a + b*x)/(1062347*b**2) + 6*a**5*x**6*sqrt(a + b*x)/(96577*b) + 7426*a**4*x**7*sqrt(a + b*x)/52003 + 25540*a**3*b*x**8*sqrt(a + b*x)/52003 + 1980*a**2*b**2*x**9*sqrt(a + b*x)/3059 + 62*a*b**3*x**10*sqrt(a + b*x)/161 + 2*b**4*x**11*sqrt(a + b*x)/23, Ne(b, 0)), (a**(9/2)*x**7/7, True))","A",0
311,1,235,0,28.759691," ","integrate(x**5*(b*x+a)**(9/2),x)","\begin{cases} - \frac{512 a^{10} \sqrt{a + b x}}{969969 b^{6}} + \frac{256 a^{9} x \sqrt{a + b x}}{969969 b^{5}} - \frac{64 a^{8} x^{2} \sqrt{a + b x}}{323323 b^{4}} + \frac{160 a^{7} x^{3} \sqrt{a + b x}}{969969 b^{3}} - \frac{20 a^{6} x^{4} \sqrt{a + b x}}{138567 b^{2}} + \frac{6 a^{5} x^{5} \sqrt{a + b x}}{46189 b} + \frac{2098 a^{4} x^{6} \sqrt{a + b x}}{12597} + \frac{3796 a^{3} b x^{7} \sqrt{a + b x}}{6783} + \frac{1640 a^{2} b^{2} x^{8} \sqrt{a + b x}}{2261} + \frac{170 a b^{3} x^{9} \sqrt{a + b x}}{399} + \frac{2 b^{4} x^{10} \sqrt{a + b x}}{21} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-512*a**10*sqrt(a + b*x)/(969969*b**6) + 256*a**9*x*sqrt(a + b*x)/(969969*b**5) - 64*a**8*x**2*sqrt(a + b*x)/(323323*b**4) + 160*a**7*x**3*sqrt(a + b*x)/(969969*b**3) - 20*a**6*x**4*sqrt(a + b*x)/(138567*b**2) + 6*a**5*x**5*sqrt(a + b*x)/(46189*b) + 2098*a**4*x**6*sqrt(a + b*x)/12597 + 3796*a**3*b*x**7*sqrt(a + b*x)/6783 + 1640*a**2*b**2*x**8*sqrt(a + b*x)/2261 + 170*a*b**3*x**9*sqrt(a + b*x)/399 + 2*b**4*x**10*sqrt(a + b*x)/21, Ne(b, 0)), (a**(9/2)*x**6/6, True))","A",0
312,1,212,0,25.700121," ","integrate(x**4*(b*x+a)**(9/2),x)","\begin{cases} \frac{256 a^{9} \sqrt{a + b x}}{230945 b^{5}} - \frac{128 a^{8} x \sqrt{a + b x}}{230945 b^{4}} + \frac{96 a^{7} x^{2} \sqrt{a + b x}}{230945 b^{3}} - \frac{16 a^{6} x^{3} \sqrt{a + b x}}{46189 b^{2}} + \frac{14 a^{5} x^{4} \sqrt{a + b x}}{46189 b} + \frac{46126 a^{4} x^{5} \sqrt{a + b x}}{230945} + \frac{13652 a^{3} b x^{6} \sqrt{a + b x}}{20995} + \frac{1332 a^{2} b^{2} x^{7} \sqrt{a + b x}}{1615} + \frac{154 a b^{3} x^{8} \sqrt{a + b x}}{323} + \frac{2 b^{4} x^{9} \sqrt{a + b x}}{19} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((256*a**9*sqrt(a + b*x)/(230945*b**5) - 128*a**8*x*sqrt(a + b*x)/(230945*b**4) + 96*a**7*x**2*sqrt(a + b*x)/(230945*b**3) - 16*a**6*x**3*sqrt(a + b*x)/(46189*b**2) + 14*a**5*x**4*sqrt(a + b*x)/(46189*b) + 46126*a**4*x**5*sqrt(a + b*x)/230945 + 13652*a**3*b*x**6*sqrt(a + b*x)/20995 + 1332*a**2*b**2*x**7*sqrt(a + b*x)/1615 + 154*a*b**3*x**8*sqrt(a + b*x)/323 + 2*b**4*x**9*sqrt(a + b*x)/19, Ne(b, 0)), (a**(9/2)*x**5/5, True))","A",0
313,1,190,0,20.346361," ","integrate(x**3*(b*x+a)**(9/2),x)","\begin{cases} - \frac{32 a^{8} \sqrt{a + b x}}{12155 b^{4}} + \frac{16 a^{7} x \sqrt{a + b x}}{12155 b^{3}} - \frac{12 a^{6} x^{2} \sqrt{a + b x}}{12155 b^{2}} + \frac{2 a^{5} x^{3} \sqrt{a + b x}}{2431 b} + \frac{606 a^{4} x^{4} \sqrt{a + b x}}{2431} + \frac{9428 a^{3} b x^{5} \sqrt{a + b x}}{12155} + \frac{1056 a^{2} b^{2} x^{6} \sqrt{a + b x}}{1105} + \frac{46 a b^{3} x^{7} \sqrt{a + b x}}{85} + \frac{2 b^{4} x^{8} \sqrt{a + b x}}{17} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**8*sqrt(a + b*x)/(12155*b**4) + 16*a**7*x*sqrt(a + b*x)/(12155*b**3) - 12*a**6*x**2*sqrt(a + b*x)/(12155*b**2) + 2*a**5*x**3*sqrt(a + b*x)/(2431*b) + 606*a**4*x**4*sqrt(a + b*x)/2431 + 9428*a**3*b*x**5*sqrt(a + b*x)/12155 + 1056*a**2*b**2*x**6*sqrt(a + b*x)/1105 + 46*a*b**3*x**7*sqrt(a + b*x)/85 + 2*b**4*x**8*sqrt(a + b*x)/17, Ne(b, 0)), (a**(9/2)*x**4/4, True))","A",0
314,1,168,0,16.856349," ","integrate(x**2*(b*x+a)**(9/2),x)","\begin{cases} \frac{16 a^{7} \sqrt{a + b x}}{2145 b^{3}} - \frac{8 a^{6} x \sqrt{a + b x}}{2145 b^{2}} + \frac{2 a^{5} x^{2} \sqrt{a + b x}}{715 b} + \frac{142 a^{4} x^{3} \sqrt{a + b x}}{429} + \frac{412 a^{3} b x^{4} \sqrt{a + b x}}{429} + \frac{812 a^{2} b^{2} x^{5} \sqrt{a + b x}}{715} + \frac{122 a b^{3} x^{6} \sqrt{a + b x}}{195} + \frac{2 b^{4} x^{7} \sqrt{a + b x}}{15} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**7*sqrt(a + b*x)/(2145*b**3) - 8*a**6*x*sqrt(a + b*x)/(2145*b**2) + 2*a**5*x**2*sqrt(a + b*x)/(715*b) + 142*a**4*x**3*sqrt(a + b*x)/429 + 412*a**3*b*x**4*sqrt(a + b*x)/429 + 812*a**2*b**2*x**5*sqrt(a + b*x)/715 + 122*a*b**3*x**6*sqrt(a + b*x)/195 + 2*b**4*x**7*sqrt(a + b*x)/15, Ne(b, 0)), (a**(9/2)*x**3/3, True))","A",0
315,1,146,0,14.850817," ","integrate(x*(b*x+a)**(9/2),x)","\begin{cases} - \frac{4 a^{6} \sqrt{a + b x}}{143 b^{2}} + \frac{2 a^{5} x \sqrt{a + b x}}{143 b} + \frac{70 a^{4} x^{2} \sqrt{a + b x}}{143} + \frac{180 a^{3} b x^{3} \sqrt{a + b x}}{143} + \frac{200 a^{2} b^{2} x^{4} \sqrt{a + b x}}{143} + \frac{106 a b^{3} x^{5} \sqrt{a + b x}}{143} + \frac{2 b^{4} x^{6} \sqrt{a + b x}}{13} & \text{for}\: b \neq 0 \\\frac{a^{\frac{9}{2}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a**6*sqrt(a + b*x)/(143*b**2) + 2*a**5*x*sqrt(a + b*x)/(143*b) + 70*a**4*x**2*sqrt(a + b*x)/143 + 180*a**3*b*x**3*sqrt(a + b*x)/143 + 200*a**2*b**2*x**4*sqrt(a + b*x)/143 + 106*a*b**3*x**5*sqrt(a + b*x)/143 + 2*b**4*x**6*sqrt(a + b*x)/13, Ne(b, 0)), (a**(9/2)*x**2/2, True))","A",0
316,1,12,0,0.082669," ","integrate((b*x+a)**(9/2),x)","\frac{2 \left(a + b x\right)^{\frac{11}{2}}}{11 b}"," ",0,"2*(a + b*x)**(11/2)/(11*b)","A",0
317,1,148,0,11.101547," ","integrate((b*x+a)**(9/2)/x,x)","\frac{1126 a^{\frac{9}{2}} \sqrt{1 + \frac{b x}{a}}}{315} + a^{\frac{9}{2}} \log{\left(\frac{b x}{a} \right)} - 2 a^{\frac{9}{2}} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)} + \frac{1012 a^{\frac{7}{2}} b x \sqrt{1 + \frac{b x}{a}}}{315} + \frac{272 a^{\frac{5}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{105} + \frac{74 a^{\frac{3}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{63} + \frac{2 \sqrt{a} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{9}"," ",0,"1126*a**(9/2)*sqrt(1 + b*x/a)/315 + a**(9/2)*log(b*x/a) - 2*a**(9/2)*log(sqrt(1 + b*x/a) + 1) + 1012*a**(7/2)*b*x*sqrt(1 + b*x/a)/315 + 272*a**(5/2)*b**2*x**2*sqrt(1 + b*x/a)/105 + 74*a**(3/2)*b**3*x**3*sqrt(1 + b*x/a)/63 + 2*sqrt(a)*b**4*x**4*sqrt(1 + b*x/a)/9","A",0
318,1,150,0,9.921675," ","integrate((b*x+a)**(9/2)/x**2,x)","- \frac{a^{\frac{9}{2}} \sqrt{1 + \frac{b x}{a}}}{x} + \frac{388 a^{\frac{7}{2}} b \sqrt{1 + \frac{b x}{a}}}{35} + \frac{9 a^{\frac{7}{2}} b \log{\left(\frac{b x}{a} \right)}}{2} - 9 a^{\frac{7}{2}} b \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)} + \frac{156 a^{\frac{5}{2}} b^{2} x \sqrt{1 + \frac{b x}{a}}}{35} + \frac{58 a^{\frac{3}{2}} b^{3} x^{2} \sqrt{1 + \frac{b x}{a}}}{35} + \frac{2 \sqrt{a} b^{4} x^{3} \sqrt{1 + \frac{b x}{a}}}{7}"," ",0,"-a**(9/2)*sqrt(1 + b*x/a)/x + 388*a**(7/2)*b*sqrt(1 + b*x/a)/35 + 9*a**(7/2)*b*log(b*x/a)/2 - 9*a**(7/2)*b*log(sqrt(1 + b*x/a) + 1) + 156*a**(5/2)*b**2*x*sqrt(1 + b*x/a)/35 + 58*a**(3/2)*b**3*x**2*sqrt(1 + b*x/a)/35 + 2*sqrt(a)*b**4*x**3*sqrt(1 + b*x/a)/7","A",0
319,1,184,0,8.988915," ","integrate((b*x+a)**(9/2)/x**3,x)","- \frac{63 a^{\frac{5}{2}} b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4} - \frac{a^{5}}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{19 a^{4} \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{203 a^{3} b^{\frac{3}{2}}}{20 \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{86 a^{2} b^{\frac{5}{2}} \sqrt{x}}{5 \sqrt{\frac{a}{b x} + 1}} + \frac{16 a b^{\frac{7}{2}} x^{\frac{3}{2}}}{5 \sqrt{\frac{a}{b x} + 1}} + \frac{2 b^{\frac{9}{2}} x^{\frac{5}{2}}}{5 \sqrt{\frac{a}{b x} + 1}}"," ",0,"-63*a**(5/2)*b**2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/4 - a**5/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) + 1)) - 19*a**4*sqrt(b)/(4*x**(3/2)*sqrt(a/(b*x) + 1)) + 203*a**3*b**(3/2)/(20*sqrt(x)*sqrt(a/(b*x) + 1)) + 86*a**2*b**(5/2)*sqrt(x)/(5*sqrt(a/(b*x) + 1)) + 16*a*b**(7/2)*x**(3/2)/(5*sqrt(a/(b*x) + 1)) + 2*b**(9/2)*x**(5/2)/(5*sqrt(a/(b*x) + 1))","A",0
320,1,184,0,7.912450," ","integrate((b*x+a)**(9/2)/x**4,x)","- \frac{105 a^{\frac{3}{2}} b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{8} - \frac{a^{5}}{3 \sqrt{b} x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{29 a^{4} \sqrt{b}}{12 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{215 a^{3} b^{\frac{3}{2}}}{24 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{43 a^{2} b^{\frac{5}{2}}}{24 \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{28 a b^{\frac{7}{2}} \sqrt{x}}{3 \sqrt{\frac{a}{b x} + 1}} + \frac{2 b^{\frac{9}{2}} x^{\frac{3}{2}}}{3 \sqrt{\frac{a}{b x} + 1}}"," ",0,"-105*a**(3/2)*b**3*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/8 - a**5/(3*sqrt(b)*x**(7/2)*sqrt(a/(b*x) + 1)) - 29*a**4*sqrt(b)/(12*x**(5/2)*sqrt(a/(b*x) + 1)) - 215*a**3*b**(3/2)/(24*x**(3/2)*sqrt(a/(b*x) + 1)) + 43*a**2*b**(5/2)/(24*sqrt(x)*sqrt(a/(b*x) + 1)) + 28*a*b**(7/2)*sqrt(x)/(3*sqrt(a/(b*x) + 1)) + 2*b**(9/2)*x**(3/2)/(3*sqrt(a/(b*x) + 1))","A",0
321,1,182,0,8.547479," ","integrate((b*x+a)**(9/2)/x**5,x)","- \frac{315 \sqrt{a} b^{4} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{64} - \frac{a^{5}}{4 \sqrt{b} x^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{13 a^{4} \sqrt{b}}{8 x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{149 a^{3} b^{\frac{3}{2}}}{32 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{535 a^{2} b^{\frac{5}{2}}}{64 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{197 a b^{\frac{7}{2}}}{64 \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{2 b^{\frac{9}{2}} \sqrt{x}}{\sqrt{\frac{a}{b x} + 1}}"," ",0,"-315*sqrt(a)*b**4*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/64 - a**5/(4*sqrt(b)*x**(9/2)*sqrt(a/(b*x) + 1)) - 13*a**4*sqrt(b)/(8*x**(7/2)*sqrt(a/(b*x) + 1)) - 149*a**3*b**(3/2)/(32*x**(5/2)*sqrt(a/(b*x) + 1)) - 535*a**2*b**(5/2)/(64*x**(3/2)*sqrt(a/(b*x) + 1)) - 197*a*b**(7/2)/(64*sqrt(x)*sqrt(a/(b*x) + 1)) + 2*b**(9/2)*sqrt(x)/sqrt(a/(b*x) + 1)","A",0
322,1,158,0,10.249809," ","integrate((b*x+a)**(9/2)/x**6,x)","- \frac{a^{4} \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{5 x^{\frac{9}{2}}} - \frac{41 a^{3} b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{40 x^{\frac{7}{2}}} - \frac{171 a^{2} b^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}}{80 x^{\frac{5}{2}}} - \frac{149 a b^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}}{64 x^{\frac{3}{2}}} - \frac{193 b^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}}{128 \sqrt{x}} - \frac{63 b^{5} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{128 \sqrt{a}}"," ",0,"-a**4*sqrt(b)*sqrt(a/(b*x) + 1)/(5*x**(9/2)) - 41*a**3*b**(3/2)*sqrt(a/(b*x) + 1)/(40*x**(7/2)) - 171*a**2*b**(5/2)*sqrt(a/(b*x) + 1)/(80*x**(5/2)) - 149*a*b**(7/2)*sqrt(a/(b*x) + 1)/(64*x**(3/2)) - 193*b**(9/2)*sqrt(a/(b*x) + 1)/(128*sqrt(x)) - 63*b**5*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(128*sqrt(a))","A",0
323,1,209,0,15.689236," ","integrate((b*x+a)**(9/2)/x**7,x)","- \frac{a^{5}}{6 \sqrt{b} x^{\frac{13}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{59 a^{4} \sqrt{b}}{60 x^{\frac{11}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{1151 a^{3} b^{\frac{3}{2}}}{480 x^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{2947 a^{2} b^{\frac{5}{2}}}{960 x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{8171 a b^{\frac{7}{2}}}{3840 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{1045 b^{\frac{9}{2}}}{1536 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{21 b^{\frac{11}{2}}}{512 a \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{21 b^{6} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{512 a^{\frac{3}{2}}}"," ",0,"-a**5/(6*sqrt(b)*x**(13/2)*sqrt(a/(b*x) + 1)) - 59*a**4*sqrt(b)/(60*x**(11/2)*sqrt(a/(b*x) + 1)) - 1151*a**3*b**(3/2)/(480*x**(9/2)*sqrt(a/(b*x) + 1)) - 2947*a**2*b**(5/2)/(960*x**(7/2)*sqrt(a/(b*x) + 1)) - 8171*a*b**(7/2)/(3840*x**(5/2)*sqrt(a/(b*x) + 1)) - 1045*b**(9/2)/(1536*x**(3/2)*sqrt(a/(b*x) + 1)) - 21*b**(11/2)/(512*a*sqrt(x)*sqrt(a/(b*x) + 1)) + 21*b**6*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(512*a**(3/2))","A",0
324,1,236,0,22.199837," ","integrate((b*x+a)**(9/2)/x**8,x)","- \frac{a^{5}}{7 \sqrt{b} x^{\frac{15}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{23 a^{4} \sqrt{b}}{28 x^{\frac{13}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{541 a^{3} b^{\frac{3}{2}}}{280 x^{\frac{11}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{5249 a^{2} b^{\frac{5}{2}}}{2240 x^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{6653 a b^{\frac{7}{2}}}{4480 x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{1027 b^{\frac{9}{2}}}{2560 x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{3 b^{\frac{11}{2}}}{1024 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{9 b^{\frac{13}{2}}}{1024 a^{2} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} - \frac{9 b^{7} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{1024 a^{\frac{5}{2}}}"," ",0,"-a**5/(7*sqrt(b)*x**(15/2)*sqrt(a/(b*x) + 1)) - 23*a**4*sqrt(b)/(28*x**(13/2)*sqrt(a/(b*x) + 1)) - 541*a**3*b**(3/2)/(280*x**(11/2)*sqrt(a/(b*x) + 1)) - 5249*a**2*b**(5/2)/(2240*x**(9/2)*sqrt(a/(b*x) + 1)) - 6653*a*b**(7/2)/(4480*x**(7/2)*sqrt(a/(b*x) + 1)) - 1027*b**(9/2)/(2560*x**(5/2)*sqrt(a/(b*x) + 1)) + 3*b**(11/2)/(1024*a*x**(3/2)*sqrt(a/(b*x) + 1)) + 9*b**(13/2)/(1024*a**2*sqrt(x)*sqrt(a/(b*x) + 1)) - 9*b**7*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(1024*a**(5/2))","A",0
325,1,148,0,1.737129," ","integrate((b*x-a)**(1/2)/x,x)","\begin{cases} - 2 i \sqrt{a} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{2 i a}{\sqrt{b} \sqrt{x} \sqrt{\frac{a}{b x} - 1}} - \frac{2 i \sqrt{b} \sqrt{x}}{\sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\2 \sqrt{a} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} - \frac{2 a}{\sqrt{b} \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} + \frac{2 \sqrt{b} \sqrt{x}}{\sqrt{- \frac{a}{b x} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*sqrt(a)*acosh(sqrt(a)/(sqrt(b)*sqrt(x))) + 2*I*a/(sqrt(b)*sqrt(x)*sqrt(a/(b*x) - 1)) - 2*I*sqrt(b)*sqrt(x)/sqrt(a/(b*x) - 1), Abs(a/(b*x)) > 1), (2*sqrt(a)*asin(sqrt(a)/(sqrt(b)*sqrt(x))) - 2*a/(sqrt(b)*sqrt(x)*sqrt(-a/(b*x) + 1)) + 2*sqrt(b)*sqrt(x)/sqrt(-a/(b*x) + 1), True))","B",0
326,1,121,0,2.140411," ","integrate((b*x-a)**(1/2)/x**2,x)","\begin{cases} - \frac{i a}{\sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{i \sqrt{b}}{\sqrt{x} \sqrt{\frac{a}{b x} - 1}} + \frac{i b \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{\sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{\sqrt{x}} - \frac{b \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a/(sqrt(b)*x**(3/2)*sqrt(a/(b*x) - 1)) + I*sqrt(b)/(sqrt(x)*sqrt(a/(b*x) - 1)) + I*b*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a), Abs(a/(b*x)) > 1), (-sqrt(b)*sqrt(-a/(b*x) + 1)/sqrt(x) - b*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a), True))","A",0
327,1,207,0,4.161031," ","integrate((b*x-a)**(1/2)/x**3,x)","\begin{cases} - \frac{i a}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{3 i \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{i b^{\frac{3}{2}}}{4 a \sqrt{x} \sqrt{\frac{a}{b x} - 1}} + \frac{i b^{2} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{3}{2}}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{a}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{3 \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{b^{\frac{3}{2}}}{4 a \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} - \frac{b^{2} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) - 1)) + 3*I*sqrt(b)/(4*x**(3/2)*sqrt(a/(b*x) - 1)) - I*b**(3/2)/(4*a*sqrt(x)*sqrt(a/(b*x) - 1)) + I*b**2*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(3/2)), Abs(a/(b*x)) > 1), (a/(2*sqrt(b)*x**(5/2)*sqrt(-a/(b*x) + 1)) - 3*sqrt(b)/(4*x**(3/2)*sqrt(-a/(b*x) + 1)) + b**(3/2)/(4*a*sqrt(x)*sqrt(-a/(b*x) + 1)) - b**2*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(3/2)), True))","A",0
328,1,187,0,2.462877," ","integrate((b*x-a)**(3/2)/x,x)","\begin{cases} - \frac{8 a^{\frac{3}{2}} \sqrt{-1 + \frac{b x}{a}}}{3} - i a^{\frac{3}{2}} \log{\left(\frac{b x}{a} \right)} + 2 i a^{\frac{3}{2}} \log{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} - 2 a^{\frac{3}{2}} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{2 \sqrt{a} b x \sqrt{-1 + \frac{b x}{a}}}{3} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{8 i a^{\frac{3}{2}} \sqrt{1 - \frac{b x}{a}}}{3} - i a^{\frac{3}{2}} \log{\left(\frac{b x}{a} \right)} + 2 i a^{\frac{3}{2}} \log{\left(\sqrt{1 - \frac{b x}{a}} + 1 \right)} + \frac{2 i \sqrt{a} b x \sqrt{1 - \frac{b x}{a}}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*a**(3/2)*sqrt(-1 + b*x/a)/3 - I*a**(3/2)*log(b*x/a) + 2*I*a**(3/2)*log(sqrt(b)*sqrt(x)/sqrt(a)) - 2*a**(3/2)*asin(sqrt(a)/(sqrt(b)*sqrt(x))) + 2*sqrt(a)*b*x*sqrt(-1 + b*x/a)/3, Abs(b*x/a) > 1), (-8*I*a**(3/2)*sqrt(1 - b*x/a)/3 - I*a**(3/2)*log(b*x/a) + 2*I*a**(3/2)*log(sqrt(1 - b*x/a) + 1) + 2*I*sqrt(a)*b*x*sqrt(1 - b*x/a)/3, True))","C",0
329,1,197,0,2.837066," ","integrate((b*x-a)**(3/2)/x**2,x)","\begin{cases} - 3 i \sqrt{a} b \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{i a^{2}}{\sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{i a \sqrt{b}}{\sqrt{x} \sqrt{\frac{a}{b x} - 1}} - \frac{2 i b^{\frac{3}{2}} \sqrt{x}}{\sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\3 \sqrt{a} b \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} - \frac{a^{2}}{\sqrt{b} x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{a \sqrt{b}}{\sqrt{x} \sqrt{- \frac{a}{b x} + 1}} + \frac{2 b^{\frac{3}{2}} \sqrt{x}}{\sqrt{- \frac{a}{b x} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*sqrt(a)*b*acosh(sqrt(a)/(sqrt(b)*sqrt(x))) + I*a**2/(sqrt(b)*x**(3/2)*sqrt(a/(b*x) - 1)) + I*a*sqrt(b)/(sqrt(x)*sqrt(a/(b*x) - 1)) - 2*I*b**(3/2)*sqrt(x)/sqrt(a/(b*x) - 1), Abs(a/(b*x)) > 1), (3*sqrt(a)*b*asin(sqrt(a)/(sqrt(b)*sqrt(x))) - a**2/(sqrt(b)*x**(3/2)*sqrt(-a/(b*x) + 1)) - a*sqrt(b)/(sqrt(x)*sqrt(-a/(b*x) + 1)) + 2*b**(3/2)*sqrt(x)/sqrt(-a/(b*x) + 1), True))","B",0
330,1,190,0,3.302045," ","integrate((b*x-a)**(3/2)/x**3,x)","\begin{cases} \frac{i a^{2}}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{7 i a \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{5 i b^{\frac{3}{2}}}{4 \sqrt{x} \sqrt{\frac{a}{b x} - 1}} + \frac{3 i b^{2} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 \sqrt{a}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{a \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{2 x^{\frac{3}{2}}} - \frac{5 b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{4 \sqrt{x}} - \frac{3 b^{2} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 \sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a**2/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) - 1)) - 7*I*a*sqrt(b)/(4*x**(3/2)*sqrt(a/(b*x) - 1)) + 5*I*b**(3/2)/(4*sqrt(x)*sqrt(a/(b*x) - 1)) + 3*I*b**2*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*sqrt(a)), Abs(a/(b*x)) > 1), (a*sqrt(b)*sqrt(-a/(b*x) + 1)/(2*x**(3/2)) - 5*b**(3/2)*sqrt(-a/(b*x) + 1)/(4*sqrt(x)) - 3*b**2*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*sqrt(a)), True))","A",0
331,1,240,0,4.241248," ","integrate((b*x-a)**(5/2)/x,x)","\begin{cases} \frac{46 a^{\frac{5}{2}} \sqrt{-1 + \frac{b x}{a}}}{15} + i a^{\frac{5}{2}} \log{\left(\frac{b x}{a} \right)} - 2 i a^{\frac{5}{2}} \log{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} + 2 a^{\frac{5}{2}} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} - \frac{22 a^{\frac{3}{2}} b x \sqrt{-1 + \frac{b x}{a}}}{15} + \frac{2 \sqrt{a} b^{2} x^{2} \sqrt{-1 + \frac{b x}{a}}}{5} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{46 i a^{\frac{5}{2}} \sqrt{1 - \frac{b x}{a}}}{15} + i a^{\frac{5}{2}} \log{\left(\frac{b x}{a} \right)} - 2 i a^{\frac{5}{2}} \log{\left(\sqrt{1 - \frac{b x}{a}} + 1 \right)} - \frac{22 i a^{\frac{3}{2}} b x \sqrt{1 - \frac{b x}{a}}}{15} + \frac{2 i \sqrt{a} b^{2} x^{2} \sqrt{1 - \frac{b x}{a}}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((46*a**(5/2)*sqrt(-1 + b*x/a)/15 + I*a**(5/2)*log(b*x/a) - 2*I*a**(5/2)*log(sqrt(b)*sqrt(x)/sqrt(a)) + 2*a**(5/2)*asin(sqrt(a)/(sqrt(b)*sqrt(x))) - 22*a**(3/2)*b*x*sqrt(-1 + b*x/a)/15 + 2*sqrt(a)*b**2*x**2*sqrt(-1 + b*x/a)/5, Abs(b*x/a) > 1), (46*I*a**(5/2)*sqrt(1 - b*x/a)/15 + I*a**(5/2)*log(b*x/a) - 2*I*a**(5/2)*log(sqrt(1 - b*x/a) + 1) - 22*I*a**(3/2)*b*x*sqrt(1 - b*x/a)/15 + 2*I*sqrt(a)*b**2*x**2*sqrt(1 - b*x/a)/5, True))","C",0
332,1,245,0,3.685967," ","integrate((b*x-a)**(5/2)/x**2,x)","\begin{cases} - \frac{a^{\frac{5}{2}} \sqrt{-1 + \frac{b x}{a}}}{x} - \frac{14 a^{\frac{3}{2}} b \sqrt{-1 + \frac{b x}{a}}}{3} - \frac{5 i a^{\frac{3}{2}} b \log{\left(\frac{b x}{a} \right)}}{2} + 5 i a^{\frac{3}{2}} b \log{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} - 5 a^{\frac{3}{2}} b \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{2 \sqrt{a} b^{2} x \sqrt{-1 + \frac{b x}{a}}}{3} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{i a^{\frac{5}{2}} \sqrt{1 - \frac{b x}{a}}}{x} - \frac{14 i a^{\frac{3}{2}} b \sqrt{1 - \frac{b x}{a}}}{3} - \frac{5 i a^{\frac{3}{2}} b \log{\left(\frac{b x}{a} \right)}}{2} + 5 i a^{\frac{3}{2}} b \log{\left(\sqrt{1 - \frac{b x}{a}} + 1 \right)} + \frac{2 i \sqrt{a} b^{2} x \sqrt{1 - \frac{b x}{a}}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**(5/2)*sqrt(-1 + b*x/a)/x - 14*a**(3/2)*b*sqrt(-1 + b*x/a)/3 - 5*I*a**(3/2)*b*log(b*x/a)/2 + 5*I*a**(3/2)*b*log(sqrt(b)*sqrt(x)/sqrt(a)) - 5*a**(3/2)*b*asin(sqrt(a)/(sqrt(b)*sqrt(x))) + 2*sqrt(a)*b**2*x*sqrt(-1 + b*x/a)/3, Abs(b*x/a) > 1), (-I*a**(5/2)*sqrt(1 - b*x/a)/x - 14*I*a**(3/2)*b*sqrt(1 - b*x/a)/3 - 5*I*a**(3/2)*b*log(b*x/a)/2 + 5*I*a**(3/2)*b*log(sqrt(1 - b*x/a) + 1) + 2*I*sqrt(a)*b**2*x*sqrt(1 - b*x/a)/3, True))","C",0
333,1,267,0,3.926843," ","integrate((b*x-a)**(5/2)/x**3,x)","\begin{cases} - \frac{15 i \sqrt{a} b^{2} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4} - \frac{i a^{3}}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{11 i a^{2} \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{i a b^{\frac{3}{2}}}{4 \sqrt{x} \sqrt{\frac{a}{b x} - 1}} - \frac{2 i b^{\frac{5}{2}} \sqrt{x}}{\sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{15 \sqrt{a} b^{2} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4} + \frac{a^{3}}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{11 a^{2} \sqrt{b}}{4 x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{a b^{\frac{3}{2}}}{4 \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} + \frac{2 b^{\frac{5}{2}} \sqrt{x}}{\sqrt{- \frac{a}{b x} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*I*sqrt(a)*b**2*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/4 - I*a**3/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) - 1)) + 11*I*a**2*sqrt(b)/(4*x**(3/2)*sqrt(a/(b*x) - 1)) - I*a*b**(3/2)/(4*sqrt(x)*sqrt(a/(b*x) - 1)) - 2*I*b**(5/2)*sqrt(x)/sqrt(a/(b*x) - 1), Abs(a/(b*x)) > 1), (15*sqrt(a)*b**2*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/4 + a**3/(2*sqrt(b)*x**(5/2)*sqrt(-a/(b*x) + 1)) - 11*a**2*sqrt(b)/(4*x**(3/2)*sqrt(-a/(b*x) + 1)) + a*b**(3/2)/(4*sqrt(x)*sqrt(-a/(b*x) + 1)) + 2*b**(5/2)*sqrt(x)/sqrt(-a/(b*x) + 1), True))","A",0
334,1,3755,0,4.838540," ","integrate(x**4/(b*x+a)**(1/2),x)","\frac{256 a^{\frac{89}{2}} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{256 a^{\frac{89}{2}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{2432 a^{\frac{87}{2}} b x \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{2560 a^{\frac{87}{2}} b x}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{10336 a^{\frac{85}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{11520 a^{\frac{85}{2}} b^{2} x^{2}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{25840 a^{\frac{83}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{30720 a^{\frac{83}{2}} b^{3} x^{3}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{41990 a^{\frac{81}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{53760 a^{\frac{81}{2}} b^{4} x^{4}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{46252 a^{\frac{79}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{64512 a^{\frac{79}{2}} b^{5} x^{5}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{35214 a^{\frac{77}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{53760 a^{\frac{77}{2}} b^{6} x^{6}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{19632 a^{\frac{75}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{30720 a^{\frac{75}{2}} b^{7} x^{7}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{10860 a^{\frac{73}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{11520 a^{\frac{73}{2}} b^{8} x^{8}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{9160 a^{\frac{71}{2}} b^{9} x^{9} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{2560 a^{\frac{71}{2}} b^{9} x^{9}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{8396 a^{\frac{69}{2}} b^{10} x^{10} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} - \frac{256 a^{\frac{69}{2}} b^{10} x^{10}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{5632 a^{\frac{67}{2}} b^{11} x^{11} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{2446 a^{\frac{65}{2}} b^{12} x^{12} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{620 a^{\frac{63}{2}} b^{13} x^{13} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}} + \frac{70 a^{\frac{61}{2}} b^{14} x^{14} \sqrt{1 + \frac{b x}{a}}}{315 a^{40} b^{5} + 3150 a^{39} b^{6} x + 14175 a^{38} b^{7} x^{2} + 37800 a^{37} b^{8} x^{3} + 66150 a^{36} b^{9} x^{4} + 79380 a^{35} b^{10} x^{5} + 66150 a^{34} b^{11} x^{6} + 37800 a^{33} b^{12} x^{7} + 14175 a^{32} b^{13} x^{8} + 3150 a^{31} b^{14} x^{9} + 315 a^{30} b^{15} x^{10}}"," ",0,"256*a**(89/2)*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 256*a**(89/2)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 2432*a**(87/2)*b*x*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 2560*a**(87/2)*b*x/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 10336*a**(85/2)*b**2*x**2*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 11520*a**(85/2)*b**2*x**2/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 25840*a**(83/2)*b**3*x**3*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 30720*a**(83/2)*b**3*x**3/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 41990*a**(81/2)*b**4*x**4*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 53760*a**(81/2)*b**4*x**4/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 46252*a**(79/2)*b**5*x**5*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 64512*a**(79/2)*b**5*x**5/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 35214*a**(77/2)*b**6*x**6*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 53760*a**(77/2)*b**6*x**6/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 19632*a**(75/2)*b**7*x**7*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 30720*a**(75/2)*b**7*x**7/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 10860*a**(73/2)*b**8*x**8*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 11520*a**(73/2)*b**8*x**8/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 9160*a**(71/2)*b**9*x**9*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 2560*a**(71/2)*b**9*x**9/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 8396*a**(69/2)*b**10*x**10*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) - 256*a**(69/2)*b**10*x**10/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 5632*a**(67/2)*b**11*x**11*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 2446*a**(65/2)*b**12*x**12*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 620*a**(63/2)*b**13*x**13*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10) + 70*a**(61/2)*b**14*x**14*sqrt(1 + b*x/a)/(315*a**40*b**5 + 3150*a**39*b**6*x + 14175*a**38*b**7*x**2 + 37800*a**37*b**8*x**3 + 66150*a**36*b**9*x**4 + 79380*a**35*b**10*x**5 + 66150*a**34*b**11*x**6 + 37800*a**33*b**12*x**7 + 14175*a**32*b**13*x**8 + 3150*a**31*b**14*x**9 + 315*a**30*b**15*x**10)","B",0
335,1,1640,0,2.702638," ","integrate(x**3/(b*x+a)**(1/2),x)","- \frac{32 a^{\frac{47}{2}} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{32 a^{\frac{47}{2}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} - \frac{176 a^{\frac{45}{2}} b x \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{192 a^{\frac{45}{2}} b x}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} - \frac{396 a^{\frac{43}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{480 a^{\frac{43}{2}} b^{2} x^{2}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} - \frac{462 a^{\frac{41}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{640 a^{\frac{41}{2}} b^{3} x^{3}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} - \frac{280 a^{\frac{39}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{480 a^{\frac{39}{2}} b^{4} x^{4}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} - \frac{42 a^{\frac{37}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{192 a^{\frac{37}{2}} b^{5} x^{5}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{84 a^{\frac{35}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{32 a^{\frac{35}{2}} b^{6} x^{6}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{94 a^{\frac{33}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{48 a^{\frac{31}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}} + \frac{10 a^{\frac{29}{2}} b^{9} x^{9} \sqrt{1 + \frac{b x}{a}}}{35 a^{20} b^{4} + 210 a^{19} b^{5} x + 525 a^{18} b^{6} x^{2} + 700 a^{17} b^{7} x^{3} + 525 a^{16} b^{8} x^{4} + 210 a^{15} b^{9} x^{5} + 35 a^{14} b^{10} x^{6}}"," ",0,"-32*a**(47/2)*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 32*a**(47/2)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) - 176*a**(45/2)*b*x*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 192*a**(45/2)*b*x/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) - 396*a**(43/2)*b**2*x**2*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 480*a**(43/2)*b**2*x**2/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) - 462*a**(41/2)*b**3*x**3*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 640*a**(41/2)*b**3*x**3/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) - 280*a**(39/2)*b**4*x**4*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 480*a**(39/2)*b**4*x**4/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) - 42*a**(37/2)*b**5*x**5*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 192*a**(37/2)*b**5*x**5/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 84*a**(35/2)*b**6*x**6*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 32*a**(35/2)*b**6*x**6/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 94*a**(33/2)*b**7*x**7*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 48*a**(31/2)*b**8*x**8*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6) + 10*a**(29/2)*b**9*x**9*sqrt(1 + b*x/a)/(35*a**20*b**4 + 210*a**19*b**5*x + 525*a**18*b**6*x**2 + 700*a**17*b**7*x**3 + 525*a**16*b**8*x**4 + 210*a**15*b**9*x**5 + 35*a**14*b**10*x**6)","B",0
336,1,600,0,1.766762," ","integrate(x**2/(b*x+a)**(1/2),x)","\frac{16 a^{\frac{21}{2}} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{21}{2}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{40 a^{\frac{19}{2}} b x \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{19}{2}} b x}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{30 a^{\frac{17}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{48 a^{\frac{17}{2}} b^{2} x^{2}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{10 a^{\frac{15}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} - \frac{16 a^{\frac{15}{2}} b^{3} x^{3}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{10 a^{\frac{13}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}} + \frac{6 a^{\frac{11}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{15 a^{8} b^{3} + 45 a^{7} b^{4} x + 45 a^{6} b^{5} x^{2} + 15 a^{5} b^{6} x^{3}}"," ",0,"16*a**(21/2)*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 16*a**(21/2)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 40*a**(19/2)*b*x*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 48*a**(19/2)*b*x/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 30*a**(17/2)*b**2*x**2*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 48*a**(17/2)*b**2*x**2/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 10*a**(15/2)*b**3*x**3*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) - 16*a**(15/2)*b**3*x**3/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 10*a**(13/2)*b**4*x**4*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3) + 6*a**(11/2)*b**5*x**5*sqrt(1 + b*x/a)/(15*a**8*b**3 + 45*a**7*b**4*x + 45*a**6*b**5*x**2 + 15*a**5*b**6*x**3)","B",0
337,1,162,0,1.160305," ","integrate(x/(b*x+a)**(1/2),x)","- \frac{4 a^{\frac{7}{2}} \sqrt{1 + \frac{b x}{a}}}{3 a^{2} b^{2} + 3 a b^{3} x} + \frac{4 a^{\frac{7}{2}}}{3 a^{2} b^{2} + 3 a b^{3} x} - \frac{2 a^{\frac{5}{2}} b x \sqrt{1 + \frac{b x}{a}}}{3 a^{2} b^{2} + 3 a b^{3} x} + \frac{4 a^{\frac{5}{2}} b x}{3 a^{2} b^{2} + 3 a b^{3} x} + \frac{2 a^{\frac{3}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{3 a^{2} b^{2} + 3 a b^{3} x}"," ",0,"-4*a**(7/2)*sqrt(1 + b*x/a)/(3*a**2*b**2 + 3*a*b**3*x) + 4*a**(7/2)/(3*a**2*b**2 + 3*a*b**3*x) - 2*a**(5/2)*b*x*sqrt(1 + b*x/a)/(3*a**2*b**2 + 3*a*b**3*x) + 4*a**(5/2)*b*x/(3*a**2*b**2 + 3*a*b**3*x) + 2*a**(3/2)*b**2*x**2*sqrt(1 + b*x/a)/(3*a**2*b**2 + 3*a*b**3*x)","B",0
338,1,10,0,0.066094," ","integrate(1/(b*x+a)**(1/2),x)","\frac{2 \sqrt{a + b x}}{b}"," ",0,"2*sqrt(a + b*x)/b","A",0
339,1,24,0,1.107857," ","integrate(1/x/(b*x+a)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}}"," ",0,"-2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a)","A",0
340,1,44,0,2.302218," ","integrate(1/x**2/(b*x+a)**(1/2),x)","- \frac{\sqrt{b} \sqrt{\frac{a}{b x} + 1}}{a \sqrt{x}} + \frac{b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{3}{2}}}"," ",0,"-sqrt(b)*sqrt(a/(b*x) + 1)/(a*sqrt(x)) + b*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(3/2)","A",0
341,1,102,0,4.365720," ","integrate(1/x**3/(b*x+a)**(1/2),x)","- \frac{1}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{\sqrt{b}}{4 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{3 b^{\frac{3}{2}}}{4 a^{2} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} - \frac{3 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{5}{2}}}"," ",0,"-1/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) + 1)) + sqrt(b)/(4*a*x**(3/2)*sqrt(a/(b*x) + 1)) + 3*b**(3/2)/(4*a**2*sqrt(x)*sqrt(a/(b*x) + 1)) - 3*b**2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(5/2))","A",0
342,1,129,0,7.022491," ","integrate(1/x**4/(b*x+a)**(1/2),x)","- \frac{1}{3 \sqrt{b} x^{\frac{7}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{\sqrt{b}}{12 a x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{5 b^{\frac{3}{2}}}{24 a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{5 b^{\frac{5}{2}}}{8 a^{3} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{5 b^{3} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{8 a^{\frac{7}{2}}}"," ",0,"-1/(3*sqrt(b)*x**(7/2)*sqrt(a/(b*x) + 1)) + sqrt(b)/(12*a*x**(5/2)*sqrt(a/(b*x) + 1)) - 5*b**(3/2)/(24*a**2*x**(3/2)*sqrt(a/(b*x) + 1)) - 5*b**(5/2)/(8*a**3*sqrt(x)*sqrt(a/(b*x) + 1)) + 5*b**3*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(8*a**(7/2))","A",0
343,1,3606,0,4.806201," ","integrate(x**4/(b*x+a)**(3/2),x)","- \frac{256 a^{\frac{87}{2}} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{256 a^{\frac{87}{2}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{2432 a^{\frac{85}{2}} b x \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{2560 a^{\frac{85}{2}} b x}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{10336 a^{\frac{83}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{11520 a^{\frac{83}{2}} b^{2} x^{2}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{25840 a^{\frac{81}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{30720 a^{\frac{81}{2}} b^{3} x^{3}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{41990 a^{\frac{79}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{53760 a^{\frac{79}{2}} b^{4} x^{4}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{46182 a^{\frac{77}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{64512 a^{\frac{77}{2}} b^{5} x^{5}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{34584 a^{\frac{75}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{53760 a^{\frac{75}{2}} b^{6} x^{6}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{17112 a^{\frac{73}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{30720 a^{\frac{73}{2}} b^{7} x^{7}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{4980 a^{\frac{71}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{11520 a^{\frac{71}{2}} b^{8} x^{8}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} - \frac{340 a^{\frac{69}{2}} b^{9} x^{9} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{2560 a^{\frac{69}{2}} b^{9} x^{9}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{424 a^{\frac{67}{2}} b^{10} x^{10} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{256 a^{\frac{67}{2}} b^{10} x^{10}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{248 a^{\frac{65}{2}} b^{11} x^{11} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{74 a^{\frac{63}{2}} b^{12} x^{12} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}} + \frac{10 a^{\frac{61}{2}} b^{13} x^{13} \sqrt{1 + \frac{b x}{a}}}{35 a^{40} b^{5} + 350 a^{39} b^{6} x + 1575 a^{38} b^{7} x^{2} + 4200 a^{37} b^{8} x^{3} + 7350 a^{36} b^{9} x^{4} + 8820 a^{35} b^{10} x^{5} + 7350 a^{34} b^{11} x^{6} + 4200 a^{33} b^{12} x^{7} + 1575 a^{32} b^{13} x^{8} + 350 a^{31} b^{14} x^{9} + 35 a^{30} b^{15} x^{10}}"," ",0,"-256*a**(87/2)*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 256*a**(87/2)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 2432*a**(85/2)*b*x*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 2560*a**(85/2)*b*x/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 10336*a**(83/2)*b**2*x**2*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 11520*a**(83/2)*b**2*x**2/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 25840*a**(81/2)*b**3*x**3*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 30720*a**(81/2)*b**3*x**3/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 41990*a**(79/2)*b**4*x**4*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 53760*a**(79/2)*b**4*x**4/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 46182*a**(77/2)*b**5*x**5*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 64512*a**(77/2)*b**5*x**5/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 34584*a**(75/2)*b**6*x**6*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 53760*a**(75/2)*b**6*x**6/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 17112*a**(73/2)*b**7*x**7*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 30720*a**(73/2)*b**7*x**7/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 4980*a**(71/2)*b**8*x**8*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 11520*a**(71/2)*b**8*x**8/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) - 340*a**(69/2)*b**9*x**9*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 2560*a**(69/2)*b**9*x**9/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 424*a**(67/2)*b**10*x**10*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 256*a**(67/2)*b**10*x**10/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 248*a**(65/2)*b**11*x**11*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 74*a**(63/2)*b**12*x**12*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10) + 10*a**(61/2)*b**13*x**13*sqrt(1 + b*x/a)/(35*a**40*b**5 + 350*a**39*b**6*x + 1575*a**38*b**7*x**2 + 4200*a**37*b**8*x**3 + 7350*a**36*b**9*x**4 + 8820*a**35*b**10*x**5 + 7350*a**34*b**11*x**6 + 4200*a**33*b**12*x**7 + 1575*a**32*b**13*x**8 + 350*a**31*b**14*x**9 + 35*a**30*b**15*x**10)","B",0
344,1,1538,0,2.935410," ","integrate(x**3/(b*x+a)**(3/2),x)","\frac{32 a^{\frac{45}{2}} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{32 a^{\frac{45}{2}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{176 a^{\frac{43}{2}} b x \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{192 a^{\frac{43}{2}} b x}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{396 a^{\frac{41}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{480 a^{\frac{41}{2}} b^{2} x^{2}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{462 a^{\frac{39}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{640 a^{\frac{39}{2}} b^{3} x^{3}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{290 a^{\frac{37}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{480 a^{\frac{37}{2}} b^{4} x^{4}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{92 a^{\frac{35}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{192 a^{\frac{35}{2}} b^{5} x^{5}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{16 a^{\frac{33}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} - \frac{32 a^{\frac{33}{2}} b^{6} x^{6}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{6 a^{\frac{31}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}} + \frac{2 a^{\frac{29}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{5 a^{20} b^{4} + 30 a^{19} b^{5} x + 75 a^{18} b^{6} x^{2} + 100 a^{17} b^{7} x^{3} + 75 a^{16} b^{8} x^{4} + 30 a^{15} b^{9} x^{5} + 5 a^{14} b^{10} x^{6}}"," ",0,"32*a**(45/2)*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 32*a**(45/2)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 176*a**(43/2)*b*x*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 192*a**(43/2)*b*x/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 396*a**(41/2)*b**2*x**2*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 480*a**(41/2)*b**2*x**2/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 462*a**(39/2)*b**3*x**3*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 640*a**(39/2)*b**3*x**3/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 290*a**(37/2)*b**4*x**4*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 480*a**(37/2)*b**4*x**4/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 92*a**(35/2)*b**5*x**5*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 192*a**(35/2)*b**5*x**5/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 16*a**(33/2)*b**6*x**6*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) - 32*a**(33/2)*b**6*x**6/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 6*a**(31/2)*b**7*x**7*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6) + 2*a**(29/2)*b**8*x**8*sqrt(1 + b*x/a)/(5*a**20*b**4 + 30*a**19*b**5*x + 75*a**18*b**6*x**2 + 100*a**17*b**7*x**3 + 75*a**16*b**8*x**4 + 30*a**15*b**9*x**5 + 5*a**14*b**10*x**6)","B",0
345,1,534,0,1.826833," ","integrate(x**2/(b*x+a)**(3/2),x)","- \frac{16 a^{\frac{19}{2}} \sqrt{1 + \frac{b x}{a}}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} + \frac{16 a^{\frac{19}{2}}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} - \frac{40 a^{\frac{17}{2}} b x \sqrt{1 + \frac{b x}{a}}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} + \frac{48 a^{\frac{17}{2}} b x}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} - \frac{30 a^{\frac{15}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} + \frac{48 a^{\frac{15}{2}} b^{2} x^{2}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} - \frac{4 a^{\frac{13}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} + \frac{16 a^{\frac{13}{2}} b^{3} x^{3}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}} + \frac{2 a^{\frac{11}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{3 a^{8} b^{3} + 9 a^{7} b^{4} x + 9 a^{6} b^{5} x^{2} + 3 a^{5} b^{6} x^{3}}"," ",0,"-16*a**(19/2)*sqrt(1 + b*x/a)/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) + 16*a**(19/2)/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) - 40*a**(17/2)*b*x*sqrt(1 + b*x/a)/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) + 48*a**(17/2)*b*x/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) - 30*a**(15/2)*b**2*x**2*sqrt(1 + b*x/a)/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) + 48*a**(15/2)*b**2*x**2/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) - 4*a**(13/2)*b**3*x**3*sqrt(1 + b*x/a)/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) + 16*a**(13/2)*b**3*x**3/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3) + 2*a**(11/2)*b**4*x**4*sqrt(1 + b*x/a)/(3*a**8*b**3 + 9*a**7*b**4*x + 9*a**6*b**5*x**2 + 3*a**5*b**6*x**3)","B",0
346,1,37,0,0.669463," ","integrate(x/(b*x+a)**(3/2),x)","\begin{cases} \frac{4 a}{b^{2} \sqrt{a + b x}} + \frac{2 x}{b \sqrt{a + b x}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a/(b**2*sqrt(a + b*x)) + 2*x/(b*sqrt(a + b*x)), Ne(b, 0)), (x**2/(2*a**(3/2)), True))","A",0
347,1,12,0,0.069782," ","integrate(1/(b*x+a)**(3/2),x)","- \frac{2}{b \sqrt{a + b x}}"," ",0,"-2/(b*sqrt(a + b*x))","A",0
348,1,146,0,1.866453," ","integrate(1/x/(b*x+a)**(3/2),x)","\frac{2 a^{3} \sqrt{1 + \frac{b x}{a}}}{a^{\frac{9}{2}} + a^{\frac{7}{2}} b x} + \frac{a^{3} \log{\left(\frac{b x}{a} \right)}}{a^{\frac{9}{2}} + a^{\frac{7}{2}} b x} - \frac{2 a^{3} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{a^{\frac{9}{2}} + a^{\frac{7}{2}} b x} + \frac{a^{2} b x \log{\left(\frac{b x}{a} \right)}}{a^{\frac{9}{2}} + a^{\frac{7}{2}} b x} - \frac{2 a^{2} b x \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{a^{\frac{9}{2}} + a^{\frac{7}{2}} b x}"," ",0,"2*a**3*sqrt(1 + b*x/a)/(a**(9/2) + a**(7/2)*b*x) + a**3*log(b*x/a)/(a**(9/2) + a**(7/2)*b*x) - 2*a**3*log(sqrt(1 + b*x/a) + 1)/(a**(9/2) + a**(7/2)*b*x) + a**2*b*x*log(b*x/a)/(a**(9/2) + a**(7/2)*b*x) - 2*a**2*b*x*log(sqrt(1 + b*x/a) + 1)/(a**(9/2) + a**(7/2)*b*x)","B",0
349,1,73,0,3.411444," ","integrate(1/x**2/(b*x+a)**(3/2),x)","- \frac{1}{a \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{3 \sqrt{b}}{a^{2} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{3 b \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{5}{2}}}"," ",0,"-1/(a*sqrt(b)*x**(3/2)*sqrt(a/(b*x) + 1)) - 3*sqrt(b)/(a**2*sqrt(x)*sqrt(a/(b*x) + 1)) + 3*b*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(5/2)","A",0
350,1,107,0,5.982501," ","integrate(1/x**3/(b*x+a)**(3/2),x)","- \frac{1}{2 a \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{5 \sqrt{b}}{4 a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{15 b^{\frac{3}{2}}}{4 a^{3} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} - \frac{15 b^{2} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{7}{2}}}"," ",0,"-1/(2*a*sqrt(b)*x**(5/2)*sqrt(a/(b*x) + 1)) + 5*sqrt(b)/(4*a**2*x**(3/2)*sqrt(a/(b*x) + 1)) + 15*b**(3/2)/(4*a**3*sqrt(x)*sqrt(a/(b*x) + 1)) - 15*b**2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(7/2))","A",0
351,1,3456,0,4.574826," ","integrate(x**4/(b*x+a)**(5/2),x)","\frac{256 a^{\frac{85}{2}} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{256 a^{\frac{85}{2}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{2432 a^{\frac{83}{2}} b x \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{2560 a^{\frac{83}{2}} b x}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{10336 a^{\frac{81}{2}} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{11520 a^{\frac{81}{2}} b^{2} x^{2}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{25840 a^{\frac{79}{2}} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{30720 a^{\frac{79}{2}} b^{3} x^{3}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{41990 a^{\frac{77}{2}} b^{4} x^{4} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{53760 a^{\frac{77}{2}} b^{4} x^{4}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{46192 a^{\frac{75}{2}} b^{5} x^{5} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{64512 a^{\frac{75}{2}} b^{5} x^{5}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{34664 a^{\frac{73}{2}} b^{6} x^{6} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{53760 a^{\frac{73}{2}} b^{6} x^{6}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{17392 a^{\frac{71}{2}} b^{7} x^{7} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{30720 a^{\frac{71}{2}} b^{7} x^{7}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{5540 a^{\frac{69}{2}} b^{8} x^{8} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{11520 a^{\frac{69}{2}} b^{8} x^{8}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{1040 a^{\frac{67}{2}} b^{9} x^{9} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{2560 a^{\frac{67}{2}} b^{9} x^{9}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{136 a^{\frac{65}{2}} b^{10} x^{10} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} - \frac{256 a^{\frac{65}{2}} b^{10} x^{10}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{32 a^{\frac{63}{2}} b^{11} x^{11} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}} + \frac{6 a^{\frac{61}{2}} b^{12} x^{12} \sqrt{1 + \frac{b x}{a}}}{15 a^{40} b^{5} + 150 a^{39} b^{6} x + 675 a^{38} b^{7} x^{2} + 1800 a^{37} b^{8} x^{3} + 3150 a^{36} b^{9} x^{4} + 3780 a^{35} b^{10} x^{5} + 3150 a^{34} b^{11} x^{6} + 1800 a^{33} b^{12} x^{7} + 675 a^{32} b^{13} x^{8} + 150 a^{31} b^{14} x^{9} + 15 a^{30} b^{15} x^{10}}"," ",0,"256*a**(85/2)*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 256*a**(85/2)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 2432*a**(83/2)*b*x*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 2560*a**(83/2)*b*x/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 10336*a**(81/2)*b**2*x**2*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 11520*a**(81/2)*b**2*x**2/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 25840*a**(79/2)*b**3*x**3*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 30720*a**(79/2)*b**3*x**3/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 41990*a**(77/2)*b**4*x**4*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 53760*a**(77/2)*b**4*x**4/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 46192*a**(75/2)*b**5*x**5*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 64512*a**(75/2)*b**5*x**5/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 34664*a**(73/2)*b**6*x**6*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 53760*a**(73/2)*b**6*x**6/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 17392*a**(71/2)*b**7*x**7*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 30720*a**(71/2)*b**7*x**7/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 5540*a**(69/2)*b**8*x**8*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 11520*a**(69/2)*b**8*x**8/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 1040*a**(67/2)*b**9*x**9*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 2560*a**(67/2)*b**9*x**9/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 136*a**(65/2)*b**10*x**10*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) - 256*a**(65/2)*b**10*x**10/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 32*a**(63/2)*b**11*x**11*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10) + 6*a**(61/2)*b**12*x**12*sqrt(1 + b*x/a)/(15*a**40*b**5 + 150*a**39*b**6*x + 675*a**38*b**7*x**2 + 1800*a**37*b**8*x**3 + 3150*a**36*b**9*x**4 + 3780*a**35*b**10*x**5 + 3150*a**34*b**11*x**6 + 1800*a**33*b**12*x**7 + 675*a**32*b**13*x**8 + 150*a**31*b**14*x**9 + 15*a**30*b**15*x**10)","B",0
352,1,163,0,1.199973," ","integrate(x**3/(b*x+a)**(5/2),x)","\begin{cases} - \frac{32 a^{3}}{3 a b^{4} \sqrt{a + b x} + 3 b^{5} x \sqrt{a + b x}} - \frac{48 a^{2} b x}{3 a b^{4} \sqrt{a + b x} + 3 b^{5} x \sqrt{a + b x}} - \frac{12 a b^{2} x^{2}}{3 a b^{4} \sqrt{a + b x} + 3 b^{5} x \sqrt{a + b x}} + \frac{2 b^{3} x^{3}}{3 a b^{4} \sqrt{a + b x} + 3 b^{5} x \sqrt{a + b x}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*a**3/(3*a*b**4*sqrt(a + b*x) + 3*b**5*x*sqrt(a + b*x)) - 48*a**2*b*x/(3*a*b**4*sqrt(a + b*x) + 3*b**5*x*sqrt(a + b*x)) - 12*a*b**2*x**2/(3*a*b**4*sqrt(a + b*x) + 3*b**5*x*sqrt(a + b*x)) + 2*b**3*x**3/(3*a*b**4*sqrt(a + b*x) + 3*b**5*x*sqrt(a + b*x)), Ne(b, 0)), (x**4/(4*a**(5/2)), True))","A",0
353,1,121,0,1.275184," ","integrate(x**2/(b*x+a)**(5/2),x)","\begin{cases} \frac{16 a^{2}}{3 a b^{3} \sqrt{a + b x} + 3 b^{4} x \sqrt{a + b x}} + \frac{24 a b x}{3 a b^{3} \sqrt{a + b x} + 3 b^{4} x \sqrt{a + b x}} + \frac{6 b^{2} x^{2}}{3 a b^{3} \sqrt{a + b x} + 3 b^{4} x \sqrt{a + b x}} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**2/(3*a*b**3*sqrt(a + b*x) + 3*b**4*x*sqrt(a + b*x)) + 24*a*b*x/(3*a*b**3*sqrt(a + b*x) + 3*b**4*x*sqrt(a + b*x)) + 6*b**2*x**2/(3*a*b**3*sqrt(a + b*x) + 3*b**4*x*sqrt(a + b*x)), Ne(b, 0)), (x**3/(3*a**(5/2)), True))","A",0
354,1,80,0,1.127841," ","integrate(x/(b*x+a)**(5/2),x)","\begin{cases} - \frac{4 a}{3 a b^{2} \sqrt{a + b x} + 3 b^{3} x \sqrt{a + b x}} - \frac{6 b x}{3 a b^{2} \sqrt{a + b x} + 3 b^{3} x \sqrt{a + b x}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a/(3*a*b**2*sqrt(a + b*x) + 3*b**3*x*sqrt(a + b*x)) - 6*b*x/(3*a*b**2*sqrt(a + b*x) + 3*b**3*x*sqrt(a + b*x)), Ne(b, 0)), (x**2/(2*a**(5/2)), True))","A",0
355,1,14,0,0.074754," ","integrate(1/(b*x+a)**(5/2),x)","- \frac{2}{3 b \left(a + b x\right)^{\frac{3}{2}}}"," ",0,"-2/(3*b*(a + b*x)**(3/2))","A",0
356,1,697,0,2.993281," ","integrate(1/x/(b*x+a)**(5/2),x)","\frac{8 a^{7} \sqrt{1 + \frac{b x}{a}}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} + \frac{3 a^{7} \log{\left(\frac{b x}{a} \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} - \frac{6 a^{7} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} + \frac{14 a^{6} b x \sqrt{1 + \frac{b x}{a}}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} + \frac{9 a^{6} b x \log{\left(\frac{b x}{a} \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} - \frac{18 a^{6} b x \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} + \frac{6 a^{5} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} + \frac{9 a^{5} b^{2} x^{2} \log{\left(\frac{b x}{a} \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} - \frac{18 a^{5} b^{2} x^{2} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} + \frac{3 a^{4} b^{3} x^{3} \log{\left(\frac{b x}{a} \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}} - \frac{6 a^{4} b^{3} x^{3} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{3 a^{\frac{19}{2}} + 9 a^{\frac{17}{2}} b x + 9 a^{\frac{15}{2}} b^{2} x^{2} + 3 a^{\frac{13}{2}} b^{3} x^{3}}"," ",0,"8*a**7*sqrt(1 + b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) + 3*a**7*log(b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) - 6*a**7*log(sqrt(1 + b*x/a) + 1)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) + 14*a**6*b*x*sqrt(1 + b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) + 9*a**6*b*x*log(b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) - 18*a**6*b*x*log(sqrt(1 + b*x/a) + 1)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) + 6*a**5*b**2*x**2*sqrt(1 + b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) + 9*a**5*b**2*x**2*log(b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) - 18*a**5*b**2*x**2*log(sqrt(1 + b*x/a) + 1)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) + 3*a**4*b**3*x**3*log(b*x/a)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3) - 6*a**4*b**3*x**3*log(sqrt(1 + b*x/a) + 1)/(3*a**(19/2) + 9*a**(17/2)*b*x + 9*a**(15/2)*b**2*x**2 + 3*a**(13/2)*b**3*x**3)","B",0
357,1,818,0,5.596113," ","integrate(1/x**2/(b*x+a)**(5/2),x)","- \frac{6 a^{17} \sqrt{1 + \frac{b x}{a}}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{46 a^{16} b x \sqrt{1 + \frac{b x}{a}}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{15 a^{16} b x \log{\left(\frac{b x}{a} \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} + \frac{30 a^{16} b x \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{70 a^{15} b^{2} x^{2} \sqrt{1 + \frac{b x}{a}}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{45 a^{15} b^{2} x^{2} \log{\left(\frac{b x}{a} \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} + \frac{90 a^{15} b^{2} x^{2} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{30 a^{14} b^{3} x^{3} \sqrt{1 + \frac{b x}{a}}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{45 a^{14} b^{3} x^{3} \log{\left(\frac{b x}{a} \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} + \frac{90 a^{14} b^{3} x^{3} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} - \frac{15 a^{13} b^{4} x^{4} \log{\left(\frac{b x}{a} \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}} + \frac{30 a^{13} b^{4} x^{4} \log{\left(\sqrt{1 + \frac{b x}{a}} + 1 \right)}}{6 a^{\frac{39}{2}} x + 18 a^{\frac{37}{2}} b x^{2} + 18 a^{\frac{35}{2}} b^{2} x^{3} + 6 a^{\frac{33}{2}} b^{3} x^{4}}"," ",0,"-6*a**17*sqrt(1 + b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 46*a**16*b*x*sqrt(1 + b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 15*a**16*b*x*log(b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) + 30*a**16*b*x*log(sqrt(1 + b*x/a) + 1)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 70*a**15*b**2*x**2*sqrt(1 + b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 45*a**15*b**2*x**2*log(b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) + 90*a**15*b**2*x**2*log(sqrt(1 + b*x/a) + 1)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 30*a**14*b**3*x**3*sqrt(1 + b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 45*a**14*b**3*x**3*log(b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) + 90*a**14*b**3*x**3*log(sqrt(1 + b*x/a) + 1)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) - 15*a**13*b**4*x**4*log(b*x/a)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4) + 30*a**13*b**4*x**4*log(sqrt(1 + b*x/a) + 1)/(6*a**(39/2)*x + 18*a**(37/2)*b*x**2 + 18*a**(35/2)*b**2*x**3 + 6*a**(33/2)*b**3*x**4)","B",0
358,1,464,0,8.570831," ","integrate(1/x**3/(b*x+a)**(5/2),x)","- \frac{6 a^{\frac{89}{2}} b^{75} x^{75}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{21 a^{\frac{87}{2}} b^{76} x^{76}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{140 a^{\frac{85}{2}} b^{77} x^{77}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1}} + \frac{105 a^{\frac{83}{2}} b^{78} x^{78}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{105 a^{42} b^{\frac{155}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1}} - \frac{105 a^{41} b^{\frac{157}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1} \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} + 1} + 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} + 1}}"," ",0,"-6*a**(89/2)*b**75*x**75/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) + 1) + 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) + 1)) + 21*a**(87/2)*b**76*x**76/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) + 1) + 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) + 1)) + 140*a**(85/2)*b**77*x**77/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) + 1) + 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) + 1)) + 105*a**(83/2)*b**78*x**78/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) + 1) + 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) + 1)) - 105*a**42*b**(155/2)*x**(155/2)*sqrt(a/(b*x) + 1)*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) + 1) + 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) + 1)) - 105*a**41*b**(157/2)*x**(157/2)*sqrt(a/(b*x) + 1)*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) + 1) + 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) + 1))","B",0
359,1,54,0,1.226223," ","integrate(1/x/(b*x-a)**(1/2),x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a), Abs(a/(b*x)) > 1), (-2*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a), True))","A",0
360,1,121,0,2.457527," ","integrate(1/x**2/(b*x-a)**(1/2),x)","\begin{cases} \frac{i \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{a \sqrt{x}} + \frac{i b \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{3}{2}}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{1}{\sqrt{b} x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{\sqrt{b}}{a \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} - \frac{b \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(b)*sqrt(a/(b*x) - 1)/(a*sqrt(x)) + I*b*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(3/2), Abs(a/(b*x)) > 1), (-1/(sqrt(b)*x**(3/2)*sqrt(-a/(b*x) + 1)) + sqrt(b)/(a*sqrt(x)*sqrt(-a/(b*x) + 1)) - b*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(3/2), True))","B",0
361,1,216,0,4.199097," ","integrate(1/x**3/(b*x-a)**(1/2),x)","\begin{cases} \frac{i}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{i \sqrt{b}}{4 a x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{3 i b^{\frac{3}{2}}}{4 a^{2} \sqrt{x} \sqrt{\frac{a}{b x} - 1}} + \frac{3 i b^{2} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{5}{2}}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{1}{2 \sqrt{b} x^{\frac{5}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{\sqrt{b}}{4 a x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{3 b^{\frac{3}{2}}}{4 a^{2} \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} - \frac{3 b^{2} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I/(2*sqrt(b)*x**(5/2)*sqrt(a/(b*x) - 1)) + I*sqrt(b)/(4*a*x**(3/2)*sqrt(a/(b*x) - 1)) - 3*I*b**(3/2)/(4*a**2*sqrt(x)*sqrt(a/(b*x) - 1)) + 3*I*b**2*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(5/2)), Abs(a/(b*x)) > 1), (-1/(2*sqrt(b)*x**(5/2)*sqrt(-a/(b*x) + 1)) - sqrt(b)/(4*a*x**(3/2)*sqrt(-a/(b*x) + 1)) + 3*b**(3/2)/(4*a**2*sqrt(x)*sqrt(-a/(b*x) + 1)) - 3*b**2*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(5/2)), True))","A",0
362,1,478,0,2.199386," ","integrate(1/x/(b*x-a)**(3/2),x)","\begin{cases} \frac{2 i a^{3} \sqrt{-1 + \frac{b x}{a}}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} - \frac{a^{3} \log{\left(\frac{b x}{a} \right)}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} + \frac{2 a^{3} \log{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} + \frac{2 i a^{3} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} + \frac{a^{2} b x \log{\left(\frac{b x}{a} \right)}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} - \frac{2 a^{2} b x \log{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} - \frac{2 i a^{2} b x \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{i a^{\frac{9}{2}} - i a^{\frac{7}{2}} b x} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{2 a^{3} \sqrt{1 - \frac{b x}{a}}}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} + \frac{a^{3} \log{\left(\frac{b x}{a} \right)}}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} - \frac{2 a^{3} \log{\left(\sqrt{1 - \frac{b x}{a}} + 1 \right)}}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} - \frac{i \pi a^{3}}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} - \frac{a^{2} b x \log{\left(\frac{b x}{a} \right)}}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} + \frac{2 a^{2} b x \log{\left(\sqrt{1 - \frac{b x}{a}} + 1 \right)}}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} + \frac{i \pi a^{2} b x}{- i a^{\frac{9}{2}} + i a^{\frac{7}{2}} b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*a**3*sqrt(-1 + b*x/a)/(I*a**(9/2) - I*a**(7/2)*b*x) - a**3*log(b*x/a)/(I*a**(9/2) - I*a**(7/2)*b*x) + 2*a**3*log(sqrt(b)*sqrt(x)/sqrt(a))/(I*a**(9/2) - I*a**(7/2)*b*x) + 2*I*a**3*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(I*a**(9/2) - I*a**(7/2)*b*x) + a**2*b*x*log(b*x/a)/(I*a**(9/2) - I*a**(7/2)*b*x) - 2*a**2*b*x*log(sqrt(b)*sqrt(x)/sqrt(a))/(I*a**(9/2) - I*a**(7/2)*b*x) - 2*I*a**2*b*x*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(I*a**(9/2) - I*a**(7/2)*b*x), Abs(b*x/a) > 1), (2*a**3*sqrt(1 - b*x/a)/(-I*a**(9/2) + I*a**(7/2)*b*x) + a**3*log(b*x/a)/(-I*a**(9/2) + I*a**(7/2)*b*x) - 2*a**3*log(sqrt(1 - b*x/a) + 1)/(-I*a**(9/2) + I*a**(7/2)*b*x) - I*pi*a**3/(-I*a**(9/2) + I*a**(7/2)*b*x) - a**2*b*x*log(b*x/a)/(-I*a**(9/2) + I*a**(7/2)*b*x) + 2*a**2*b*x*log(sqrt(1 - b*x/a) + 1)/(-I*a**(9/2) + I*a**(7/2)*b*x) + I*pi*a**2*b*x/(-I*a**(9/2) + I*a**(7/2)*b*x), True))","C",0
363,1,156,0,3.498726," ","integrate(1/x**2/(b*x-a)**(3/2),x)","\begin{cases} - \frac{i}{a \sqrt{b} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{3 i \sqrt{b}}{a^{2} \sqrt{x} \sqrt{\frac{a}{b x} - 1}} - \frac{3 i b \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{5}{2}}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{1}{a \sqrt{b} x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{3 \sqrt{b}}{a^{2} \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} + \frac{3 b \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{a^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I/(a*sqrt(b)*x**(3/2)*sqrt(a/(b*x) - 1)) + 3*I*sqrt(b)/(a**2*sqrt(x)*sqrt(a/(b*x) - 1)) - 3*I*b*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(5/2), Abs(a/(b*x)) > 1), (1/(a*sqrt(b)*x**(3/2)*sqrt(-a/(b*x) + 1)) - 3*sqrt(b)/(a**2*sqrt(x)*sqrt(-a/(b*x) + 1)) + 3*b*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/a**(5/2), True))","A",0
364,1,226,0,5.566964," ","integrate(1/x**3/(b*x-a)**(3/2),x)","\begin{cases} - \frac{i}{2 a \sqrt{b} x^{\frac{5}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{5 i \sqrt{b}}{4 a^{2} x^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{15 i b^{\frac{3}{2}}}{4 a^{3} \sqrt{x} \sqrt{\frac{a}{b x} - 1}} - \frac{15 i b^{2} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{7}{2}}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{1}{2 a \sqrt{b} x^{\frac{5}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{5 \sqrt{b}}{4 a^{2} x^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{15 b^{\frac{3}{2}}}{4 a^{3} \sqrt{x} \sqrt{- \frac{a}{b x} + 1}} + \frac{15 b^{2} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{4 a^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I/(2*a*sqrt(b)*x**(5/2)*sqrt(a/(b*x) - 1)) - 5*I*sqrt(b)/(4*a**2*x**(3/2)*sqrt(a/(b*x) - 1)) + 15*I*b**(3/2)/(4*a**3*sqrt(x)*sqrt(a/(b*x) - 1)) - 15*I*b**2*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(7/2)), Abs(a/(b*x)) > 1), (1/(2*a*sqrt(b)*x**(5/2)*sqrt(-a/(b*x) + 1)) + 5*sqrt(b)/(4*a**2*x**(3/2)*sqrt(-a/(b*x) + 1)) - 15*b**(3/2)/(4*a**3*sqrt(x)*sqrt(-a/(b*x) + 1)) + 15*b**2*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(4*a**(7/2)), True))","A",0
365,-1,0,0,0.000000," ","integrate(1/x/(b*x-a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate(1/x**2/(b*x-a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,1,1108,0,11.218650," ","integrate(1/x**3/(b*x-a)**(5/2),x)","\begin{cases} \frac{12 i a^{\frac{89}{2}} b^{75} x^{75}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{42 i a^{\frac{87}{2}} b^{76} x^{76}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{280 i a^{\frac{85}{2}} b^{77} x^{77}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{210 i a^{\frac{83}{2}} b^{78} x^{78}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{210 i a^{42} b^{\frac{155}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{105 \pi a^{42} b^{\frac{155}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} - \frac{210 i a^{41} b^{\frac{157}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1} \operatorname{acosh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} + \frac{105 \pi a^{41} b^{\frac{157}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}}{24 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{\frac{a}{b x} - 1} - 24 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{6 a^{\frac{89}{2}} b^{75} x^{75}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} - 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{21 a^{\frac{87}{2}} b^{76} x^{76}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} - 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{140 a^{\frac{85}{2}} b^{77} x^{77}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} - 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{105 a^{\frac{83}{2}} b^{78} x^{78}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} - 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1}} - \frac{105 a^{42} b^{\frac{155}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} - 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1}} + \frac{105 a^{41} b^{\frac{157}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1} \operatorname{asin}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{12 a^{\frac{93}{2}} b^{\frac{151}{2}} x^{\frac{155}{2}} \sqrt{- \frac{a}{b x} + 1} - 12 a^{\frac{91}{2}} b^{\frac{153}{2}} x^{\frac{157}{2}} \sqrt{- \frac{a}{b x} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*I*a**(89/2)*b**75*x**75/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) + 42*I*a**(87/2)*b**76*x**76/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) - 280*I*a**(85/2)*b**77*x**77/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) + 210*I*a**(83/2)*b**78*x**78/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) + 210*I*a**42*b**(155/2)*x**(155/2)*sqrt(a/(b*x) - 1)*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) - 105*pi*a**42*b**(155/2)*x**(155/2)*sqrt(a/(b*x) - 1)/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) - 210*I*a**41*b**(157/2)*x**(157/2)*sqrt(a/(b*x) - 1)*acosh(sqrt(a)/(sqrt(b)*sqrt(x)))/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)) + 105*pi*a**41*b**(157/2)*x**(157/2)*sqrt(a/(b*x) - 1)/(24*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(a/(b*x) - 1) - 24*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(a/(b*x) - 1)), Abs(a/(b*x)) > 1), (-6*a**(89/2)*b**75*x**75/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(-a/(b*x) + 1) - 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(-a/(b*x) + 1)) - 21*a**(87/2)*b**76*x**76/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(-a/(b*x) + 1) - 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(-a/(b*x) + 1)) + 140*a**(85/2)*b**77*x**77/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(-a/(b*x) + 1) - 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(-a/(b*x) + 1)) - 105*a**(83/2)*b**78*x**78/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(-a/(b*x) + 1) - 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(-a/(b*x) + 1)) - 105*a**42*b**(155/2)*x**(155/2)*sqrt(-a/(b*x) + 1)*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(-a/(b*x) + 1) - 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(-a/(b*x) + 1)) + 105*a**41*b**(157/2)*x**(157/2)*sqrt(-a/(b*x) + 1)*asin(sqrt(a)/(sqrt(b)*sqrt(x)))/(12*a**(93/2)*b**(151/2)*x**(155/2)*sqrt(-a/(b*x) + 1) - 12*a**(91/2)*b**(153/2)*x**(157/2)*sqrt(-a/(b*x) + 1)), True))","B",0
368,1,78,0,84.074315," ","integrate(1/2*x**(-1+m)*(2*a*m+b*(-1+2*m)*x)/(b*x+a)**(3/2),x)","\frac{m x^{m} \Gamma\left(m\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, m \\ m + 1 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 1\right)} + \frac{b x x^{m} \left(2 m - 1\right) \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(m + 2\right)}"," ",0,"m*x**m*gamma(m)*hyper((3/2, m), (m + 1,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 1)) + b*x*x**m*(2*m - 1)*gamma(m + 1)*hyper((3/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m + 2))","C",0
369,1,73,0,5.344308," ","integrate(-1/2*b*x**m/(b*x+a)**(3/2)+m*x**(-1+m)/(b*x+a)**(1/2),x)","\frac{m x^{m} \Gamma\left(m\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m \\ m + 1 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 1\right)} - \frac{b x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{2 a^{\frac{3}{2}} \Gamma\left(m + 2\right)}"," ",0,"m*x**m*gamma(m)*hyper((1/2, m), (m + 1,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 1)) - b*x*x**m*gamma(m + 1)*hyper((3/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(2*a**(3/2)*gamma(m + 2))","C",0
370,1,24,0,1.091468," ","integrate(1/x/(b*x+a)**(1/2),x)","- \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)}}{\sqrt{a}}"," ",0,"-2*asinh(sqrt(a)/(sqrt(b)*sqrt(x)))/sqrt(a)","A",0
371,1,1742,0,2.832799," ","integrate(x**3*(b*x+a)**(1/3),x)","- \frac{243 a^{\frac{73}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{73}{3}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} - \frac{1377 a^{\frac{70}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{70}{3}} b x}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} - \frac{3213 a^{\frac{67}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{67}{3}} b^{2} x^{2}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} - \frac{3927 a^{\frac{64}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{4860 a^{\frac{64}{3}} b^{3} x^{3}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} - \frac{2163 a^{\frac{61}{3}} b^{4} x^{4} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{61}{3}} b^{4} x^{4}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{1827 a^{\frac{58}{3}} b^{5} x^{5} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{58}{3}} b^{5} x^{5}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{6573 a^{\frac{55}{3}} b^{6} x^{6} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{55}{3}} b^{6} x^{6}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{8787 a^{\frac{52}{3}} b^{7} x^{7} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{6498 a^{\frac{49}{3}} b^{8} x^{8} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{2562 a^{\frac{46}{3}} b^{9} x^{9} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}} + \frac{420 a^{\frac{43}{3}} b^{10} x^{10} \sqrt[3]{1 + \frac{b x}{a}}}{1820 a^{20} b^{4} + 10920 a^{19} b^{5} x + 27300 a^{18} b^{6} x^{2} + 36400 a^{17} b^{7} x^{3} + 27300 a^{16} b^{8} x^{4} + 10920 a^{15} b^{9} x^{5} + 1820 a^{14} b^{10} x^{6}}"," ",0,"-243*a**(73/3)*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 243*a**(73/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) - 1377*a**(70/3)*b*x*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 1458*a**(70/3)*b*x/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) - 3213*a**(67/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 3645*a**(67/3)*b**2*x**2/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) - 3927*a**(64/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 4860*a**(64/3)*b**3*x**3/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) - 2163*a**(61/3)*b**4*x**4*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 3645*a**(61/3)*b**4*x**4/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 1827*a**(58/3)*b**5*x**5*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 1458*a**(58/3)*b**5*x**5/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 6573*a**(55/3)*b**6*x**6*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 243*a**(55/3)*b**6*x**6/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 8787*a**(52/3)*b**7*x**7*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 6498*a**(49/3)*b**8*x**8*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 2562*a**(46/3)*b**9*x**9*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6) + 420*a**(43/3)*b**10*x**10*(1 + b*x/a)**(1/3)/(1820*a**20*b**4 + 10920*a**19*b**5*x + 27300*a**18*b**6*x**2 + 36400*a**17*b**7*x**3 + 27300*a**16*b**8*x**4 + 10920*a**15*b**9*x**5 + 1820*a**14*b**10*x**6)","B",0
372,1,666,0,1.855566," ","integrate(x**2*(b*x+a)**(1/3),x)","\frac{27 a^{\frac{34}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{34}{3}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} + \frac{72 a^{\frac{31}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{31}{3}} b x}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} + \frac{60 a^{\frac{28}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{28}{3}} b^{2} x^{2}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} + \frac{60 a^{\frac{25}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{25}{3}} b^{3} x^{3}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} + \frac{135 a^{\frac{22}{3}} b^{4} x^{4} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} + \frac{132 a^{\frac{19}{3}} b^{5} x^{5} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}} + \frac{42 a^{\frac{16}{3}} b^{6} x^{6} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{8} b^{3} + 420 a^{7} b^{4} x + 420 a^{6} b^{5} x^{2} + 140 a^{5} b^{6} x^{3}}"," ",0,"27*a**(34/3)*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) - 27*a**(34/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) + 72*a**(31/3)*b*x*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) - 81*a**(31/3)*b*x/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) + 60*a**(28/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) - 81*a**(28/3)*b**2*x**2/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) + 60*a**(25/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) - 27*a**(25/3)*b**3*x**3/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) + 135*a**(22/3)*b**4*x**4*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) + 132*a**(19/3)*b**5*x**5*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3) + 42*a**(16/3)*b**6*x**6*(1 + b*x/a)**(1/3)/(140*a**8*b**3 + 420*a**7*b**4*x + 420*a**6*b**5*x**2 + 140*a**5*b**6*x**3)","B",0
373,1,202,0,1.201129," ","integrate(x*(b*x+a)**(1/3),x)","- \frac{9 a^{\frac{13}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{9 a^{\frac{13}{3}}}{28 a^{2} b^{2} + 28 a b^{3} x} - \frac{6 a^{\frac{10}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{9 a^{\frac{10}{3}} b x}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{15 a^{\frac{7}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x} + \frac{12 a^{\frac{4}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{28 a^{2} b^{2} + 28 a b^{3} x}"," ",0,"-9*a**(13/3)*(1 + b*x/a)**(1/3)/(28*a**2*b**2 + 28*a*b**3*x) + 9*a**(13/3)/(28*a**2*b**2 + 28*a*b**3*x) - 6*a**(10/3)*b*x*(1 + b*x/a)**(1/3)/(28*a**2*b**2 + 28*a*b**3*x) + 9*a**(10/3)*b*x/(28*a**2*b**2 + 28*a*b**3*x) + 15*a**(7/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(28*a**2*b**2 + 28*a*b**3*x) + 12*a**(4/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(28*a**2*b**2 + 28*a*b**3*x)","B",0
374,1,12,0,0.065188," ","integrate((b*x+a)**(1/3),x)","\frac{3 \left(a + b x\right)^{\frac{4}{3}}}{4 b}"," ",0,"3*(a + b*x)**(4/3)/(4*b)","A",0
375,1,180,0,2.017864," ","integrate((b*x+a)**(1/3)/x,x)","\frac{4 \sqrt[3]{a} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{a} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{a} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} \Gamma\left(\frac{4}{3}\right)}{\Gamma\left(\frac{7}{3}\right)}"," ",0,"4*a**(1/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(3*gamma(7/3)) + 4*a**(1/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(3*gamma(7/3)) + 4*a**(1/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(3*gamma(7/3)) + 4*b**(1/3)*(a/b + x)**(1/3)*gamma(4/3)/gamma(7/3)","C",0
376,1,643,0,2.185470," ","integrate((b*x+a)**(1/3)/x**2,x)","\frac{4 a^{\frac{7}{3}} b e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{4 a^{\frac{7}{3}} b \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{4 a^{\frac{7}{3}} b e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{4 a^{\frac{4}{3}} b^{2} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{4 a^{\frac{4}{3}} b^{2} \left(\frac{a}{b} + x\right) \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{4 a^{\frac{4}{3}} b^{2} \left(\frac{a}{b} + x\right) e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{12 a^{2} b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"4*a**(7/3)*b*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3)) + 4*a**(7/3)*b*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3)) + 4*a**(7/3)*b*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3)) - 4*a**(4/3)*b**2*(a/b + x)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3)) - 4*a**(4/3)*b**2*(a/b + x)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3)) - 4*a**(4/3)*b**2*(a/b + x)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3)) + 12*a**2*b**(4/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(4/3)/(9*a**3*exp(2*I*pi/3)*gamma(7/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3))","C",0
377,1,2266,0,2.577403," ","integrate((b*x+a)**(1/3)/x**3,x)","- \frac{4 a^{\frac{16}{3}} b^{2} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{4 a^{\frac{16}{3}} b^{2} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{4 a^{\frac{16}{3}} b^{2} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{12 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{12 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right) \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{12 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right) e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{12 a^{\frac{10}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{12 a^{\frac{10}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{12 a^{\frac{10}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{4 a^{\frac{7}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{4 a^{\frac{7}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{4 a^{\frac{7}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} - \frac{12 a^{5} b^{\frac{7}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{6 a^{4} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)} + \frac{6 a^{3} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)}{27 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 81 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) + 81 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right) - 27 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}"," ",0,"-4*a**(16/3)*b**2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) - 4*a**(16/3)*b**2*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) - 4*a**(16/3)*b**2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 12*a**(13/3)*b**3*(a/b + x)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 12*a**(13/3)*b**3*(a/b + x)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 12*a**(13/3)*b**3*(a/b + x)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) - 12*a**(10/3)*b**4*(a/b + x)**2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) - 12*a**(10/3)*b**4*(a/b + x)**2*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) - 12*a**(10/3)*b**4*(a/b + x)**2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 4*a**(7/3)*b**5*(a/b + x)**3*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 4*a**(7/3)*b**5*(a/b + x)**3*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 4*a**(7/3)*b**5*(a/b + x)**3*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) - 12*a**5*b**(7/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 6*a**4*b**(10/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3)) + 6*a**3*b**(13/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(4/3)/(27*a**7*exp(2*I*pi/3)*gamma(7/3) - 81*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(7/3) + 81*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(7/3) - 27*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(7/3))","C",0
378,1,1742,0,3.073442," ","integrate(x**3*(b*x+a)**(2/3),x)","- \frac{243 a^{\frac{74}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{74}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} - \frac{1296 a^{\frac{71}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{71}{3}} b x}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} - \frac{2808 a^{\frac{68}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{68}{3}} b^{2} x^{2}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} - \frac{3120 a^{\frac{65}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{4860 a^{\frac{65}{3}} b^{3} x^{3}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} - \frac{1050 a^{\frac{62}{3}} b^{4} x^{4} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{62}{3}} b^{4} x^{4}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{4032 a^{\frac{59}{3}} b^{5} x^{5} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{59}{3}} b^{5} x^{5}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{11004 a^{\frac{56}{3}} b^{6} x^{6} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{56}{3}} b^{6} x^{6}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{14352 a^{\frac{53}{3}} b^{7} x^{7} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{10485 a^{\frac{50}{3}} b^{8} x^{8} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{4080 a^{\frac{47}{3}} b^{9} x^{9} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}} + \frac{660 a^{\frac{44}{3}} b^{10} x^{10} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{3080 a^{20} b^{4} + 18480 a^{19} b^{5} x + 46200 a^{18} b^{6} x^{2} + 61600 a^{17} b^{7} x^{3} + 46200 a^{16} b^{8} x^{4} + 18480 a^{15} b^{9} x^{5} + 3080 a^{14} b^{10} x^{6}}"," ",0,"-243*a**(74/3)*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 243*a**(74/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) - 1296*a**(71/3)*b*x*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 1458*a**(71/3)*b*x/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) - 2808*a**(68/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 3645*a**(68/3)*b**2*x**2/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) - 3120*a**(65/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 4860*a**(65/3)*b**3*x**3/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) - 1050*a**(62/3)*b**4*x**4*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 3645*a**(62/3)*b**4*x**4/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 4032*a**(59/3)*b**5*x**5*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 1458*a**(59/3)*b**5*x**5/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 11004*a**(56/3)*b**6*x**6*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 243*a**(56/3)*b**6*x**6/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 14352*a**(53/3)*b**7*x**7*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 10485*a**(50/3)*b**8*x**8*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 4080*a**(47/3)*b**9*x**9*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6) + 660*a**(44/3)*b**10*x**10*(1 + b*x/a)**(2/3)/(3080*a**20*b**4 + 18480*a**19*b**5*x + 46200*a**18*b**6*x**2 + 61600*a**17*b**7*x**3 + 46200*a**16*b**8*x**4 + 18480*a**15*b**9*x**5 + 3080*a**14*b**10*x**6)","B",0
379,1,666,0,1.938212," ","integrate(x**2*(b*x+a)**(2/3),x)","\frac{27 a^{\frac{35}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{35}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} + \frac{63 a^{\frac{32}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{32}{3}} b x}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} + \frac{42 a^{\frac{29}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{29}{3}} b^{2} x^{2}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} + \frac{78 a^{\frac{26}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{26}{3}} b^{3} x^{3}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} + \frac{207 a^{\frac{23}{3}} b^{4} x^{4} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} + \frac{195 a^{\frac{20}{3}} b^{5} x^{5} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}} + \frac{60 a^{\frac{17}{3}} b^{6} x^{6} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{220 a^{8} b^{3} + 660 a^{7} b^{4} x + 660 a^{6} b^{5} x^{2} + 220 a^{5} b^{6} x^{3}}"," ",0,"27*a**(35/3)*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) - 27*a**(35/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) + 63*a**(32/3)*b*x*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) - 81*a**(32/3)*b*x/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) + 42*a**(29/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) - 81*a**(29/3)*b**2*x**2/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) + 78*a**(26/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) - 27*a**(26/3)*b**3*x**3/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) + 207*a**(23/3)*b**4*x**4*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) + 195*a**(20/3)*b**5*x**5*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3) + 60*a**(17/3)*b**6*x**6*(1 + b*x/a)**(2/3)/(220*a**8*b**3 + 660*a**7*b**4*x + 660*a**6*b**5*x**2 + 220*a**5*b**6*x**3)","B",0
380,1,202,0,1.275785," ","integrate(x*(b*x+a)**(2/3),x)","- \frac{9 a^{\frac{14}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{2} b^{2} + 40 a b^{3} x} + \frac{9 a^{\frac{14}{3}}}{40 a^{2} b^{2} + 40 a b^{3} x} - \frac{3 a^{\frac{11}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{2} b^{2} + 40 a b^{3} x} + \frac{9 a^{\frac{11}{3}} b x}{40 a^{2} b^{2} + 40 a b^{3} x} + \frac{21 a^{\frac{8}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{2} b^{2} + 40 a b^{3} x} + \frac{15 a^{\frac{5}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{2} b^{2} + 40 a b^{3} x}"," ",0,"-9*a**(14/3)*(1 + b*x/a)**(2/3)/(40*a**2*b**2 + 40*a*b**3*x) + 9*a**(14/3)/(40*a**2*b**2 + 40*a*b**3*x) - 3*a**(11/3)*b*x*(1 + b*x/a)**(2/3)/(40*a**2*b**2 + 40*a*b**3*x) + 9*a**(11/3)*b*x/(40*a**2*b**2 + 40*a*b**3*x) + 21*a**(8/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(40*a**2*b**2 + 40*a*b**3*x) + 15*a**(5/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(40*a**2*b**2 + 40*a*b**3*x)","B",0
381,1,12,0,0.064895," ","integrate((b*x+a)**(2/3),x)","\frac{3 \left(a + b x\right)^{\frac{5}{3}}}{5 b}"," ",0,"3*(a + b*x)**(5/3)/(5*b)","A",0
382,1,182,0,2.056360," ","integrate((b*x+a)**(2/3)/x,x)","\frac{5 a^{\frac{2}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{5 a^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{5 a^{\frac{2}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{3 \Gamma\left(\frac{8}{3}\right)} + \frac{5 b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} \Gamma\left(\frac{5}{3}\right)}{2 \Gamma\left(\frac{8}{3}\right)}"," ",0,"5*a**(2/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(3*gamma(8/3)) + 5*a**(2/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(3*gamma(8/3)) + 5*a**(2/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(3*gamma(8/3)) + 5*b**(2/3)*(a/b + x)**(2/3)*gamma(5/3)/(2*gamma(8/3))","C",0
383,1,643,0,2.237843," ","integrate((b*x+a)**(2/3)/x**2,x)","\frac{10 a^{\frac{8}{3}} b e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{10 a^{\frac{8}{3}} b e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{10 a^{\frac{8}{3}} b \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{10 a^{\frac{5}{3}} b^{2} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{10 a^{\frac{5}{3}} b^{2} \left(\frac{a}{b} + x\right) e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{10 a^{\frac{5}{3}} b^{2} \left(\frac{a}{b} + x\right) \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{15 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"10*a**(8/3)*b*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3)) + 10*a**(8/3)*b*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3)) + 10*a**(8/3)*b*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3)) - 10*a**(5/3)*b**2*(a/b + x)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3)) - 10*a**(5/3)*b**2*(a/b + x)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3)) - 10*a**(5/3)*b**2*(a/b + x)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3)) + 15*a**2*b**(5/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(5/3)/(9*a**3*exp(2*I*pi/3)*gamma(8/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3))","C",0
384,1,2266,0,2.654717," ","integrate((b*x+a)**(2/3)/x**3,x)","- \frac{10 a^{\frac{17}{3}} b^{2} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{10 a^{\frac{17}{3}} b^{2} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{10 a^{\frac{17}{3}} b^{2} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{30 a^{\frac{14}{3}} b^{3} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{30 a^{\frac{14}{3}} b^{3} \left(\frac{a}{b} + x\right) e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{30 a^{\frac{14}{3}} b^{3} \left(\frac{a}{b} + x\right) \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{30 a^{\frac{11}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{30 a^{\frac{11}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{30 a^{\frac{11}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{10 a^{\frac{8}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{10 a^{\frac{8}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{10 a^{\frac{8}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{15 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} - \frac{15 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)} + \frac{30 a^{3} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{8}{3}\right)}"," ",0,"-10*a**(17/3)*b**2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 10*a**(17/3)*b**2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 10*a**(17/3)*b**2*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 30*a**(14/3)*b**3*(a/b + x)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 30*a**(14/3)*b**3*(a/b + x)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 30*a**(14/3)*b**3*(a/b + x)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 30*a**(11/3)*b**4*(a/b + x)**2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 30*a**(11/3)*b**4*(a/b + x)**2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 30*a**(11/3)*b**4*(a/b + x)**2*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 10*a**(8/3)*b**5*(a/b + x)**3*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 10*a**(8/3)*b**5*(a/b + x)**3*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 10*a**(8/3)*b**5*(a/b + x)**3*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 15*a**5*b**(8/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) - 15*a**4*b**(11/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3)) + 30*a**3*b**(14/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(5/3)/(54*a**7*exp(2*I*pi/3)*gamma(8/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(8/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(8/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(8/3))","C",0
385,1,1844,0,3.177831," ","integrate(x**3*(b*x+a)**(4/3),x)","- \frac{243 a^{\frac{76}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{76}{3}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} - \frac{1377 a^{\frac{73}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{73}{3}} b x}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} - \frac{3213 a^{\frac{70}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{70}{3}} b^{2} x^{2}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} - \frac{3927 a^{\frac{67}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{4860 a^{\frac{67}{3}} b^{3} x^{3}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} - \frac{798 a^{\frac{64}{3}} b^{4} x^{4} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{64}{3}} b^{4} x^{4}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{11382 a^{\frac{61}{3}} b^{5} x^{5} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{61}{3}} b^{5} x^{5}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{35238 a^{\frac{58}{3}} b^{6} x^{6} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{58}{3}} b^{6} x^{6}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{56562 a^{\frac{55}{3}} b^{7} x^{7} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{54273 a^{\frac{52}{3}} b^{8} x^{8} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{31227 a^{\frac{49}{3}} b^{9} x^{9} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{9975 a^{\frac{46}{3}} b^{10} x^{10} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}} + \frac{1365 a^{\frac{43}{3}} b^{11} x^{11} \sqrt[3]{1 + \frac{b x}{a}}}{7280 a^{20} b^{4} + 43680 a^{19} b^{5} x + 109200 a^{18} b^{6} x^{2} + 145600 a^{17} b^{7} x^{3} + 109200 a^{16} b^{8} x^{4} + 43680 a^{15} b^{9} x^{5} + 7280 a^{14} b^{10} x^{6}}"," ",0,"-243*a**(76/3)*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 243*a**(76/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) - 1377*a**(73/3)*b*x*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 1458*a**(73/3)*b*x/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) - 3213*a**(70/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 3645*a**(70/3)*b**2*x**2/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) - 3927*a**(67/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 4860*a**(67/3)*b**3*x**3/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) - 798*a**(64/3)*b**4*x**4*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 3645*a**(64/3)*b**4*x**4/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 11382*a**(61/3)*b**5*x**5*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 1458*a**(61/3)*b**5*x**5/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 35238*a**(58/3)*b**6*x**6*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 243*a**(58/3)*b**6*x**6/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 56562*a**(55/3)*b**7*x**7*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 54273*a**(52/3)*b**8*x**8*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 31227*a**(49/3)*b**9*x**9*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 9975*a**(46/3)*b**10*x**10*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6) + 1365*a**(43/3)*b**11*x**11*(1 + b*x/a)**(1/3)/(7280*a**20*b**4 + 43680*a**19*b**5*x + 109200*a**18*b**6*x**2 + 145600*a**17*b**7*x**3 + 109200*a**16*b**8*x**4 + 43680*a**15*b**9*x**5 + 7280*a**14*b**10*x**6)","B",0
386,1,733,0,2.159754," ","integrate(x**2*(b*x+a)**(4/3),x)","\frac{27 a^{\frac{37}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{37}{3}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{72 a^{\frac{34}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{34}{3}} b x}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{60 a^{\frac{31}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{31}{3}} b^{2} x^{2}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{165 a^{\frac{28}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{28}{3}} b^{3} x^{3}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{555 a^{\frac{25}{3}} b^{4} x^{4} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{762 a^{\frac{22}{3}} b^{5} x^{5} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{462 a^{\frac{19}{3}} b^{6} x^{6} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}} + \frac{105 a^{\frac{16}{3}} b^{7} x^{7} \sqrt[3]{1 + \frac{b x}{a}}}{455 a^{8} b^{3} + 1365 a^{7} b^{4} x + 1365 a^{6} b^{5} x^{2} + 455 a^{5} b^{6} x^{3}}"," ",0,"27*a**(37/3)*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) - 27*a**(37/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 72*a**(34/3)*b*x*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) - 81*a**(34/3)*b*x/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 60*a**(31/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) - 81*a**(31/3)*b**2*x**2/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 165*a**(28/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) - 27*a**(28/3)*b**3*x**3/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 555*a**(25/3)*b**4*x**4*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 762*a**(22/3)*b**5*x**5*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 462*a**(19/3)*b**6*x**6*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3) + 105*a**(16/3)*b**7*x**7*(1 + b*x/a)**(1/3)/(455*a**8*b**3 + 1365*a**7*b**4*x + 1365*a**6*b**5*x**2 + 455*a**5*b**6*x**3)","B",0
387,1,80,0,1.492757," ","integrate(x*(b*x+a)**(4/3),x)","\begin{cases} - \frac{9 a^{3} \sqrt[3]{a + b x}}{70 b^{2}} + \frac{3 a^{2} x \sqrt[3]{a + b x}}{70 b} + \frac{33 a x^{2} \sqrt[3]{a + b x}}{70} + \frac{3 b x^{3} \sqrt[3]{a + b x}}{10} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{3}} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*a**3*(a + b*x)**(1/3)/(70*b**2) + 3*a**2*x*(a + b*x)**(1/3)/(70*b) + 33*a*x**2*(a + b*x)**(1/3)/70 + 3*b*x**3*(a + b*x)**(1/3)/10, Ne(b, 0)), (a**(4/3)*x**2/2, True))","A",0
388,1,12,0,0.065571," ","integrate((b*x+a)**(4/3),x)","\frac{3 \left(a + b x\right)^{\frac{7}{3}}}{7 b}"," ",0,"3*(a + b*x)**(7/3)/(7*b)","A",0
389,1,209,0,2.387751," ","integrate((b*x+a)**(4/3)/x,x)","\frac{7 a^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{7 a^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{7 a^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{3 \Gamma\left(\frac{10}{3}\right)} + \frac{7 a \sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} \Gamma\left(\frac{7}{3}\right)}{\Gamma\left(\frac{10}{3}\right)} + \frac{7 b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} \Gamma\left(\frac{7}{3}\right)}{4 \Gamma\left(\frac{10}{3}\right)}"," ",0,"7*a**(4/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(3*gamma(10/3)) + 7*a**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(3*gamma(10/3)) + 7*a**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(3*gamma(10/3)) + 7*a*b**(1/3)*(a/b + x)**(1/3)*gamma(7/3)/gamma(10/3) + 7*b**(4/3)*(a/b + x)**(4/3)*gamma(7/3)/(4*gamma(10/3))","C",0
390,1,719,0,2.580023," ","integrate((b*x+a)**(4/3)/x**2,x)","\frac{28 a^{\frac{10}{3}} b e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{28 a^{\frac{10}{3}} b \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{28 a^{\frac{10}{3}} b e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 a^{\frac{7}{3}} b^{2} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 a^{\frac{7}{3}} b^{2} \left(\frac{a}{b} + x\right) \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 a^{\frac{7}{3}} b^{2} \left(\frac{a}{b} + x\right) e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 a^{3} b^{\frac{4}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{63 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{9 a^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 9 a^{2} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"28*a**(10/3)*b*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) + 28*a**(10/3)*b*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) + 28*a**(10/3)*b*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) - 28*a**(7/3)*b**2*(a/b + x)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) - 28*a**(7/3)*b**2*(a/b + x)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) - 28*a**(7/3)*b**2*(a/b + x)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) + 84*a**3*b**(4/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3)) - 63*a**2*b**(7/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(7/3)/(9*a**3*exp(2*I*pi/3)*gamma(10/3) - 9*a**2*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3))","C",0
391,1,2266,0,2.737850," ","integrate((b*x+a)**(4/3)/x**3,x)","\frac{28 a^{\frac{19}{3}} b^{2} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{28 a^{\frac{19}{3}} b^{2} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{28 a^{\frac{19}{3}} b^{2} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{84 a^{\frac{16}{3}} b^{3} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{84 a^{\frac{16}{3}} b^{3} \left(\frac{a}{b} + x\right) \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{84 a^{\frac{16}{3}} b^{3} \left(\frac{a}{b} + x\right) e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 a^{\frac{13}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 a^{\frac{13}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 a^{\frac{13}{3}} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 a^{\frac{10}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 a^{\frac{10}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{28 a^{\frac{10}{3}} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{84 a^{6} b^{\frac{7}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} - \frac{231 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)} + \frac{147 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{7}{3}\right)}{54 a^{7} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 162 a^{6} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) + 162 a^{5} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right) - 54 a^{4} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{10}{3}\right)}"," ",0,"28*a**(19/3)*b**2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 28*a**(19/3)*b**2*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 28*a**(19/3)*b**2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 84*a**(16/3)*b**3*(a/b + x)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 84*a**(16/3)*b**3*(a/b + x)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 84*a**(16/3)*b**3*(a/b + x)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 84*a**(13/3)*b**4*(a/b + x)**2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 84*a**(13/3)*b**4*(a/b + x)**2*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 84*a**(13/3)*b**4*(a/b + x)**2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 28*a**(10/3)*b**5*(a/b + x)**3*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 28*a**(10/3)*b**5*(a/b + x)**3*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 28*a**(10/3)*b**5*(a/b + x)**3*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 84*a**6*b**(7/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) - 231*a**5*b**(10/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3)) + 147*a**4*b**(13/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(7/3)/(54*a**7*exp(2*I*pi/3)*gamma(10/3) - 162*a**6*b*(a/b + x)*exp(2*I*pi/3)*gamma(10/3) + 162*a**5*b**2*(a/b + x)**2*exp(2*I*pi/3)*gamma(10/3) - 54*a**4*b**3*(a/b + x)**3*exp(2*I*pi/3)*gamma(10/3))","C",0
392,1,1640,0,2.776629," ","integrate(x**3/(b*x+a)**(1/3),x)","- \frac{243 a^{\frac{71}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{71}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} - \frac{1296 a^{\frac{68}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{68}{3}} b x}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} - \frac{2808 a^{\frac{65}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{65}{3}} b^{2} x^{2}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} - \frac{3120 a^{\frac{62}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{4860 a^{\frac{62}{3}} b^{3} x^{3}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} - \frac{1710 a^{\frac{59}{3}} b^{4} x^{4} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{59}{3}} b^{4} x^{4}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{72 a^{\frac{56}{3}} b^{5} x^{5} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{56}{3}} b^{5} x^{5}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{1104 a^{\frac{53}{3}} b^{6} x^{6} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{53}{3}} b^{6} x^{6}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{1152 a^{\frac{50}{3}} b^{7} x^{7} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{585 a^{\frac{47}{3}} b^{8} x^{8} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}} + \frac{120 a^{\frac{44}{3}} b^{9} x^{9} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} + 2640 a^{19} b^{5} x + 6600 a^{18} b^{6} x^{2} + 8800 a^{17} b^{7} x^{3} + 6600 a^{16} b^{8} x^{4} + 2640 a^{15} b^{9} x^{5} + 440 a^{14} b^{10} x^{6}}"," ",0,"-243*a**(71/3)*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 243*a**(71/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) - 1296*a**(68/3)*b*x*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 1458*a**(68/3)*b*x/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) - 2808*a**(65/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 3645*a**(65/3)*b**2*x**2/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) - 3120*a**(62/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 4860*a**(62/3)*b**3*x**3/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) - 1710*a**(59/3)*b**4*x**4*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 3645*a**(59/3)*b**4*x**4/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 72*a**(56/3)*b**5*x**5*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 1458*a**(56/3)*b**5*x**5/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 1104*a**(53/3)*b**6*x**6*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 243*a**(53/3)*b**6*x**6/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 1152*a**(50/3)*b**7*x**7*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 585*a**(47/3)*b**8*x**8*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6) + 120*a**(44/3)*b**9*x**9*(1 + b*x/a)**(2/3)/(440*a**20*b**4 + 2640*a**19*b**5*x + 6600*a**18*b**6*x**2 + 8800*a**17*b**7*x**3 + 6600*a**16*b**8*x**4 + 2640*a**15*b**9*x**5 + 440*a**14*b**10*x**6)","B",0
393,1,600,0,1.770458," ","integrate(x**2/(b*x+a)**(1/3),x)","\frac{27 a^{\frac{32}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{32}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{63 a^{\frac{29}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{29}{3}} b x}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{42 a^{\frac{26}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{26}{3}} b^{2} x^{2}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{18 a^{\frac{23}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{23}{3}} b^{3} x^{3}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{20}{3}} b^{4} x^{4} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{15 a^{\frac{17}{3}} b^{5} x^{5} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{8} b^{3} + 120 a^{7} b^{4} x + 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}}"," ",0,"27*a**(32/3)*(1 + b*x/a)**(2/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 27*a**(32/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 63*a**(29/3)*b*x*(1 + b*x/a)**(2/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 81*a**(29/3)*b*x/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 42*a**(26/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 81*a**(26/3)*b**2*x**2/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 18*a**(23/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 27*a**(23/3)*b**3*x**3/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 27*a**(20/3)*b**4*x**4*(1 + b*x/a)**(2/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 15*a**(17/3)*b**5*x**5*(1 + b*x/a)**(2/3)/(40*a**8*b**3 + 120*a**7*b**4*x + 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3)","B",0
394,1,162,0,1.156600," ","integrate(x/(b*x+a)**(1/3),x)","- \frac{9 a^{\frac{11}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{10 a^{2} b^{2} + 10 a b^{3} x} + \frac{9 a^{\frac{11}{3}}}{10 a^{2} b^{2} + 10 a b^{3} x} - \frac{3 a^{\frac{8}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{10 a^{2} b^{2} + 10 a b^{3} x} + \frac{9 a^{\frac{8}{3}} b x}{10 a^{2} b^{2} + 10 a b^{3} x} + \frac{6 a^{\frac{5}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{10 a^{2} b^{2} + 10 a b^{3} x}"," ",0,"-9*a**(11/3)*(1 + b*x/a)**(2/3)/(10*a**2*b**2 + 10*a*b**3*x) + 9*a**(11/3)/(10*a**2*b**2 + 10*a*b**3*x) - 3*a**(8/3)*b*x*(1 + b*x/a)**(2/3)/(10*a**2*b**2 + 10*a*b**3*x) + 9*a**(8/3)*b*x/(10*a**2*b**2 + 10*a*b**3*x) + 6*a**(5/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(10*a**2*b**2 + 10*a*b**3*x)","B",0
395,1,12,0,0.063720," ","integrate(1/(b*x+a)**(1/3),x)","\frac{3 \left(a + b x\right)^{\frac{2}{3}}}{2 b}"," ",0,"3*(a + b*x)**(2/3)/(2*b)","A",0
396,1,155,0,1.881266," ","integrate(1/x/(b*x+a)**(1/3),x)","\frac{2 \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)} + \frac{2 e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)} + \frac{2 e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"2*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(3*a**(1/3)*gamma(5/3)) + 2*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(3*a**(1/3)*gamma(5/3)) + 2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(3*a**(1/3)*gamma(5/3))","C",0
397,1,831,0,2.203847," ","integrate(1/x**2/(b*x+a)**(1/3),x)","- \frac{2 a^{\frac{5}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{5}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{5}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{2 a^{\frac{2}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{2 a^{\frac{2}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{2 a^{\frac{2}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{6 a b^{3} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 a^{2} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-2*a**(5/3)*b**(7/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(5/3)*b**(7/3)*(a/b + x)**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(5/3)*b**(7/3)*(a/b + x)**(4/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) + 2*a**(2/3)*b**(10/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) + 2*a**(2/3)*b**(10/3)*(a/b + x)**(7/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) + 2*a**(2/3)*b**(10/3)*(a/b + x)**(7/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) + 6*a*b**3*(a/b + x)**2*exp(2*I*pi/3)*gamma(2/3)/(9*a**3*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 9*a**2*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3))","C",0
398,1,2730,0,2.585527," ","integrate(1/x**3/(b*x+a)**(1/3),x)","\frac{4 a^{\frac{14}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{4 a^{\frac{14}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{4 a^{\frac{14}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{11}{3}} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{11}{3}} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{11}{3}} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{12 a^{\frac{8}{3}} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{12 a^{\frac{8}{3}} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{12 a^{\frac{8}{3}} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{5}{3}} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{5}{3}} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{5}{3}} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{21 a^{4} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{33 a^{3} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{2} b^{6} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 81 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 27 a^{4} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"4*a**(14/3)*b**(10/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 4*a**(14/3)*b**(10/3)*(a/b + x)**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 4*a**(14/3)*b**(10/3)*(a/b + x)**(4/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(11/3)*b**(13/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(11/3)*b**(13/3)*(a/b + x)**(7/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(11/3)*b**(13/3)*(a/b + x)**(7/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 12*a**(8/3)*b**(16/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 12*a**(8/3)*b**(16/3)*(a/b + x)**(10/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 12*a**(8/3)*b**(16/3)*(a/b + x)**(10/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(5/3)*b**(19/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(5/3)*b**(19/3)*(a/b + x)**(13/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(5/3)*b**(19/3)*(a/b + x)**(13/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 21*a**4*b**4*(a/b + x)**2*exp(2*I*pi/3)*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 33*a**3*b**5*(a/b + x)**3*exp(2*I*pi/3)*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**2*b**6*(a/b + x)**4*exp(2*I*pi/3)*gamma(2/3)/(27*a**7*b**(4/3)*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) - 81*a**6*b**(7/3)*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) - 27*a**4*b**(13/3)*(a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3))","C",0
399,1,4974,0,2.977006," ","integrate(x**3/(b*x-a)**(1/3),x)","\begin{cases} \frac{243 a^{\frac{71}{3}} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{71}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1296 a^{\frac{68}{3}} b x \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{68}{3}} b x}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{2808 a^{\frac{65}{3}} b^{2} x^{2} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{65}{3}} b^{2} x^{2}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{3120 a^{\frac{62}{3}} b^{3} x^{3} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{4860 a^{\frac{62}{3}} b^{3} x^{3}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{1710 a^{\frac{59}{3}} b^{4} x^{4} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{59}{3}} b^{4} x^{4}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{72 a^{\frac{56}{3}} b^{5} x^{5} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{56}{3}} b^{5} x^{5}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1104 a^{\frac{53}{3}} b^{6} x^{6} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{53}{3}} b^{6} x^{6}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{1152 a^{\frac{50}{3}} b^{7} x^{7} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{585 a^{\frac{47}{3}} b^{8} x^{8} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{120 a^{\frac{44}{3}} b^{9} x^{9} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{243 a^{\frac{71}{3}} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{71}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{1296 a^{\frac{68}{3}} b x \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{68}{3}} b x}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{2808 a^{\frac{65}{3}} b^{2} x^{2} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{65}{3}} b^{2} x^{2}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{3120 a^{\frac{62}{3}} b^{3} x^{3} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{4860 a^{\frac{62}{3}} b^{3} x^{3}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1710 a^{\frac{59}{3}} b^{4} x^{4} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{59}{3}} b^{4} x^{4}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{72 a^{\frac{56}{3}} b^{5} x^{5} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{56}{3}} b^{5} x^{5}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{1104 a^{\frac{53}{3}} b^{6} x^{6} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{53}{3}} b^{6} x^{6}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{1152 a^{\frac{50}{3}} b^{7} x^{7} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} + \frac{585 a^{\frac{47}{3}} b^{8} x^{8} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} - \frac{120 a^{\frac{44}{3}} b^{9} x^{9} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{4} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{5} x e^{\frac{i \pi}{3}} + 6600 a^{18} b^{6} x^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{7} x^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{8} x^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{9} x^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{10} x^{6} e^{\frac{i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((243*a**(71/3)*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 243*a**(71/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1296*a**(68/3)*b*x*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1458*a**(68/3)*b*x/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 2808*a**(65/3)*b**2*x**2*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 3645*a**(65/3)*b**2*x**2/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 3120*a**(62/3)*b**3*x**3*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 4860*a**(62/3)*b**3*x**3/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 1710*a**(59/3)*b**4*x**4*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 3645*a**(59/3)*b**4*x**4/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 72*a**(56/3)*b**5*x**5*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1458*a**(56/3)*b**5*x**5/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1104*a**(53/3)*b**6*x**6*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 243*a**(53/3)*b**6*x**6/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 1152*a**(50/3)*b**7*x**7*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 585*a**(47/3)*b**8*x**8*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 120*a**(44/3)*b**9*x**9*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)), Abs(b*x/a) > 1), (-243*a**(71/3)*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 243*a**(71/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 1296*a**(68/3)*b*x*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1458*a**(68/3)*b*x/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 2808*a**(65/3)*b**2*x**2*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 3645*a**(65/3)*b**2*x**2/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 3120*a**(62/3)*b**3*x**3*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 4860*a**(62/3)*b**3*x**3/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1710*a**(59/3)*b**4*x**4*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 3645*a**(59/3)*b**4*x**4/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 72*a**(56/3)*b**5*x**5*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1458*a**(56/3)*b**5*x**5/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 1104*a**(53/3)*b**6*x**6*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 243*a**(53/3)*b**6*x**6/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 1152*a**(50/3)*b**7*x**7*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) + 585*a**(47/3)*b**8*x**8*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)) - 120*a**(44/3)*b**9*x**9*(1 - b*x/a)**(2/3)/(440*a**20*b**4*exp(I*pi/3) - 2640*a**19*b**5*x*exp(I*pi/3) + 6600*a**18*b**6*x**2*exp(I*pi/3) - 8800*a**17*b**7*x**3*exp(I*pi/3) + 6600*a**16*b**8*x**4*exp(I*pi/3) - 2640*a**15*b**9*x**5*exp(I*pi/3) + 440*a**14*b**10*x**6*exp(I*pi/3)), True))","C",0
400,1,1326,0,1.896523," ","integrate(x**2/(b*x-a)**(1/3),x)","\begin{cases} - \frac{27 a^{\frac{32}{3}} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{32}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{63 a^{\frac{29}{3}} b x \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{29}{3}} b x e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{42 a^{\frac{26}{3}} b^{2} x^{2} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{81 a^{\frac{26}{3}} b^{2} x^{2} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{18 a^{\frac{23}{3}} b^{3} x^{3} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{23}{3}} b^{3} x^{3} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{20}{3}} b^{4} x^{4} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{15 a^{\frac{17}{3}} b^{5} x^{5} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{27 a^{\frac{32}{3}} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{32}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{63 a^{\frac{29}{3}} b x \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{29}{3}} b x e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{42 a^{\frac{26}{3}} b^{2} x^{2} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{81 a^{\frac{26}{3}} b^{2} x^{2} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{18 a^{\frac{23}{3}} b^{3} x^{3} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{23}{3}} b^{3} x^{3} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{20}{3}} b^{4} x^{4} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} + \frac{15 a^{\frac{17}{3}} b^{5} x^{5} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{3} + 120 a^{7} b^{4} x - 120 a^{6} b^{5} x^{2} + 40 a^{5} b^{6} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-27*a**(32/3)*(-1 + b*x/a)**(2/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 27*a**(32/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 63*a**(29/3)*b*x*(-1 + b*x/a)**(2/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 81*a**(29/3)*b*x*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 42*a**(26/3)*b**2*x**2*(-1 + b*x/a)**(2/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 81*a**(26/3)*b**2*x**2*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 18*a**(23/3)*b**3*x**3*(-1 + b*x/a)**(2/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 27*a**(23/3)*b**3*x**3*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 27*a**(20/3)*b**4*x**4*(-1 + b*x/a)**(2/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 15*a**(17/3)*b**5*x**5*(-1 + b*x/a)**(2/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3), Abs(b*x/a) > 1), (-27*a**(32/3)*(1 - b*x/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 27*a**(32/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 63*a**(29/3)*b*x*(1 - b*x/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 81*a**(29/3)*b*x*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 42*a**(26/3)*b**2*x**2*(1 - b*x/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 81*a**(26/3)*b**2*x**2*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 18*a**(23/3)*b**3*x**3*(1 - b*x/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 27*a**(23/3)*b**3*x**3*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) - 27*a**(20/3)*b**4*x**4*(1 - b*x/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3) + 15*a**(17/3)*b**5*x**5*(1 - b*x/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**3 + 120*a**7*b**4*x - 120*a**6*b**5*x**2 + 40*a**5*b**6*x**3), True))","C",0
401,1,486,0,1.260549," ","integrate(x/(b*x-a)**(1/3),x)","\begin{cases} - \frac{9 a^{\frac{11}{3}} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} - \frac{9 a^{\frac{11}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} + \frac{3 a^{\frac{8}{3}} b x \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} + \frac{9 a^{\frac{8}{3}} b x}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} + \frac{6 a^{\frac{5}{3}} b^{2} x^{2} \left(-1 + \frac{b x}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{9 a^{\frac{11}{3}} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} - \frac{9 a^{\frac{11}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} - \frac{3 a^{\frac{8}{3}} b x \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} + \frac{9 a^{\frac{8}{3}} b x}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} - \frac{6 a^{\frac{5}{3}} b^{2} x^{2} \left(1 - \frac{b x}{a}\right)^{\frac{2}{3}}}{- 10 a^{2} b^{2} e^{\frac{i \pi}{3}} + 10 a b^{3} x e^{\frac{i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*a**(11/3)*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) - 9*a**(11/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) + 3*a**(8/3)*b*x*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) + 9*a**(8/3)*b*x/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) + 6*a**(5/3)*b**2*x**2*(-1 + b*x/a)**(2/3)*exp(I*pi/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)), Abs(b*x/a) > 1), (9*a**(11/3)*(1 - b*x/a)**(2/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) - 9*a**(11/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) - 3*a**(8/3)*b*x*(1 - b*x/a)**(2/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) + 9*a**(8/3)*b*x/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)) - 6*a**(5/3)*b**2*x**2*(1 - b*x/a)**(2/3)/(-10*a**2*b**2*exp(I*pi/3) + 10*a*b**3*x*exp(I*pi/3)), True))","C",0
402,1,12,0,0.065720," ","integrate(1/(b*x-a)**(1/3),x)","\frac{3 \left(- a + b x\right)^{\frac{2}{3}}}{2 b}"," ",0,"3*(-a + b*x)**(2/3)/(2*b)","A",0
403,1,160,0,1.877597," ","integrate(1/x/(b*x-a)**(1/3),x)","- \frac{2 e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)} - \frac{2 \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)} - \frac{2 e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{3 \sqrt[3]{a} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-2*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(3*a**(1/3)*gamma(5/3)) - 2*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(3*a**(1/3)*gamma(5/3)) - 2*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(3*a**(1/3)*gamma(5/3))","C",0
404,1,838,0,2.236202," ","integrate(1/x**2/(b*x-a)**(1/3),x)","- \frac{2 a^{\frac{5}{3}} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{5}{3}} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{5}{3}} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{2}{3}} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{2}{3}} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 a^{\frac{2}{3}} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{6 a b^{3} \left(- \frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{9 a^{3} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 9 a^{2} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-2*a**(5/3)*b**(7/3)*(-a/b + x)**(4/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(5/3)*b**(7/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(5/3)*b**(7/3)*(-a/b + x)**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(2/3)*b**(10/3)*(-a/b + x)**(7/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(2/3)*b**(10/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) - 2*a**(2/3)*b**(10/3)*(-a/b + x)**(7/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3)) + 6*a*b**3*(-a/b + x)**2*exp(2*I*pi/3)*gamma(2/3)/(9*a**3*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 9*a**2*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3))","C",0
405,1,2744,0,2.615067," ","integrate(1/x**3/(b*x-a)**(1/3),x)","- \frac{4 a^{\frac{14}{3}} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{14}{3}} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{14}{3}} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{11}{3}} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{11}{3}} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{11}{3}} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{8}{3}} b^{\frac{16}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{8}{3}} b^{\frac{16}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{12 a^{\frac{8}{3}} b^{\frac{16}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{5}{3}} b^{\frac{19}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{5}{3}} b^{\frac{19}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{i \pi}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{4 a^{\frac{5}{3}} b^{\frac{19}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{- \frac{a}{b} + x} e^{\frac{5 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{21 a^{4} b^{4} \left(- \frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{33 a^{3} b^{5} \left(- \frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{12 a^{2} b^{6} \left(- \frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{27 a^{7} b^{\frac{4}{3}} \left(- \frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{6} b^{\frac{7}{3}} \left(- \frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 81 a^{5} b^{\frac{10}{3}} \left(- \frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) + 27 a^{4} b^{\frac{13}{3}} \left(- \frac{a}{b} + x\right)^{\frac{13}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}"," ",0,"-4*a**(14/3)*b**(10/3)*(-a/b + x)**(4/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(14/3)*b**(10/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(14/3)*b**(10/3)*(-a/b + x)**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(11/3)*b**(13/3)*(-a/b + x)**(7/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(11/3)*b**(13/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(11/3)*b**(13/3)*(-a/b + x)**(7/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(8/3)*b**(16/3)*(-a/b + x)**(10/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(8/3)*b**(16/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 12*a**(8/3)*b**(16/3)*(-a/b + x)**(10/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(5/3)*b**(19/3)*(-a/b + x)**(13/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(5/3)*b**(19/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(I*pi)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) - 4*a**(5/3)*b**(19/3)*(-a/b + x)**(13/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(-a/b + x)**(1/3)*exp_polar(5*I*pi/3)/a**(1/3))*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 21*a**4*b**4*(-a/b + x)**2*exp(2*I*pi/3)*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 33*a**3*b**5*(-a/b + x)**3*exp(2*I*pi/3)*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3)) + 12*a**2*b**6*(-a/b + x)**4*exp(2*I*pi/3)*gamma(2/3)/(27*a**7*b**(4/3)*(-a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**6*b**(7/3)*(-a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(5/3) + 81*a**5*b**(10/3)*(-a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(5/3) + 27*a**4*b**(13/3)*(-a/b + x)**(13/3)*exp(2*I*pi/3)*gamma(5/3))","C",0
406,1,1640,0,2.786816," ","integrate(x**3/(b*x+a)**(2/3),x)","- \frac{243 a^{\frac{70}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{70}{3}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} - \frac{1377 a^{\frac{67}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{67}{3}} b x}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} - \frac{3213 a^{\frac{64}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{64}{3}} b^{2} x^{2}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} - \frac{3927 a^{\frac{61}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{4860 a^{\frac{61}{3}} b^{3} x^{3}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} - \frac{2583 a^{\frac{58}{3}} b^{4} x^{4} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{3645 a^{\frac{58}{3}} b^{4} x^{4}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} - \frac{693 a^{\frac{55}{3}} b^{5} x^{5} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{1458 a^{\frac{55}{3}} b^{5} x^{5}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{273 a^{\frac{52}{3}} b^{6} x^{6} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{243 a^{\frac{52}{3}} b^{6} x^{6}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{387 a^{\frac{49}{3}} b^{7} x^{7} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{198 a^{\frac{46}{3}} b^{8} x^{8} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}} + \frac{42 a^{\frac{43}{3}} b^{9} x^{9} \sqrt[3]{1 + \frac{b x}{a}}}{140 a^{20} b^{4} + 840 a^{19} b^{5} x + 2100 a^{18} b^{6} x^{2} + 2800 a^{17} b^{7} x^{3} + 2100 a^{16} b^{8} x^{4} + 840 a^{15} b^{9} x^{5} + 140 a^{14} b^{10} x^{6}}"," ",0,"-243*a**(70/3)*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 243*a**(70/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) - 1377*a**(67/3)*b*x*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 1458*a**(67/3)*b*x/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) - 3213*a**(64/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 3645*a**(64/3)*b**2*x**2/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) - 3927*a**(61/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 4860*a**(61/3)*b**3*x**3/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) - 2583*a**(58/3)*b**4*x**4*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 3645*a**(58/3)*b**4*x**4/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) - 693*a**(55/3)*b**5*x**5*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 1458*a**(55/3)*b**5*x**5/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 273*a**(52/3)*b**6*x**6*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 243*a**(52/3)*b**6*x**6/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 387*a**(49/3)*b**7*x**7*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 198*a**(46/3)*b**8*x**8*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6) + 42*a**(43/3)*b**9*x**9*(1 + b*x/a)**(1/3)/(140*a**20*b**4 + 840*a**19*b**5*x + 2100*a**18*b**6*x**2 + 2800*a**17*b**7*x**3 + 2100*a**16*b**8*x**4 + 840*a**15*b**9*x**5 + 140*a**14*b**10*x**6)","B",0
407,1,600,0,1.816650," ","integrate(x**2/(b*x+a)**(2/3),x)","\frac{27 a^{\frac{31}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{31}{3}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} + \frac{72 a^{\frac{28}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{28}{3}} b x}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} + \frac{60 a^{\frac{25}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} - \frac{81 a^{\frac{25}{3}} b^{2} x^{2}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} + \frac{18 a^{\frac{22}{3}} b^{3} x^{3} \sqrt[3]{1 + \frac{b x}{a}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} - \frac{27 a^{\frac{22}{3}} b^{3} x^{3}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} + \frac{9 a^{\frac{19}{3}} b^{4} x^{4} \sqrt[3]{1 + \frac{b x}{a}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}} + \frac{6 a^{\frac{16}{3}} b^{5} x^{5} \sqrt[3]{1 + \frac{b x}{a}}}{14 a^{8} b^{3} + 42 a^{7} b^{4} x + 42 a^{6} b^{5} x^{2} + 14 a^{5} b^{6} x^{3}}"," ",0,"27*a**(31/3)*(1 + b*x/a)**(1/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) - 27*a**(31/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) + 72*a**(28/3)*b*x*(1 + b*x/a)**(1/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) - 81*a**(28/3)*b*x/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) + 60*a**(25/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) - 81*a**(25/3)*b**2*x**2/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) + 18*a**(22/3)*b**3*x**3*(1 + b*x/a)**(1/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) - 27*a**(22/3)*b**3*x**3/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) + 9*a**(19/3)*b**4*x**4*(1 + b*x/a)**(1/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3) + 6*a**(16/3)*b**5*x**5*(1 + b*x/a)**(1/3)/(14*a**8*b**3 + 42*a**7*b**4*x + 42*a**6*b**5*x**2 + 14*a**5*b**6*x**3)","B",0
408,1,162,0,1.190461," ","integrate(x/(b*x+a)**(2/3),x)","- \frac{9 a^{\frac{10}{3}} \sqrt[3]{1 + \frac{b x}{a}}}{4 a^{2} b^{2} + 4 a b^{3} x} + \frac{9 a^{\frac{10}{3}}}{4 a^{2} b^{2} + 4 a b^{3} x} - \frac{6 a^{\frac{7}{3}} b x \sqrt[3]{1 + \frac{b x}{a}}}{4 a^{2} b^{2} + 4 a b^{3} x} + \frac{9 a^{\frac{7}{3}} b x}{4 a^{2} b^{2} + 4 a b^{3} x} + \frac{3 a^{\frac{4}{3}} b^{2} x^{2} \sqrt[3]{1 + \frac{b x}{a}}}{4 a^{2} b^{2} + 4 a b^{3} x}"," ",0,"-9*a**(10/3)*(1 + b*x/a)**(1/3)/(4*a**2*b**2 + 4*a*b**3*x) + 9*a**(10/3)/(4*a**2*b**2 + 4*a*b**3*x) - 6*a**(7/3)*b*x*(1 + b*x/a)**(1/3)/(4*a**2*b**2 + 4*a*b**3*x) + 9*a**(7/3)*b*x/(4*a**2*b**2 + 4*a*b**3*x) + 3*a**(4/3)*b**2*x**2*(1 + b*x/a)**(1/3)/(4*a**2*b**2 + 4*a*b**3*x)","B",0
409,1,10,0,0.063245," ","integrate(1/(b*x+a)**(2/3),x)","\frac{3 \sqrt[3]{a + b x}}{b}"," ",0,"3*(a + b*x)**(1/3)/b","A",0
410,1,150,0,1.930006," ","integrate(1/x/(b*x+a)**(2/3),x)","\frac{\log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{\frac{2}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(3*a**(2/3)*gamma(4/3)) + exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(3*a**(2/3)*gamma(4/3)) + exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(3*a**(2/3)*gamma(4/3))","C",0
411,1,830,0,2.265935," ","integrate(1/x**2/(b*x+a)**(2/3),x)","- \frac{2 a^{\frac{4}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{2 a^{\frac{4}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{2 a^{\frac{4}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{2 \sqrt[3]{a} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{2 \sqrt[3]{a} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{2 \sqrt[3]{a} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{3 a b^{2} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{1}{3}\right)}{9 a^{3} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 9 a^{2} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-2*a**(4/3)*b**(5/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3)) - 2*a**(4/3)*b**(5/3)*(a/b + x)**(2/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3)) - 2*a**(4/3)*b**(5/3)*(a/b + x)**(2/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3)) + 2*a**(1/3)*b**(8/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3)) + 2*a**(1/3)*b**(8/3)*(a/b + x)**(5/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3)) + 2*a**(1/3)*b**(8/3)*(a/b + x)**(5/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3)) + 3*a*b**2*(a/b + x)*exp(2*I*pi/3)*gamma(1/3)/(9*a**3*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 9*a**2*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3))","C",0
412,1,2728,0,2.726566," ","integrate(1/x**3/(b*x+a)**(2/3),x)","\frac{10 a^{\frac{13}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{10 a^{\frac{13}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{10 a^{\frac{13}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{30 a^{\frac{10}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{30 a^{\frac{10}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{30 a^{\frac{10}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{30 a^{\frac{7}{3}} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{30 a^{\frac{7}{3}} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{30 a^{\frac{7}{3}} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{10 a^{\frac{4}{3}} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{10 a^{\frac{4}{3}} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{10 a^{\frac{4}{3}} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{24 a^{4} b^{3} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} + \frac{39 a^{3} b^{4} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)} - \frac{15 a^{2} b^{5} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{1}{3}\right)}{54 a^{7} b^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 162 a^{6} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) + 162 a^{5} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{\frac{8}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right) - 54 a^{4} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{\frac{11}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{4}{3}\right)}"," ",0,"10*a**(13/3)*b**(8/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) + 10*a**(13/3)*b**(8/3)*(a/b + x)**(2/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) + 10*a**(13/3)*b**(8/3)*(a/b + x)**(2/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 30*a**(10/3)*b**(11/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 30*a**(10/3)*b**(11/3)*(a/b + x)**(5/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 30*a**(10/3)*b**(11/3)*(a/b + x)**(5/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) + 30*a**(7/3)*b**(14/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) + 30*a**(7/3)*b**(14/3)*(a/b + x)**(8/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) + 30*a**(7/3)*b**(14/3)*(a/b + x)**(8/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 10*a**(4/3)*b**(17/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 10*a**(4/3)*b**(17/3)*(a/b + x)**(11/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 10*a**(4/3)*b**(17/3)*(a/b + x)**(11/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 24*a**4*b**3*(a/b + x)*exp(2*I*pi/3)*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) + 39*a**3*b**4*(a/b + x)**2*exp(2*I*pi/3)*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3)) - 15*a**2*b**5*(a/b + x)**3*exp(2*I*pi/3)*gamma(1/3)/(54*a**7*b**(2/3)*(a/b + x)**(2/3)*exp(2*I*pi/3)*gamma(4/3) - 162*a**6*b**(5/3)*(a/b + x)**(5/3)*exp(2*I*pi/3)*gamma(4/3) + 162*a**5*b**(8/3)*(a/b + x)**(8/3)*exp(2*I*pi/3)*gamma(4/3) - 54*a**4*b**(11/3)*(a/b + x)**(11/3)*exp(2*I*pi/3)*gamma(4/3))","C",0
413,1,1538,0,2.890969," ","integrate(x**3/(b*x+a)**(4/3),x)","\frac{243 a^{\frac{68}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{243 a^{\frac{68}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{1296 a^{\frac{65}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{1458 a^{\frac{65}{3}} b x}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{2808 a^{\frac{62}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{3645 a^{\frac{62}{3}} b^{2} x^{2}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{3120 a^{\frac{59}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{4860 a^{\frac{59}{3}} b^{3} x^{3}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{1830 a^{\frac{56}{3}} b^{4} x^{4} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{3645 a^{\frac{56}{3}} b^{4} x^{4}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{528 a^{\frac{53}{3}} b^{5} x^{5} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{1458 a^{\frac{53}{3}} b^{5} x^{5}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{96 a^{\frac{50}{3}} b^{6} x^{6} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} - \frac{243 a^{\frac{50}{3}} b^{6} x^{6}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{48 a^{\frac{47}{3}} b^{7} x^{7} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}} + \frac{15 a^{\frac{44}{3}} b^{8} x^{8} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{40 a^{20} b^{4} + 240 a^{19} b^{5} x + 600 a^{18} b^{6} x^{2} + 800 a^{17} b^{7} x^{3} + 600 a^{16} b^{8} x^{4} + 240 a^{15} b^{9} x^{5} + 40 a^{14} b^{10} x^{6}}"," ",0,"243*a**(68/3)*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 243*a**(68/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 1296*a**(65/3)*b*x*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 1458*a**(65/3)*b*x/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 2808*a**(62/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 3645*a**(62/3)*b**2*x**2/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 3120*a**(59/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 4860*a**(59/3)*b**3*x**3/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 1830*a**(56/3)*b**4*x**4*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 3645*a**(56/3)*b**4*x**4/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 528*a**(53/3)*b**5*x**5*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 1458*a**(53/3)*b**5*x**5/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 96*a**(50/3)*b**6*x**6*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) - 243*a**(50/3)*b**6*x**6/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 48*a**(47/3)*b**7*x**7*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6) + 15*a**(44/3)*b**8*x**8*(1 + b*x/a)**(2/3)/(40*a**20*b**4 + 240*a**19*b**5*x + 600*a**18*b**6*x**2 + 800*a**17*b**7*x**3 + 600*a**16*b**8*x**4 + 240*a**15*b**9*x**5 + 40*a**14*b**10*x**6)","B",0
414,1,534,0,1.881757," ","integrate(x**2/(b*x+a)**(4/3),x)","- \frac{27 a^{\frac{29}{3}} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{29}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} - \frac{63 a^{\frac{26}{3}} b x \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{81 a^{\frac{26}{3}} b x}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} - \frac{42 a^{\frac{23}{3}} b^{2} x^{2} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{81 a^{\frac{23}{3}} b^{2} x^{2}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} - \frac{3 a^{\frac{20}{3}} b^{3} x^{3} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{27 a^{\frac{20}{3}} b^{3} x^{3}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}} + \frac{3 a^{\frac{17}{3}} b^{4} x^{4} \left(1 + \frac{b x}{a}\right)^{\frac{2}{3}}}{5 a^{8} b^{3} + 15 a^{7} b^{4} x + 15 a^{6} b^{5} x^{2} + 5 a^{5} b^{6} x^{3}}"," ",0,"-27*a**(29/3)*(1 + b*x/a)**(2/3)/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) + 27*a**(29/3)/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) - 63*a**(26/3)*b*x*(1 + b*x/a)**(2/3)/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) + 81*a**(26/3)*b*x/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) - 42*a**(23/3)*b**2*x**2*(1 + b*x/a)**(2/3)/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) + 81*a**(23/3)*b**2*x**2/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) - 3*a**(20/3)*b**3*x**3*(1 + b*x/a)**(2/3)/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) + 27*a**(20/3)*b**3*x**3/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3) + 3*a**(17/3)*b**4*x**4*(1 + b*x/a)**(2/3)/(5*a**8*b**3 + 15*a**7*b**4*x + 15*a**6*b**5*x**2 + 5*a**5*b**6*x**3)","B",0
415,1,41,0,0.724261," ","integrate(x/(b*x+a)**(4/3),x)","\begin{cases} \frac{9 a}{2 b^{2} \sqrt[3]{a + b x}} + \frac{3 x}{2 b \sqrt[3]{a + b x}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{4}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a/(2*b**2*(a + b*x)**(1/3)) + 3*x/(2*b*(a + b*x)**(1/3)), Ne(b, 0)), (x**2/(2*a**(4/3)), True))","A",0
416,1,12,0,0.067356," ","integrate(1/(b*x+a)**(4/3),x)","- \frac{3}{b \sqrt[3]{a + b x}}"," ",0,"-3/(b*(a + b*x)**(1/3))","A",0
417,1,184,0,2.214689," ","integrate(1/x/(b*x+a)**(4/3),x)","- \frac{\Gamma\left(- \frac{1}{3}\right)}{a \sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} \Gamma\left(\frac{2}{3}\right)} - \frac{\log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a^{\frac{4}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-gamma(-1/3)/(a*b**(1/3)*(a/b + x)**(1/3)*gamma(2/3)) - log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(3*a**(4/3)*gamma(2/3)) - exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(3*a**(4/3)*gamma(2/3)) - exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(3*a**(4/3)*gamma(2/3))","C",0
418,1,857,0,2.524780," ","integrate(1/x**2/(b*x+a)**(4/3),x)","- \frac{9 a^{\frac{4}{3}} b^{\frac{2}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{12 \sqrt[3]{a} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{4 a b \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{4 a b \sqrt[3]{\frac{a}{b} + x} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{4 a b \sqrt[3]{\frac{a}{b} + x} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{4 b^{2} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{4 b^{2} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{4 b^{2} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 9 a^{\frac{10}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 9 a^{\frac{7}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"-9*a**(4/3)*b**(2/3)*exp(2*I*pi/3)*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) + 12*a**(1/3)*b**(5/3)*(a/b + x)*exp(2*I*pi/3)*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) - 4*a*b*(a/b + x)**(1/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) - 4*a*b*(a/b + x)**(1/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) - 4*a*b*(a/b + x)**(1/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) + 4*b**2*(a/b + x)**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) + 4*b**2*(a/b + x)**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3)) + 4*b**2*(a/b + x)**(4/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(-9*a**(10/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 9*a**(7/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3))","C",0
419,1,2793,0,3.185272," ","integrate(1/x**3/(b*x+a)**(4/3),x)","\frac{54 a^{\frac{13}{3}} b^{\frac{5}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{201 a^{\frac{10}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{231 a^{\frac{7}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{84 a^{\frac{4}{3}} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{28 a^{4} b^{2} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{28 a^{4} b^{2} \sqrt[3]{\frac{a}{b} + x} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{28 a^{4} b^{2} \sqrt[3]{\frac{a}{b} + x} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{84 a^{3} b^{3} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{84 a^{3} b^{3} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{84 a^{3} b^{3} \left(\frac{a}{b} + x\right)^{\frac{4}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{84 a^{2} b^{4} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{84 a^{2} b^{4} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} + \frac{84 a^{2} b^{4} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{28 a b^{5} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{28 a b^{5} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)} - \frac{28 a b^{5} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} \log{\left(1 - \frac{\sqrt[3]{b} \sqrt[3]{\frac{a}{b} + x} e^{\frac{4 i \pi}{3}}}{\sqrt[3]{a}} \right)} \Gamma\left(- \frac{1}{3}\right)}{- 54 a^{\frac{22}{3}} \sqrt[3]{\frac{a}{b} + x} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 162 a^{\frac{19}{3}} b \left(\frac{a}{b} + x\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) - 162 a^{\frac{16}{3}} b^{2} \left(\frac{a}{b} + x\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right) + 54 a^{\frac{13}{3}} b^{3} \left(\frac{a}{b} + x\right)^{\frac{10}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}"," ",0,"54*a**(13/3)*b**(5/3)*exp(2*I*pi/3)*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 201*a**(10/3)*b**(8/3)*(a/b + x)*exp(2*I*pi/3)*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 231*a**(7/3)*b**(11/3)*(a/b + x)**2*exp(2*I*pi/3)*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 84*a**(4/3)*b**(14/3)*(a/b + x)**3*exp(2*I*pi/3)*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 28*a**4*b**2*(a/b + x)**(1/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 28*a**4*b**2*(a/b + x)**(1/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 28*a**4*b**2*(a/b + x)**(1/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 84*a**3*b**3*(a/b + x)**(4/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 84*a**3*b**3*(a/b + x)**(4/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 84*a**3*b**3*(a/b + x)**(4/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 84*a**2*b**4*(a/b + x)**(7/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 84*a**2*b**4*(a/b + x)**(7/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) + 84*a**2*b**4*(a/b + x)**(7/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 28*a*b**5*(a/b + x)**(10/3)*exp(2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 28*a*b**5*(a/b + x)**(10/3)*exp(-2*I*pi/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(2*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3)) - 28*a*b**5*(a/b + x)**(10/3)*log(1 - b**(1/3)*(a/b + x)**(1/3)*exp_polar(4*I*pi/3)/a**(1/3))*gamma(-1/3)/(-54*a**(22/3)*(a/b + x)**(1/3)*exp(2*I*pi/3)*gamma(2/3) + 162*a**(19/3)*b*(a/b + x)**(4/3)*exp(2*I*pi/3)*gamma(2/3) - 162*a**(16/3)*b**2*(a/b + x)**(7/3)*exp(2*I*pi/3)*gamma(2/3) + 54*a**(13/3)*b**3*(a/b + x)**(10/3)*exp(2*I*pi/3)*gamma(2/3))","C",0
420,1,138,0,2.134140," ","integrate(1/x/(b**3*x+a**3)**(1/3),x)","\frac{e^{\frac{i \pi}{3}} \log{\left(- \frac{a e^{\frac{2 i \pi}{3}}}{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} + \frac{e^{- \frac{i \pi}{3}} \log{\left(- \frac{a e^{\frac{4 i \pi}{3}}}{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} - \frac{\log{\left(- \frac{a e^{2 i \pi}}{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)}"," ",0,"exp(I*pi/3)*log(-a*exp_polar(2*I*pi/3)/(b*(a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) + exp(-I*pi/3)*log(-a*exp_polar(4*I*pi/3)/(b*(a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) - log(-a*exp_polar(2*I*pi)/(b*(a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3))","C",0
421,1,136,0,1.889119," ","integrate(1/x/(-b**3*x+a**3)**(1/3),x)","- \frac{e^{- \frac{2 i \pi}{3}} \log{\left(- \frac{a e^{\frac{i \pi}{3}}}{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} + \frac{e^{- \frac{i \pi}{3}} \log{\left(- \frac{a e^{i \pi}}{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} - \frac{\log{\left(- \frac{a e^{\frac{5 i \pi}{3}}}{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)}"," ",0,"-exp(-2*I*pi/3)*log(-a*exp_polar(I*pi/3)/(b*(-a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) + exp(-I*pi/3)*log(-a*exp_polar(I*pi)/(b*(-a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) - log(-a*exp_polar(5*I*pi/3)/(b*(-a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3))","C",0
422,1,134,0,1.823676," ","integrate(1/x/(b**3*x-a**3)**(1/3),x)","- \frac{e^{- \frac{i \pi}{3}} \log{\left(- \frac{a e^{\frac{i \pi}{3}}}{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} + \frac{\log{\left(- \frac{a e^{i \pi}}{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} - \frac{e^{\frac{i \pi}{3}} \log{\left(- \frac{a e^{\frac{5 i \pi}{3}}}{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)}"," ",0,"-exp(-I*pi/3)*log(-a*exp_polar(I*pi/3)/(b*(-a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) + log(-a*exp_polar(I*pi)/(b*(-a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) - exp(I*pi/3)*log(-a*exp_polar(5*I*pi/3)/(b*(-a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3))","C",0
423,1,139,0,1.826571," ","integrate(1/x/(-b**3*x-a**3)**(1/3),x)","\frac{\log{\left(- \frac{a e^{\frac{2 i \pi}{3}}}{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} - \frac{e^{\frac{i \pi}{3}} \log{\left(- \frac{a e^{\frac{4 i \pi}{3}}}{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)} + \frac{e^{\frac{2 i \pi}{3}} \log{\left(- \frac{a e^{2 i \pi}}{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}} + 1 \right)} \Gamma\left(- \frac{1}{3}\right)}{3 a \Gamma\left(\frac{2}{3}\right)}"," ",0,"log(-a*exp_polar(2*I*pi/3)/(b*(a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) - exp(I*pi/3)*log(-a*exp_polar(4*I*pi/3)/(b*(a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3)) + exp(2*I*pi/3)*log(-a*exp_polar(2*I*pi)/(b*(a**3/b**3 + x)**(1/3)) + 1)*gamma(-1/3)/(3*a*gamma(2/3))","C",0
424,1,134,0,1.856952," ","integrate(1/x/(b**3*x+a**3)**(2/3),x)","\frac{\log{\left(1 - \frac{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} + \frac{e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x} e^{\frac{2 i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} + \frac{e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x} e^{\frac{4 i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)}"," ",0,"log(1 - b*(a**3/b**3 + x)**(1/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) + exp(-2*I*pi/3)*log(1 - b*(a**3/b**3 + x)**(1/3)*exp_polar(2*I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) + exp(2*I*pi/3)*log(1 - b*(a**3/b**3 + x)**(1/3)*exp_polar(4*I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3))","C",0
425,1,136,0,1.921452," ","integrate(1/x/(-b**3*x+a**3)**(2/3),x)","\frac{\log{\left(1 - \frac{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x} e^{\frac{i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} - \frac{e^{\frac{i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x} e^{i \pi}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} + \frac{e^{\frac{2 i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x} e^{\frac{5 i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)}"," ",0,"log(1 - b*(-a**3/b**3 + x)**(1/3)*exp_polar(I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) - exp(I*pi/3)*log(1 - b*(-a**3/b**3 + x)**(1/3)*exp_polar(I*pi)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) + exp(2*I*pi/3)*log(1 - b*(-a**3/b**3 + x)**(1/3)*exp_polar(5*I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3))","C",0
426,1,134,0,1.983083," ","integrate(1/x/(b**3*x-a**3)**(2/3),x)","- \frac{e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x} e^{\frac{i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} + \frac{\log{\left(1 - \frac{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x} e^{i \pi}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} - \frac{e^{\frac{i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{- \frac{a^{3}}{b^{3}} + x} e^{\frac{5 i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)}"," ",0,"-exp(-I*pi/3)*log(1 - b*(-a**3/b**3 + x)**(1/3)*exp_polar(I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) + log(1 - b*(-a**3/b**3 + x)**(1/3)*exp_polar(I*pi)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) - exp(I*pi/3)*log(1 - b*(-a**3/b**3 + x)**(1/3)*exp_polar(5*I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3))","C",0
427,1,133,0,1.895383," ","integrate(1/x/(-b**3*x-a**3)**(2/3),x)","\frac{e^{- \frac{2 i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} - \frac{e^{- \frac{i \pi}{3}} \log{\left(1 - \frac{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x} e^{\frac{2 i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)} + \frac{\log{\left(1 - \frac{b \sqrt[3]{\frac{a^{3}}{b^{3}} + x} e^{\frac{4 i \pi}{3}}}{a} \right)} \Gamma\left(\frac{1}{3}\right)}{3 a^{2} \Gamma\left(\frac{4}{3}\right)}"," ",0,"exp(-2*I*pi/3)*log(1 - b*(a**3/b**3 + x)**(1/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) - exp(-I*pi/3)*log(1 - b*(a**3/b**3 + x)**(1/3)*exp_polar(2*I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3)) + log(1 - b*(a**3/b**3 + x)**(1/3)*exp_polar(4*I*pi/3)/a)*gamma(1/3)/(3*a**2*gamma(4/3))","C",0
428,1,87,0,0.299121," ","integrate(x**m*(b*x+a),x)","\begin{cases} - \frac{a}{x} + b \log{\left(x \right)} & \text{for}\: m = -2 \\a \log{\left(x \right)} + b x & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + 3 m + 2} + \frac{2 a x x^{m}}{m^{2} + 3 m + 2} + \frac{b m x^{2} x^{m}}{m^{2} + 3 m + 2} + \frac{b x^{2} x^{m}}{m^{2} + 3 m + 2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + b*log(x), Eq(m, -2)), (a*log(x) + b*x, Eq(m, -1)), (a*m*x*x**m/(m**2 + 3*m + 2) + 2*a*x*x**m/(m**2 + 3*m + 2) + b*m*x**2*x**m/(m**2 + 3*m + 2) + b*x**2*x**m/(m**2 + 3*m + 2), True))","A",0
429,1,19,0,1.588645," ","integrate(x**(5/2)*(b*x+a),x)","\frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 b x^{\frac{9}{2}}}{9}"," ",0,"2*a*x**(7/2)/7 + 2*b*x**(9/2)/9","A",0
430,1,19,0,0.547376," ","integrate(x**(3/2)*(b*x+a),x)","\frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{7}{2}}}{7}"," ",0,"2*a*x**(5/2)/5 + 2*b*x**(7/2)/7","A",0
431,1,19,0,1.621424," ","integrate((b*x+a)*x**(1/2),x)","\frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{5}{2}}}{5}"," ",0,"2*a*x**(3/2)/3 + 2*b*x**(5/2)/5","A",0
432,1,17,0,0.155804," ","integrate((b*x+a)/x**(1/2),x)","2 a \sqrt{x} + \frac{2 b x^{\frac{3}{2}}}{3}"," ",0,"2*a*sqrt(x) + 2*b*x**(3/2)/3","A",0
433,1,15,0,0.349504," ","integrate((b*x+a)/x**(3/2),x)","- \frac{2 a}{\sqrt{x}} + 2 b \sqrt{x}"," ",0,"-2*a/sqrt(x) + 2*b*sqrt(x)","A",0
434,1,19,0,0.561817," ","integrate((b*x+a)/x**(5/2),x)","- \frac{2 a}{3 x^{\frac{3}{2}}} - \frac{2 b}{\sqrt{x}}"," ",0,"-2*a/(3*x**(3/2)) - 2*b/sqrt(x)","A",0
435,1,299,0,0.534722," ","integrate(x**m*(b*x+a)**2,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} - \frac{2 a b}{x} + b^{2} \log{\left(x \right)} & \text{for}\: m = -3 \\- \frac{a^{2}}{x} + 2 a b \log{\left(x \right)} + b^{2} x & \text{for}\: m = -2 \\a^{2} \log{\left(x \right)} + 2 a b x + \frac{b^{2} x^{2}}{2} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{5 a^{2} m x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{6 a^{2} x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{2 a b m^{2} x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{8 a b m x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{6 a b x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{b^{2} m^{2} x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{3 b^{2} m x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{2 b^{2} x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) - 2*a*b/x + b**2*log(x), Eq(m, -3)), (-a**2/x + 2*a*b*log(x) + b**2*x, Eq(m, -2)), (a**2*log(x) + 2*a*b*x + b**2*x**2/2, Eq(m, -1)), (a**2*m**2*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 5*a**2*m*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 6*a**2*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 2*a*b*m**2*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + 8*a*b*m*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + 6*a*b*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + b**2*m**2*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6) + 3*b**2*m*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6) + 2*b**2*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6), True))","A",0
436,1,34,0,2.597047," ","integrate(x**(5/2)*(b*x+a)**2,x)","\frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{2 b^{2} x^{\frac{11}{2}}}{11}"," ",0,"2*a**2*x**(7/2)/7 + 4*a*b*x**(9/2)/9 + 2*b**2*x**(11/2)/11","A",0
437,1,34,0,1.031423," ","integrate(x**(3/2)*(b*x+a)**2,x)","\frac{2 a^{2} x^{\frac{5}{2}}}{5} + \frac{4 a b x^{\frac{7}{2}}}{7} + \frac{2 b^{2} x^{\frac{9}{2}}}{9}"," ",0,"2*a**2*x**(5/2)/5 + 4*a*b*x**(7/2)/7 + 2*b**2*x**(9/2)/9","A",0
438,-1,0,0,0.000000," ","integrate((b*x+a)**2*x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,1,32,0,0.262083," ","integrate((b*x+a)**2/x**(1/2),x)","2 a^{2} \sqrt{x} + \frac{4 a b x^{\frac{3}{2}}}{3} + \frac{2 b^{2} x^{\frac{5}{2}}}{5}"," ",0,"2*a**2*sqrt(x) + 4*a*b*x**(3/2)/3 + 2*b**2*x**(5/2)/5","A",0
440,1,31,0,0.429505," ","integrate((b*x+a)**2/x**(3/2),x)","- \frac{2 a^{2}}{\sqrt{x}} + 4 a b \sqrt{x} + \frac{2 b^{2} x^{\frac{3}{2}}}{3}"," ",0,"-2*a**2/sqrt(x) + 4*a*b*sqrt(x) + 2*b**2*x**(3/2)/3","A",0
441,1,31,0,0.592910," ","integrate((b*x+a)**2/x**(5/2),x)","- \frac{2 a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 a b}{\sqrt{x}} + 2 b^{2} \sqrt{x}"," ",0,"-2*a**2/(3*x**(3/2)) - 4*a*b/sqrt(x) + 2*b**2*sqrt(x)","A",0
442,1,663,0,0.884015," ","integrate(x**m*(b*x+a)**3,x)","\begin{cases} - \frac{a^{3}}{3 x^{3}} - \frac{3 a^{2} b}{2 x^{2}} - \frac{3 a b^{2}}{x} + b^{3} \log{\left(x \right)} & \text{for}\: m = -4 \\- \frac{a^{3}}{2 x^{2}} - \frac{3 a^{2} b}{x} + 3 a b^{2} \log{\left(x \right)} + b^{3} x & \text{for}\: m = -3 \\- \frac{a^{3}}{x} + 3 a^{2} b \log{\left(x \right)} + 3 a b^{2} x + \frac{b^{3} x^{2}}{2} & \text{for}\: m = -2 \\a^{3} \log{\left(x \right)} + 3 a^{2} b x + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{3}}{3} & \text{for}\: m = -1 \\\frac{a^{3} m^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{9 a^{3} m^{2} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{26 a^{3} m x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 a^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{3 a^{2} b m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 a^{2} b m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{57 a^{2} b m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{36 a^{2} b x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{3 a b^{2} m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{21 a b^{2} m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{42 a b^{2} m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 a b^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{b^{3} m^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 b^{3} m^{2} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{11 b^{3} m x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 b^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(3*x**3) - 3*a**2*b/(2*x**2) - 3*a*b**2/x + b**3*log(x), Eq(m, -4)), (-a**3/(2*x**2) - 3*a**2*b/x + 3*a*b**2*log(x) + b**3*x, Eq(m, -3)), (-a**3/x + 3*a**2*b*log(x) + 3*a*b**2*x + b**3*x**2/2, Eq(m, -2)), (a**3*log(x) + 3*a**2*b*x + 3*a*b**2*x**2/2 + b**3*x**3/3, Eq(m, -1)), (a**3*m**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 9*a**3*m**2*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 26*a**3*m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*a**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 3*a**2*b*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*a**2*b*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 57*a**2*b*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 36*a**2*b*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 3*a*b**2*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 21*a*b**2*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 42*a*b**2*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*a*b**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + b**3*m**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*b**3*m**2*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 11*b**3*m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*b**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24), True))","A",0
443,1,49,0,3.881140," ","integrate(x**(5/2)*(b*x+a)**3,x)","\frac{2 a^{3} x^{\frac{7}{2}}}{7} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a b^{2} x^{\frac{11}{2}}}{11} + \frac{2 b^{3} x^{\frac{13}{2}}}{13}"," ",0,"2*a**3*x**(7/2)/7 + 2*a**2*b*x**(9/2)/3 + 6*a*b**2*x**(11/2)/11 + 2*b**3*x**(13/2)/13","A",0
444,1,49,0,1.702965," ","integrate(x**(3/2)*(b*x+a)**3,x)","\frac{2 a^{3} x^{\frac{5}{2}}}{5} + \frac{6 a^{2} b x^{\frac{7}{2}}}{7} + \frac{2 a b^{2} x^{\frac{9}{2}}}{3} + \frac{2 b^{3} x^{\frac{11}{2}}}{11}"," ",0,"2*a**3*x**(5/2)/5 + 6*a**2*b*x**(7/2)/7 + 2*a*b**2*x**(9/2)/3 + 2*b**3*x**(11/2)/11","A",0
445,-1,0,0,0.000000," ","integrate((b*x+a)**3*x**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,1,46,0,0.444784," ","integrate((b*x+a)**3/x**(1/2),x)","2 a^{3} \sqrt{x} + 2 a^{2} b x^{\frac{3}{2}} + \frac{6 a b^{2} x^{\frac{5}{2}}}{5} + \frac{2 b^{3} x^{\frac{7}{2}}}{7}"," ",0,"2*a**3*sqrt(x) + 2*a**2*b*x**(3/2) + 6*a*b**2*x**(5/2)/5 + 2*b**3*x**(7/2)/7","A",0
447,1,44,0,0.638943," ","integrate((b*x+a)**3/x**(3/2),x)","- \frac{2 a^{3}}{\sqrt{x}} + 6 a^{2} b \sqrt{x} + 2 a b^{2} x^{\frac{3}{2}} + \frac{2 b^{3} x^{\frac{5}{2}}}{5}"," ",0,"-2*a**3/sqrt(x) + 6*a**2*b*sqrt(x) + 2*a*b**2*x**(3/2) + 2*b**3*x**(5/2)/5","A",0
448,1,46,0,0.777112," ","integrate((b*x+a)**3/x**(5/2),x)","- \frac{2 a^{3}}{3 x^{\frac{3}{2}}} - \frac{6 a^{2} b}{\sqrt{x}} + 6 a b^{2} \sqrt{x} + \frac{2 b^{3} x^{\frac{3}{2}}}{3}"," ",0,"-2*a**3/(3*x**(3/2)) - 6*a**2*b/sqrt(x) + 6*a*b**2*sqrt(x) + 2*b**3*x**(3/2)/3","A",0
449,1,121,0,7.295148," ","integrate(x**(5/2)/(b*x+a),x)","\begin{cases} \frac{i a^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{4} \sqrt{\frac{1}{b}}} - \frac{i a^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{4} \sqrt{\frac{1}{b}}} + \frac{2 a^{2} \sqrt{x}}{b^{3}} - \frac{2 a x^{\frac{3}{2}}}{3 b^{2}} + \frac{2 x^{\frac{5}{2}}}{5 b} & \text{for}\: b \neq 0 \\\frac{2 x^{\frac{7}{2}}}{7 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**4*sqrt(1/b)) - I*a**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**4*sqrt(1/b)) + 2*a**2*sqrt(x)/b**3 - 2*a*x**(3/2)/(3*b**2) + 2*x**(5/2)/(5*b), Ne(b, 0)), (2*x**(7/2)/(7*a), True))","A",0
450,1,105,0,1.926420," ","integrate(x**(3/2)/(b*x+a),x)","\begin{cases} - \frac{i a^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{3} \sqrt{\frac{1}{b}}} + \frac{i a^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{3} \sqrt{\frac{1}{b}}} - \frac{2 a \sqrt{x}}{b^{2}} + \frac{2 x^{\frac{3}{2}}}{3 b} & \text{for}\: b \neq 0 \\\frac{2 x^{\frac{5}{2}}}{5 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**3*sqrt(1/b)) + I*a**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**3*sqrt(1/b)) - 2*a*sqrt(x)/b**2 + 2*x**(3/2)/(3*b), Ne(b, 0)), (2*x**(5/2)/(5*a), True))","A",0
451,1,92,0,0.724463," ","integrate(x**(1/2)/(b*x+a),x)","\begin{cases} \frac{i \sqrt{a} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} - \frac{i \sqrt{a} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} + \frac{2 \sqrt{x}}{b} & \text{for}\: b \neq 0 \\\frac{2 x^{\frac{3}{2}}}{3 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*sqrt(a)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) - I*sqrt(a)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) + 2*sqrt(x)/b, Ne(b, 0)), (2*x**(3/2)/(3*a), True))","A",0
452,1,94,0,1.291272," ","integrate(1/(b*x+a)/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{b \sqrt{x}} & \text{for}\: a = 0 \\\frac{2 \sqrt{x}}{a} & \text{for}\: b = 0 \\- \frac{i \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{\sqrt{a} b \sqrt{\frac{1}{b}}} + \frac{i \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{\sqrt{a} b \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2/(b*sqrt(x)), Eq(a, 0)), (2*sqrt(x)/a, Eq(b, 0)), (-I*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(sqrt(a)*b*sqrt(1/b)) + I*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(sqrt(a)*b*sqrt(1/b)), True))","A",0
453,1,102,0,2.772622," ","integrate(1/x**(3/2)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a \sqrt{x}} + \frac{i \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{i \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{3}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2/(a*sqrt(x)), Eq(b, 0)), (-2/(3*b*x**(3/2)), Eq(a, 0)), (-2/(a*sqrt(x)) + I*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(3/2)*sqrt(1/b)) - I*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(3/2)*sqrt(1/b)), True))","A",0
454,1,121,0,7.834060," ","integrate(1/x**(5/2)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 a x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2}{3 a x^{\frac{3}{2}}} + \frac{2 b}{a^{2} \sqrt{x}} - \frac{i b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{i b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(3*a*x**(3/2)), Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (-2/(3*a*x**(3/2)) + 2*b/(a**2*sqrt(x)) - I*b*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(5/2)*sqrt(1/b)) + I*b*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(5/2)*sqrt(1/b)), True))","A",0
455,1,139,0,24.823200," ","integrate(1/x**(7/2)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 a x^{\frac{5}{2}}} + \frac{2 b}{3 a^{2} x^{\frac{3}{2}}} - \frac{2 b^{2}}{a^{3} \sqrt{x}} + \frac{i b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{i b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{7}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b*x**(7/2)), Eq(a, 0)), (-2/(5*a*x**(5/2)), Eq(b, 0)), (-2/(5*a*x**(5/2)) + 2*b/(3*a**2*x**(3/2)) - 2*b**2/(a**3*sqrt(x)) + I*b**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(7/2)*sqrt(1/b)) - I*b**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(7/2)*sqrt(1/b)), True))","A",0
456,1,479,0,24.566390," ","integrate(x**(5/2)/(b*x+a)**2,x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a^{2}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b^{2}} & \text{for}\: a = 0 \\- \frac{30 i a^{\frac{5}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{20 i a^{\frac{3}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{4 i \sqrt{a} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{15 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{15 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{15 a^{2} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{15 a^{2} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 i \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*x**(7/2)/(7*a**2), Eq(b, 0)), (2*x**(3/2)/(3*b**2), Eq(a, 0)), (-30*I*a**(5/2)*b*sqrt(x)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 20*I*a**(3/2)*b**2*x**(3/2)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 4*I*sqrt(a)*b**3*x**(5/2)*sqrt(1/b)/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 15*a**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 15*a**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) + 15*a**2*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)) - 15*a**2*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(3/2)*b**4*sqrt(1/b) + 6*I*sqrt(a)*b**5*x*sqrt(1/b)), True))","A",0
457,1,411,0,9.176486," ","integrate(x**(3/2)/(b*x+a)**2,x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a^{2}} & \text{for}\: b = 0 \\\frac{2 \sqrt{x}}{b^{2}} & \text{for}\: a = 0 \\\frac{6 i a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{4 i \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{3 a b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{3 a b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(5/2)/(5*a**2), Eq(b, 0)), (2*sqrt(x)/b**2, Eq(a, 0)), (6*I*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 4*I*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) - 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 3*a**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) - 3*a*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)) + 3*a*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**3*sqrt(1/b) + 2*I*sqrt(a)*b**4*x*sqrt(1/b)), True))","A",0
458,1,337,0,4.445223," ","integrate(x**(1/2)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a^{2}} & \text{for}\: b = 0 \\- \frac{2}{b^{2} \sqrt{x}} & \text{for}\: a = 0 \\- \frac{2 i \sqrt{a} b \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} + \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} + \frac{b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} - \frac{b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 i \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(3/2)/(3*a**2), Eq(b, 0)), (-2/(b**2*sqrt(x)), Eq(a, 0)), (-2*I*sqrt(a)*b*sqrt(x)*sqrt(1/b)/(2*I*a**(3/2)*b**2*sqrt(1/b) + 2*I*sqrt(a)*b**3*x*sqrt(1/b)) + a*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**2*sqrt(1/b) + 2*I*sqrt(a)*b**3*x*sqrt(1/b)) - a*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**2*sqrt(1/b) + 2*I*sqrt(a)*b**3*x*sqrt(1/b)) + b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**2*sqrt(1/b) + 2*I*sqrt(a)*b**3*x*sqrt(1/b)) - b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(3/2)*b**2*sqrt(1/b) + 2*I*sqrt(a)*b**3*x*sqrt(1/b)), True))","A",0
459,1,328,0,7.527276," ","integrate(1/(b*x+a)**2/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{a^{2}} & \text{for}\: b = 0 \\- \frac{2}{3 b^{2} x^{\frac{3}{2}}} & \text{for}\: a = 0 \\\frac{2 i \sqrt{a} b \sqrt{x} \sqrt{\frac{1}{b}}}{2 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} + \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} + \frac{b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} - \frac{b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 i a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/a**2, Eq(b, 0)), (-2/(3*b**2*x**(3/2)), Eq(a, 0)), (2*I*sqrt(a)*b*sqrt(x)*sqrt(1/b)/(2*I*a**(5/2)*b*sqrt(1/b) + 2*I*a**(3/2)*b**2*x*sqrt(1/b)) + a*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b*sqrt(1/b) + 2*I*a**(3/2)*b**2*x*sqrt(1/b)) - a*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b*sqrt(1/b) + 2*I*a**(3/2)*b**2*x*sqrt(1/b)) + b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b*sqrt(1/b) + 2*I*a**(3/2)*b**2*x*sqrt(1/b)) - b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(5/2)*b*sqrt(1/b) + 2*I*a**(3/2)*b**2*x*sqrt(1/b)), True))","A",0
460,1,434,0,17.733974," ","integrate(1/x**(3/2)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b^{2} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{2}{a^{2} \sqrt{x}} & \text{for}\: b = 0 \\- \frac{4 i a^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{2 i a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{6 i \sqrt{a} b x \sqrt{\frac{1}{b}}}{2 i a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{3 a \sqrt{x} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{3 a \sqrt{x} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{3 b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{3 b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 i a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 2 i a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b**2*x**(5/2)), Eq(a, 0)), (-2/(a**2*sqrt(x)), Eq(b, 0)), (-4*I*a**(3/2)*sqrt(1/b)/(2*I*a**(7/2)*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b*x**(3/2)*sqrt(1/b)) - 6*I*sqrt(a)*b*x*sqrt(1/b)/(2*I*a**(7/2)*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b*x**(3/2)*sqrt(1/b)) - 3*a*sqrt(x)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b*x**(3/2)*sqrt(1/b)) + 3*a*sqrt(x)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b*x**(3/2)*sqrt(1/b)) - 3*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b*x**(3/2)*sqrt(1/b)) + 3*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(2*I*a**(7/2)*sqrt(x)*sqrt(1/b) + 2*I*a**(5/2)*b*x**(3/2)*sqrt(1/b)), True))","A",0
461,1,507,0,50.523615," ","integrate(1/x**(5/2)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 a^{2} x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{7 b^{2} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{4 i a^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{20 i a^{\frac{3}{2}} b x \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{30 i \sqrt{a} b^{2} x^{2} \sqrt{\frac{1}{b}}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 a b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 a b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 i a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 6 i a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(3*a**2*x**(3/2)), Eq(b, 0)), (-2/(7*b**2*x**(7/2)), Eq(a, 0)), (-4*I*a**(5/2)*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 20*I*a**(3/2)*b*x*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 30*I*sqrt(a)*b**2*x**2*sqrt(1/b)/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 15*a*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 15*a*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 15*b**2*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 15*b**2*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(6*I*a**(9/2)*x**(3/2)*sqrt(1/b) + 6*I*a**(7/2)*b*x**(5/2)*sqrt(1/b)), True))","A",0
462,1,906,0,135.241523," ","integrate(x**(7/2)/(b*x+a)**3,x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{9}{2}}}{9 a^{3}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b^{3}} & \text{for}\: a = 0 \\- \frac{210 i a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{350 i a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{112 i a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{16 i \sqrt{a} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{105 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{105 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{210 a^{3} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{210 a^{3} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{105 a^{2} b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{105 a^{2} b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 i \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*x**(9/2)/(9*a**3), Eq(b, 0)), (2*x**(3/2)/(3*b**3), Eq(a, 0)), (-210*I*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) - 350*I*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) - 112*I*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) + 16*I*sqrt(a)*b**4*x**(7/2)*sqrt(1/b)/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) + 105*a**4*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) - 105*a**4*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) + 210*a**3*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) - 210*a**3*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) + 105*a**2*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)) - 105*a**2*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(5/2)*b**5*sqrt(1/b) + 48*I*a**(3/2)*b**6*x*sqrt(1/b) + 24*I*sqrt(a)*b**7*x**2*sqrt(1/b)), True))","A",0
463,1,816,0,53.287166," ","integrate(x**(5/2)/(b*x+a)**3,x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a^{3}} & \text{for}\: b = 0 \\\frac{2 \sqrt{x}}{b^{3}} & \text{for}\: a = 0 \\\frac{30 i a^{\frac{5}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{50 i a^{\frac{3}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{16 i \sqrt{a} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{15 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{15 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{30 a^{2} b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{30 a^{2} b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{15 a b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{15 a b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(7/2)/(7*a**3), Eq(b, 0)), (2*sqrt(x)/b**3, Eq(a, 0)), (30*I*a**(5/2)*b*sqrt(x)*sqrt(1/b)/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) + 50*I*a**(3/2)*b**2*x**(3/2)*sqrt(1/b)/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) + 16*I*sqrt(a)*b**3*x**(5/2)*sqrt(1/b)/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) - 15*a**3*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) + 15*a**3*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) - 30*a**2*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) + 30*a**2*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) - 15*a*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)) + 15*a*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**4*sqrt(1/b) + 16*I*a**(3/2)*b**5*x*sqrt(1/b) + 8*I*sqrt(a)*b**6*x**2*sqrt(1/b)), True))","A",0
464,1,726,0,29.374494," ","integrate(x**(3/2)/(b*x+a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a^{3}} & \text{for}\: b = 0 \\- \frac{2}{b^{3} \sqrt{x}} & \text{for}\: a = 0 \\- \frac{6 i a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{10 i \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} + \frac{6 a b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{6 a b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} + 16 i a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 i \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(5/2)/(5*a**3), Eq(b, 0)), (-2/(b**3*sqrt(x)), Eq(a, 0)), (-6*I*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) - 10*I*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) + 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) - 3*a**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) + 6*a*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) - 6*a*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) + 3*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)) - 3*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(5/2)*b**3*sqrt(1/b) + 16*I*a**(3/2)*b**4*x*sqrt(1/b) + 8*I*sqrt(a)*b**5*x**2*sqrt(1/b)), True))","A",0
465,1,721,0,15.274548," ","integrate(x**(1/2)/(b*x+a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a^{3}} & \text{for}\: b = 0 \\- \frac{2}{3 b^{3} x^{\frac{3}{2}}} & \text{for}\: a = 0 \\- \frac{2 i a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{2 i \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{2 a b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{2 a b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} + 16 i a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*x**(3/2)/(3*a**3), Eq(b, 0)), (-2/(3*b**3*x**(3/2)), Eq(a, 0)), (-2*I*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) + 2*I*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) + a**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) - a**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) + 2*a*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) - 2*a*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) + b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)) - b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(7/2)*b**2*sqrt(1/b) + 16*I*a**(5/2)*b**3*x*sqrt(1/b) + 8*I*a**(3/2)*b**4*x**2*sqrt(1/b)), True))","A",0
466,1,712,0,25.687119," ","integrate(1/(b*x+a)**3/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{5 b^{3} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\\frac{2 \sqrt{x}}{a^{3}} & \text{for}\: b = 0 \\\frac{10 i a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{6 i \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{6 a b x \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} - \frac{6 a b x \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 b^{2} x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 b^{2} x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 i a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(5*b**3*x**(5/2)), Eq(a, 0)), (2*sqrt(x)/a**3, Eq(b, 0)), (10*I*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) + 6*I*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) + 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) - 3*a**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) + 6*a*b*x*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) - 6*a*b*x*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) + 3*b**2*x**2*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)) - 3*b**2*x**2*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(9/2)*b*sqrt(1/b) + 16*I*a**(7/2)*b**2*x*sqrt(1/b) + 8*I*a**(5/2)*b**3*x**2*sqrt(1/b)), True))","A",0
467,1,865,0,54.353919," ","integrate(1/x**(3/2)/(b*x+a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{a^{3} \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{7 b^{3} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{16 i a^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{50 i a^{\frac{3}{2}} b x \sqrt{\frac{1}{b}}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{30 i \sqrt{a} b^{2} x^{2} \sqrt{\frac{1}{b}}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 a^{2} \sqrt{x} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 a^{2} \sqrt{x} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{30 a b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{30 a b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 i a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 i a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(a**3*sqrt(x)), Eq(b, 0)), (-2/(7*b**3*x**(7/2)), Eq(a, 0)), (-16*I*a**(5/2)*sqrt(1/b)/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 50*I*a**(3/2)*b*x*sqrt(1/b)/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 30*I*sqrt(a)*b**2*x**2*sqrt(1/b)/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 15*a**2*sqrt(x)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 15*a**2*sqrt(x)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 30*a*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 30*a*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 15*b**2*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 15*b**2*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(8*I*a**(11/2)*sqrt(x)*sqrt(1/b) + 16*I*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*I*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)), True))","A",0
468,1,962,0,138.083150," ","integrate(1/x**(5/2)/(b*x+a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{3 a^{3} x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{9 b^{3} x^{\frac{9}{2}}} & \text{for}\: a = 0 \\- \frac{16 i a^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{112 i a^{\frac{5}{2}} b x \sqrt{\frac{1}{b}}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{350 i a^{\frac{3}{2}} b^{2} x^{2} \sqrt{\frac{1}{b}}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{210 i \sqrt{a} b^{3} x^{3} \sqrt{\frac{1}{b}}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 a^{2} b x^{\frac{3}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 a^{2} b x^{\frac{3}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{210 a b^{2} x^{\frac{5}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{210 a b^{2} x^{\frac{5}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 b^{3} x^{\frac{7}{2}} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 b^{3} x^{\frac{7}{2}} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 i a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 48 i a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 i a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (-2/(3*a**3*x**(3/2)), Eq(b, 0)), (-2/(9*b**3*x**(9/2)), Eq(a, 0)), (-16*I*a**(7/2)*sqrt(1/b)/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 112*I*a**(5/2)*b*x*sqrt(1/b)/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 350*I*a**(3/2)*b**2*x**2*sqrt(1/b)/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 210*I*sqrt(a)*b**3*x**3*sqrt(1/b)/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 105*a**2*b*x**(3/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 105*a**2*b*x**(3/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 210*a*b**2*x**(5/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 210*a*b**2*x**(5/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 105*b**3*x**(7/2)*log(-I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 105*b**3*x**(7/2)*log(I*sqrt(a)*sqrt(1/b) + sqrt(x))/(24*I*a**(13/2)*x**(3/2)*sqrt(1/b) + 48*I*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*I*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)), True))","A",0
469,1,116,0,7.099766," ","integrate(x**(5/2)/(b*x-a),x)","\begin{cases} \frac{a^{\frac{5}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{4} \sqrt{\frac{1}{b}}} - \frac{a^{\frac{5}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{4} \sqrt{\frac{1}{b}}} + \frac{2 a^{2} \sqrt{x}}{b^{3}} + \frac{2 a x^{\frac{3}{2}}}{3 b^{2}} + \frac{2 x^{\frac{5}{2}}}{5 b} & \text{for}\: b \neq 0 \\- \frac{2 x^{\frac{7}{2}}}{7 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(5/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(b**4*sqrt(1/b)) - a**(5/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(b**4*sqrt(1/b)) + 2*a**2*sqrt(x)/b**3 + 2*a*x**(3/2)/(3*b**2) + 2*x**(5/2)/(5*b), Ne(b, 0)), (-2*x**(7/2)/(7*a), True))","A",0
470,1,100,0,1.870051," ","integrate(x**(3/2)/(b*x-a),x)","\begin{cases} \frac{a^{\frac{3}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{3} \sqrt{\frac{1}{b}}} - \frac{a^{\frac{3}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{3} \sqrt{\frac{1}{b}}} + \frac{2 a \sqrt{x}}{b^{2}} + \frac{2 x^{\frac{3}{2}}}{3 b} & \text{for}\: b \neq 0 \\- \frac{2 x^{\frac{5}{2}}}{5 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(3/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(b**3*sqrt(1/b)) - a**(3/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(b**3*sqrt(1/b)) + 2*a*sqrt(x)/b**2 + 2*x**(3/2)/(3*b), Ne(b, 0)), (-2*x**(5/2)/(5*a), True))","A",0
471,1,87,0,0.707819," ","integrate(x**(1/2)/(b*x-a),x)","\begin{cases} \frac{\sqrt{a} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} - \frac{\sqrt{a} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{b^{2} \sqrt{\frac{1}{b}}} + \frac{2 \sqrt{x}}{b} & \text{for}\: b \neq 0 \\- \frac{2 x^{\frac{3}{2}}}{3 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(a)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) - sqrt(a)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(b**2*sqrt(1/b)) + 2*sqrt(x)/b, Ne(b, 0)), (-2*x**(3/2)/(3*a), True))","A",0
472,1,88,0,1.252534," ","integrate(1/(b*x-a)/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{b \sqrt{x}} & \text{for}\: a = 0 \\- \frac{2 \sqrt{x}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{\sqrt{a} b \sqrt{\frac{1}{b}}} - \frac{\log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{\sqrt{a} b \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2/(b*sqrt(x)), Eq(a, 0)), (-2*sqrt(x)/a, Eq(b, 0)), (log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(sqrt(a)*b*sqrt(1/b)) - log(sqrt(a)*sqrt(1/b) + sqrt(x))/(sqrt(a)*b*sqrt(1/b)), True))","A",0
473,1,94,0,2.757245," ","integrate(1/x**(3/2)/(b*x-a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2}{a \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{3 b x^{\frac{3}{2}}} & \text{for}\: a = 0 \\\frac{2}{a \sqrt{x}} + \frac{\log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{\log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{3}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (2/(a*sqrt(x)), Eq(b, 0)), (-2/(3*b*x**(3/2)), Eq(a, 0)), (2/(a*sqrt(x)) + log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(3/2)*sqrt(1/b)) - log(sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(3/2)*sqrt(1/b)), True))","A",0
474,1,112,0,7.665336," ","integrate(1/x**(5/2)/(b*x-a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2}{3 a x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{5 b x^{\frac{5}{2}}} & \text{for}\: a = 0 \\\frac{2}{3 a x^{\frac{3}{2}}} + \frac{2 b}{a^{2} \sqrt{x}} + \frac{b \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{b \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (2/(3*a*x**(3/2)), Eq(b, 0)), (-2/(5*b*x**(5/2)), Eq(a, 0)), (2/(3*a*x**(3/2)) + 2*b/(a**2*sqrt(x)) + b*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(5/2)*sqrt(1/b)) - b*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(5/2)*sqrt(1/b)), True))","A",0
475,1,131,0,24.442021," ","integrate(1/x**(7/2)/(b*x-a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b x^{\frac{7}{2}}} & \text{for}\: a = 0 \\\frac{2}{5 a x^{\frac{5}{2}}} & \text{for}\: b = 0 \\\frac{2}{5 a x^{\frac{5}{2}}} + \frac{2 b}{3 a^{2} x^{\frac{3}{2}}} + \frac{2 b^{2}}{a^{3} \sqrt{x}} + \frac{b^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{b^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{a^{\frac{7}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b*x**(7/2)), Eq(a, 0)), (2/(5*a*x**(5/2)), Eq(b, 0)), (2/(5*a*x**(5/2)) + 2*b/(3*a**2*x**(3/2)) + 2*b**2/(a**3*sqrt(x)) + b**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(7/2)*sqrt(1/b)) - b**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(a**(7/2)*sqrt(1/b)), True))","A",0
476,1,444,0,24.751421," ","integrate(x**(5/2)/(b*x-a)**2,x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{7}{2}}}{7 a^{2}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b^{2}} & \text{for}\: a = 0 \\- \frac{30 a^{\frac{5}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{20 a^{\frac{3}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{4 \sqrt{a} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{15 a^{3} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{15 a^{3} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} + \frac{15 a^{2} b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} - \frac{15 a^{2} b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 6 a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} + 6 \sqrt{a} b^{5} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*x**(7/2)/(7*a**2), Eq(b, 0)), (2*x**(3/2)/(3*b**2), Eq(a, 0)), (-30*a**(5/2)*b*sqrt(x)*sqrt(1/b)/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)) + 20*a**(3/2)*b**2*x**(3/2)*sqrt(1/b)/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)) + 4*sqrt(a)*b**3*x**(5/2)*sqrt(1/b)/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)) - 15*a**3*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)) + 15*a**3*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)) + 15*a**2*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)) - 15*a**2*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-6*a**(3/2)*b**4*sqrt(1/b) + 6*sqrt(a)*b**5*x*sqrt(1/b)), True))","A",0
477,1,381,0,9.127080," ","integrate(x**(3/2)/(b*x-a)**2,x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{5}{2}}}{5 a^{2}} & \text{for}\: b = 0 \\\frac{2 \sqrt{x}}{b^{2}} & \text{for}\: a = 0 \\- \frac{6 a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{- 2 a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{4 \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{- 2 a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{3 a^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{3 a^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} + \frac{3 a b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} - \frac{3 a b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{4} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(5/2)/(5*a**2), Eq(b, 0)), (2*sqrt(x)/b**2, Eq(a, 0)), (-6*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(-2*a**(3/2)*b**3*sqrt(1/b) + 2*sqrt(a)*b**4*x*sqrt(1/b)) + 4*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(-2*a**(3/2)*b**3*sqrt(1/b) + 2*sqrt(a)*b**4*x*sqrt(1/b)) - 3*a**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**3*sqrt(1/b) + 2*sqrt(a)*b**4*x*sqrt(1/b)) + 3*a**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**3*sqrt(1/b) + 2*sqrt(a)*b**4*x*sqrt(1/b)) + 3*a*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**3*sqrt(1/b) + 2*sqrt(a)*b**4*x*sqrt(1/b)) - 3*a*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**3*sqrt(1/b) + 2*sqrt(a)*b**4*x*sqrt(1/b)), True))","A",0
478,1,311,0,4.427648," ","integrate(x**(1/2)/(b*x-a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 a^{2}} & \text{for}\: b = 0 \\- \frac{2}{b^{2} \sqrt{x}} & \text{for}\: a = 0 \\- \frac{2 \sqrt{a} b \sqrt{x} \sqrt{\frac{1}{b}}}{- 2 a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} - \frac{a \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} + \frac{a \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} + \frac{b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} - \frac{b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} + 2 \sqrt{a} b^{3} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*x**(3/2)/(3*a**2), Eq(b, 0)), (-2/(b**2*sqrt(x)), Eq(a, 0)), (-2*sqrt(a)*b*sqrt(x)*sqrt(1/b)/(-2*a**(3/2)*b**2*sqrt(1/b) + 2*sqrt(a)*b**3*x*sqrt(1/b)) - a*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**2*sqrt(1/b) + 2*sqrt(a)*b**3*x*sqrt(1/b)) + a*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**2*sqrt(1/b) + 2*sqrt(a)*b**3*x*sqrt(1/b)) + b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**2*sqrt(1/b) + 2*sqrt(a)*b**3*x*sqrt(1/b)) - b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(3/2)*b**2*sqrt(1/b) + 2*sqrt(a)*b**3*x*sqrt(1/b)), True))","A",0
479,1,303,0,7.413303," ","integrate(1/(b*x-a)**2/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{a^{2}} & \text{for}\: b = 0 \\- \frac{2}{3 b^{2} x^{\frac{3}{2}}} & \text{for}\: a = 0 \\- \frac{2 \sqrt{a} b \sqrt{x} \sqrt{\frac{1}{b}}}{- 2 a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} + \frac{a \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} - \frac{a \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} - \frac{b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} + \frac{b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{- 2 a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 2 a^{\frac{3}{2}} b^{2} x \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/a**2, Eq(b, 0)), (-2/(3*b**2*x**(3/2)), Eq(a, 0)), (-2*sqrt(a)*b*sqrt(x)*sqrt(1/b)/(-2*a**(5/2)*b*sqrt(1/b) + 2*a**(3/2)*b**2*x*sqrt(1/b)) + a*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(5/2)*b*sqrt(1/b) + 2*a**(3/2)*b**2*x*sqrt(1/b)) - a*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(5/2)*b*sqrt(1/b) + 2*a**(3/2)*b**2*x*sqrt(1/b)) - b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(5/2)*b*sqrt(1/b) + 2*a**(3/2)*b**2*x*sqrt(1/b)) + b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(-2*a**(5/2)*b*sqrt(1/b) + 2*a**(3/2)*b**2*x*sqrt(1/b)), True))","A",0
480,1,403,0,17.543638," ","integrate(1/x**(3/2)/(b*x-a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{a^{2} \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{5 b^{2} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{4 a^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{2 a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 2 a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{6 \sqrt{a} b x \sqrt{\frac{1}{b}}}{2 a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 2 a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{3 a \sqrt{x} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 2 a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{3 a \sqrt{x} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 2 a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} + \frac{3 b x^{\frac{3}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 2 a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} - \frac{3 b x^{\frac{3}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{2 a^{\frac{7}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 2 a^{\frac{5}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2/(a**2*sqrt(x)), Eq(b, 0)), (-2/(5*b**2*x**(5/2)), Eq(a, 0)), (-4*a**(3/2)*sqrt(1/b)/(2*a**(7/2)*sqrt(x)*sqrt(1/b) - 2*a**(5/2)*b*x**(3/2)*sqrt(1/b)) + 6*sqrt(a)*b*x*sqrt(1/b)/(2*a**(7/2)*sqrt(x)*sqrt(1/b) - 2*a**(5/2)*b*x**(3/2)*sqrt(1/b)) - 3*a*sqrt(x)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(2*a**(7/2)*sqrt(x)*sqrt(1/b) - 2*a**(5/2)*b*x**(3/2)*sqrt(1/b)) + 3*a*sqrt(x)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(2*a**(7/2)*sqrt(x)*sqrt(1/b) - 2*a**(5/2)*b*x**(3/2)*sqrt(1/b)) + 3*b*x**(3/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(2*a**(7/2)*sqrt(x)*sqrt(1/b) - 2*a**(5/2)*b*x**(3/2)*sqrt(1/b)) - 3*b*x**(3/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(2*a**(7/2)*sqrt(x)*sqrt(1/b) - 2*a**(5/2)*b*x**(3/2)*sqrt(1/b)), True))","A",0
481,1,471,0,50.248857," ","integrate(1/x**(5/2)/(b*x-a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2}{7 b^{2} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\- \frac{2}{3 a^{2} x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{4 a^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{20 a^{\frac{3}{2}} b x \sqrt{\frac{1}{b}}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{30 \sqrt{a} b^{2} x^{2} \sqrt{\frac{1}{b}}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 a b x^{\frac{3}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 a b x^{\frac{3}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{6 a^{\frac{9}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 6 a^{\frac{7}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (-2/(7*b**2*x**(7/2)), Eq(a, 0)), (-2/(3*a**2*x**(3/2)), Eq(b, 0)), (-4*a**(5/2)*sqrt(1/b)/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 20*a**(3/2)*b*x*sqrt(1/b)/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 30*sqrt(a)*b**2*x**2*sqrt(1/b)/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 15*a*b*x**(3/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 15*a*b*x**(3/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)) + 15*b**2*x**(5/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)) - 15*b**2*x**(5/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(6*a**(9/2)*x**(3/2)*sqrt(1/b) - 6*a**(7/2)*b*x**(5/2)*sqrt(1/b)), True))","A",0
482,1,840,0,136.149972," ","integrate(x**(7/2)/(b*x-a)**3,x)","\begin{cases} \tilde{\infty} x^{\frac{3}{2}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2 x^{\frac{9}{2}}}{9 a^{3}} & \text{for}\: b = 0 \\\frac{2 x^{\frac{3}{2}}}{3 b^{3}} & \text{for}\: a = 0 \\\frac{210 a^{\frac{7}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{350 a^{\frac{5}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{112 a^{\frac{3}{2}} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{16 \sqrt{a} b^{4} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{105 a^{4} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{105 a^{4} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{210 a^{3} b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{210 a^{3} b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} + \frac{105 a^{2} b^{2} x^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} - \frac{105 a^{2} b^{2} x^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{5}{2}} b^{5} \sqrt{\frac{1}{b}} - 48 a^{\frac{3}{2}} b^{6} x \sqrt{\frac{1}{b}} + 24 \sqrt{a} b^{7} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2*x**(9/2)/(9*a**3), Eq(b, 0)), (2*x**(3/2)/(3*b**3), Eq(a, 0)), (210*a**(7/2)*b*sqrt(x)*sqrt(1/b)/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) - 350*a**(5/2)*b**2*x**(3/2)*sqrt(1/b)/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) + 112*a**(3/2)*b**3*x**(5/2)*sqrt(1/b)/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) + 16*sqrt(a)*b**4*x**(7/2)*sqrt(1/b)/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) + 105*a**4*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) - 105*a**4*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) - 210*a**3*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) + 210*a**3*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) + 105*a**2*b**2*x**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)) - 105*a**2*b**2*x**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(5/2)*b**5*sqrt(1/b) - 48*a**(3/2)*b**6*x*sqrt(1/b) + 24*sqrt(a)*b**7*x**2*sqrt(1/b)), True))","A",0
483,1,756,0,53.453110," ","integrate(x**(5/2)/(b*x-a)**3,x)","\begin{cases} \tilde{\infty} \sqrt{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 \sqrt{x}}{b^{3}} & \text{for}\: a = 0 \\- \frac{2 x^{\frac{7}{2}}}{7 a^{3}} & \text{for}\: b = 0 \\\frac{30 a^{\frac{5}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{50 a^{\frac{3}{2}} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{16 \sqrt{a} b^{3} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{15 a^{3} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{15 a^{3} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{30 a^{2} b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{30 a^{2} b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} + \frac{15 a b^{2} x^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} - \frac{15 a b^{2} x^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{4} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{5} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{6} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*sqrt(x), Eq(a, 0) & Eq(b, 0)), (2*sqrt(x)/b**3, Eq(a, 0)), (-2*x**(7/2)/(7*a**3), Eq(b, 0)), (30*a**(5/2)*b*sqrt(x)*sqrt(1/b)/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) - 50*a**(3/2)*b**2*x**(3/2)*sqrt(1/b)/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) + 16*sqrt(a)*b**3*x**(5/2)*sqrt(1/b)/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) + 15*a**3*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) - 15*a**3*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) - 30*a**2*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) + 30*a**2*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) + 15*a*b**2*x**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)) - 15*a*b**2*x**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**4*sqrt(1/b) - 16*a**(3/2)*b**5*x*sqrt(1/b) + 8*sqrt(a)*b**6*x**2*sqrt(1/b)), True))","A",0
484,1,673,0,29.248049," ","integrate(x**(3/2)/(b*x-a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{x}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2 x^{\frac{5}{2}}}{5 a^{3}} & \text{for}\: b = 0 \\- \frac{2}{b^{3} \sqrt{x}} & \text{for}\: a = 0 \\\frac{6 a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{10 \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 a^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 a^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{6 a b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} + \frac{6 a b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 b^{2} x^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 b^{2} x^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} - 16 a^{\frac{3}{2}} b^{4} x \sqrt{\frac{1}{b}} + 8 \sqrt{a} b^{5} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sqrt(x), Eq(a, 0) & Eq(b, 0)), (-2*x**(5/2)/(5*a**3), Eq(b, 0)), (-2/(b**3*sqrt(x)), Eq(a, 0)), (6*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) - 10*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) + 3*a**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) - 3*a**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) - 6*a*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) + 6*a*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) + 3*b**2*x**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)) - 3*b**2*x**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(5/2)*b**3*sqrt(1/b) - 16*a**(3/2)*b**4*x*sqrt(1/b) + 8*sqrt(a)*b**5*x**2*sqrt(1/b)), True))","A",0
485,1,668,0,15.189444," ","integrate(x**(1/2)/(b*x-a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2 x^{\frac{3}{2}}}{3 a^{3}} & \text{for}\: b = 0 \\- \frac{2}{3 b^{3} x^{\frac{3}{2}}} & \text{for}\: a = 0 \\- \frac{2 a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{2 \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{a^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{a^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{2 a b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{2 a b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} - \frac{b^{2} x^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} + \frac{b^{2} x^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} - 16 a^{\frac{5}{2}} b^{3} x \sqrt{\frac{1}{b}} + 8 a^{\frac{3}{2}} b^{4} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(3/2), Eq(a, 0) & Eq(b, 0)), (-2*x**(3/2)/(3*a**3), Eq(b, 0)), (-2/(3*b**3*x**(3/2)), Eq(a, 0)), (-2*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) - 2*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) - a**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) + a**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) + 2*a*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) - 2*a*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) - b**2*x**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)) + b**2*x**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(7/2)*b**2*sqrt(1/b) - 16*a**(5/2)*b**3*x*sqrt(1/b) + 8*a**(3/2)*b**4*x**2*sqrt(1/b)), True))","A",0
486,1,660,0,25.674284," ","integrate(1/(b*x-a)**3/x**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{2 \sqrt{x}}{a^{3}} & \text{for}\: b = 0 \\- \frac{2}{5 b^{3} x^{\frac{5}{2}}} & \text{for}\: a = 0 \\- \frac{10 a^{\frac{3}{2}} b \sqrt{x} \sqrt{\frac{1}{b}}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{6 \sqrt{a} b^{2} x^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 a^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 a^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} - \frac{6 a b x \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{6 a b x \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} + \frac{3 b^{2} x^{2} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} - \frac{3 b^{2} x^{2} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} - 16 a^{\frac{7}{2}} b^{2} x \sqrt{\frac{1}{b}} + 8 a^{\frac{5}{2}} b^{3} x^{2} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/2), Eq(a, 0) & Eq(b, 0)), (-2*sqrt(x)/a**3, Eq(b, 0)), (-2/(5*b**3*x**(5/2)), Eq(a, 0)), (-10*a**(3/2)*b*sqrt(x)*sqrt(1/b)/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) + 6*sqrt(a)*b**2*x**(3/2)*sqrt(1/b)/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) + 3*a**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) - 3*a**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) - 6*a*b*x*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) + 6*a*b*x*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) + 3*b**2*x**2*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)) - 3*b**2*x**2*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(9/2)*b*sqrt(1/b) - 16*a**(7/2)*b**2*x*sqrt(1/b) + 8*a**(5/2)*b**3*x**2*sqrt(1/b)), True))","A",0
487,1,802,0,54.560447," ","integrate(1/x**(3/2)/(b*x-a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{7}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2}{a^{3} \sqrt{x}} & \text{for}\: b = 0 \\- \frac{2}{7 b^{3} x^{\frac{7}{2}}} & \text{for}\: a = 0 \\\frac{16 a^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{50 a^{\frac{3}{2}} b x \sqrt{\frac{1}{b}}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{30 \sqrt{a} b^{2} x^{2} \sqrt{\frac{1}{b}}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 a^{2} \sqrt{x} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 a^{2} \sqrt{x} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{30 a b x^{\frac{3}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{30 a b x^{\frac{3}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} + \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} - \frac{15 b^{2} x^{\frac{5}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{8 a^{\frac{11}{2}} \sqrt{x} \sqrt{\frac{1}{b}} - 16 a^{\frac{9}{2}} b x^{\frac{3}{2}} \sqrt{\frac{1}{b}} + 8 a^{\frac{7}{2}} b^{2} x^{\frac{5}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(7/2), Eq(a, 0) & Eq(b, 0)), (2/(a**3*sqrt(x)), Eq(b, 0)), (-2/(7*b**3*x**(7/2)), Eq(a, 0)), (16*a**(5/2)*sqrt(1/b)/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 50*a**(3/2)*b*x*sqrt(1/b)/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 30*sqrt(a)*b**2*x**2*sqrt(1/b)/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 15*a**2*sqrt(x)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 15*a**2*sqrt(x)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 30*a*b*x**(3/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 30*a*b*x**(3/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) + 15*b**2*x**(5/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)) - 15*b**2*x**(5/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(8*a**(11/2)*sqrt(x)*sqrt(1/b) - 16*a**(9/2)*b*x**(3/2)*sqrt(1/b) + 8*a**(7/2)*b**2*x**(5/2)*sqrt(1/b)), True))","A",0
488,1,892,0,138.883730," ","integrate(1/x**(5/2)/(b*x-a)**3,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{9}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{2}{3 a^{3} x^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{2}{9 b^{3} x^{\frac{9}{2}}} & \text{for}\: a = 0 \\\frac{16 a^{\frac{7}{2}} \sqrt{\frac{1}{b}}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{112 a^{\frac{5}{2}} b x \sqrt{\frac{1}{b}}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{350 a^{\frac{3}{2}} b^{2} x^{2} \sqrt{\frac{1}{b}}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{210 \sqrt{a} b^{3} x^{3} \sqrt{\frac{1}{b}}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 a^{2} b x^{\frac{3}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 a^{2} b x^{\frac{3}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{210 a b^{2} x^{\frac{5}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{210 a b^{2} x^{\frac{5}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} + \frac{105 b^{3} x^{\frac{7}{2}} \log{\left(- \sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} - \frac{105 b^{3} x^{\frac{7}{2}} \log{\left(\sqrt{a} \sqrt{\frac{1}{b}} + \sqrt{x} \right)}}{24 a^{\frac{13}{2}} x^{\frac{3}{2}} \sqrt{\frac{1}{b}} - 48 a^{\frac{11}{2}} b x^{\frac{5}{2}} \sqrt{\frac{1}{b}} + 24 a^{\frac{9}{2}} b^{2} x^{\frac{7}{2}} \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(9/2), Eq(a, 0) & Eq(b, 0)), (2/(3*a**3*x**(3/2)), Eq(b, 0)), (-2/(9*b**3*x**(9/2)), Eq(a, 0)), (16*a**(7/2)*sqrt(1/b)/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 112*a**(5/2)*b*x*sqrt(1/b)/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 350*a**(3/2)*b**2*x**2*sqrt(1/b)/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 210*sqrt(a)*b**3*x**3*sqrt(1/b)/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 105*a**2*b*x**(3/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 105*a**2*b*x**(3/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 210*a*b**2*x**(5/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 210*a*b**2*x**(5/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) + 105*b**3*x**(7/2)*log(-sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)) - 105*b**3*x**(7/2)*log(sqrt(a)*sqrt(1/b) + sqrt(x))/(24*a**(13/2)*x**(3/2)*sqrt(1/b) - 48*a**(11/2)*b*x**(5/2)*sqrt(1/b) + 24*a**(9/2)*b**2*x**(7/2)*sqrt(1/b)), True))","A",0
489,1,153,0,11.696853," ","integrate(x**(5/2)*(b*x+a)**(1/2),x)","\frac{5 a^{\frac{7}{2}} \sqrt{x}}{64 b^{3} \sqrt{1 + \frac{b x}{a}}} + \frac{5 a^{\frac{5}{2}} x^{\frac{3}{2}}}{192 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{a^{\frac{3}{2}} x^{\frac{5}{2}}}{96 b \sqrt{1 + \frac{b x}{a}}} + \frac{7 \sqrt{a} x^{\frac{7}{2}}}{24 \sqrt{1 + \frac{b x}{a}}} - \frac{5 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{7}{2}}} + \frac{b x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"5*a**(7/2)*sqrt(x)/(64*b**3*sqrt(1 + b*x/a)) + 5*a**(5/2)*x**(3/2)/(192*b**2*sqrt(1 + b*x/a)) - a**(3/2)*x**(5/2)/(96*b*sqrt(1 + b*x/a)) + 7*sqrt(a)*x**(7/2)/(24*sqrt(1 + b*x/a)) - 5*a**4*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(7/2)) + b*x**(9/2)/(4*sqrt(a)*sqrt(1 + b*x/a))","A",0
490,1,122,0,6.383177," ","integrate(x**(3/2)*(b*x+a)**(1/2),x)","- \frac{a^{\frac{5}{2}} \sqrt{x}}{8 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 b \sqrt{1 + \frac{b x}{a}}} + \frac{5 \sqrt{a} x^{\frac{5}{2}}}{12 \sqrt{1 + \frac{b x}{a}}} + \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{b x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-a**(5/2)*sqrt(x)/(8*b**2*sqrt(1 + b*x/a)) - a**(3/2)*x**(3/2)/(24*b*sqrt(1 + b*x/a)) + 5*sqrt(a)*x**(5/2)/(12*sqrt(1 + b*x/a)) + a**3*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(5/2)) + b*x**(7/2)/(3*sqrt(a)*sqrt(1 + b*x/a))","A",0
491,1,97,0,3.569529," ","integrate(x**(1/2)*(b*x+a)**(1/2),x)","\frac{a^{\frac{3}{2}} \sqrt{x}}{4 b \sqrt{1 + \frac{b x}{a}}} + \frac{3 \sqrt{a} x^{\frac{3}{2}}}{4 \sqrt{1 + \frac{b x}{a}}} - \frac{a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + \frac{b x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"a**(3/2)*sqrt(x)/(4*b*sqrt(1 + b*x/a)) + 3*sqrt(a)*x**(3/2)/(4*sqrt(1 + b*x/a)) - a**2*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(3/2)) + b*x**(5/2)/(2*sqrt(a)*sqrt(1 + b*x/a))","A",0
492,1,42,0,1.916200," ","integrate((b*x+a)**(1/2)/x**(1/2),x)","\sqrt{a} \sqrt{x} \sqrt{1 + \frac{b x}{a}} + \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"sqrt(a)*sqrt(x)*sqrt(1 + b*x/a) + a*asinh(sqrt(b)*sqrt(x)/sqrt(a))/sqrt(b)","A",0
493,1,68,0,1.561060," ","integrate((b*x+a)**(1/2)/x**(3/2),x)","- \frac{2 \sqrt{a}}{\sqrt{x} \sqrt{1 + \frac{b x}{a}}} + 2 \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} - \frac{2 b \sqrt{x}}{\sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-2*sqrt(a)/(sqrt(x)*sqrt(1 + b*x/a)) + 2*sqrt(b)*asinh(sqrt(b)*sqrt(x)/sqrt(a)) - 2*b*sqrt(x)/(sqrt(a)*sqrt(1 + b*x/a))","A",0
494,1,41,0,1.460778," ","integrate((b*x+a)**(1/2)/x**(5/2),x)","- \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 x} - \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a}"," ",0,"-2*sqrt(b)*sqrt(a/(b*x) + 1)/(3*x) - 2*b**(3/2)*sqrt(a/(b*x) + 1)/(3*a)","B",0
495,1,65,0,4.875391," ","integrate((b*x+a)**(1/2)/x**(7/2),x)","- \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{5 x^{2}} - \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{15 a x} + \frac{4 b^{\frac{5}{2}} \sqrt{\frac{a}{b x} + 1}}{15 a^{2}}"," ",0,"-2*sqrt(b)*sqrt(a/(b*x) + 1)/(5*x**2) - 2*b**(3/2)*sqrt(a/(b*x) + 1)/(15*a*x) + 4*b**(5/2)*sqrt(a/(b*x) + 1)/(15*a**2)","A",0
496,1,347,0,13.771678," ","integrate((b*x+a)**(1/2)/x**(9/2),x)","- \frac{30 a^{5} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}}{105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} + 105 a^{3} b^{6} x^{5}} - \frac{66 a^{4} b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} + 1}}{105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} + 105 a^{3} b^{6} x^{5}} - \frac{34 a^{3} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} + 105 a^{3} b^{6} x^{5}} - \frac{6 a^{2} b^{\frac{15}{2}} x^{3} \sqrt{\frac{a}{b x} + 1}}{105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} + 105 a^{3} b^{6} x^{5}} - \frac{24 a b^{\frac{17}{2}} x^{4} \sqrt{\frac{a}{b x} + 1}}{105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} + 105 a^{3} b^{6} x^{5}} - \frac{16 b^{\frac{19}{2}} x^{5} \sqrt{\frac{a}{b x} + 1}}{105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} + 105 a^{3} b^{6} x^{5}}"," ",0,"-30*a**5*b**(9/2)*sqrt(a/(b*x) + 1)/(105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 + 105*a**3*b**6*x**5) - 66*a**4*b**(11/2)*x*sqrt(a/(b*x) + 1)/(105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 + 105*a**3*b**6*x**5) - 34*a**3*b**(13/2)*x**2*sqrt(a/(b*x) + 1)/(105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 + 105*a**3*b**6*x**5) - 6*a**2*b**(15/2)*x**3*sqrt(a/(b*x) + 1)/(105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 + 105*a**3*b**6*x**5) - 24*a*b**(17/2)*x**4*sqrt(a/(b*x) + 1)/(105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 + 105*a**3*b**6*x**5) - 16*b**(19/2)*x**5*sqrt(a/(b*x) + 1)/(105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 + 105*a**3*b**6*x**5)","B",0
497,1,323,0,11.647843," ","integrate(x**(5/2)*(-b*x+a)**(1/2),x)","\begin{cases} \frac{5 i a^{\frac{7}{2}} \sqrt{x}}{64 b^{3} \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{\frac{5}{2}} x^{\frac{3}{2}}}{192 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{3}{2}} x^{\frac{5}{2}}}{96 b \sqrt{-1 + \frac{b x}{a}}} - \frac{7 i \sqrt{a} x^{\frac{7}{2}}}{24 \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{4} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{7}{2}}} + \frac{i b x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{5 a^{\frac{7}{2}} \sqrt{x}}{64 b^{3} \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{\frac{5}{2}} x^{\frac{3}{2}}}{192 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{3}{2}} x^{\frac{5}{2}}}{96 b \sqrt{1 - \frac{b x}{a}}} + \frac{7 \sqrt{a} x^{\frac{7}{2}}}{24 \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{4} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{7}{2}}} - \frac{b x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*I*a**(7/2)*sqrt(x)/(64*b**3*sqrt(-1 + b*x/a)) - 5*I*a**(5/2)*x**(3/2)/(192*b**2*sqrt(-1 + b*x/a)) - I*a**(3/2)*x**(5/2)/(96*b*sqrt(-1 + b*x/a)) - 7*I*sqrt(a)*x**(7/2)/(24*sqrt(-1 + b*x/a)) - 5*I*a**4*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(7/2)) + I*b*x**(9/2)/(4*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-5*a**(7/2)*sqrt(x)/(64*b**3*sqrt(1 - b*x/a)) + 5*a**(5/2)*x**(3/2)/(192*b**2*sqrt(1 - b*x/a)) + a**(3/2)*x**(5/2)/(96*b*sqrt(1 - b*x/a)) + 7*sqrt(a)*x**(7/2)/(24*sqrt(1 - b*x/a)) + 5*a**4*asin(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(7/2)) - b*x**(9/2)/(4*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
498,1,260,0,6.325385," ","integrate(x**(3/2)*(-b*x+a)**(1/2),x)","\begin{cases} \frac{i a^{\frac{5}{2}} \sqrt{x}}{8 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 b \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i \sqrt{a} x^{\frac{5}{2}}}{12 \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{3} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} + \frac{i b x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{a^{\frac{5}{2}} \sqrt{x}}{8 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 b \sqrt{1 - \frac{b x}{a}}} + \frac{5 \sqrt{a} x^{\frac{5}{2}}}{12 \sqrt{1 - \frac{b x}{a}}} + \frac{a^{3} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} - \frac{b x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a**(5/2)*sqrt(x)/(8*b**2*sqrt(-1 + b*x/a)) - I*a**(3/2)*x**(3/2)/(24*b*sqrt(-1 + b*x/a)) - 5*I*sqrt(a)*x**(5/2)/(12*sqrt(-1 + b*x/a)) - I*a**3*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(5/2)) + I*b*x**(7/2)/(3*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-a**(5/2)*sqrt(x)/(8*b**2*sqrt(1 - b*x/a)) + a**(3/2)*x**(3/2)/(24*b*sqrt(1 - b*x/a)) + 5*sqrt(a)*x**(5/2)/(12*sqrt(1 - b*x/a)) + a**3*asin(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(5/2)) - b*x**(7/2)/(3*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
499,1,207,0,3.595402," ","integrate(x**(1/2)*(-b*x+a)**(1/2),x)","\begin{cases} \frac{i a^{\frac{3}{2}} \sqrt{x}}{4 b \sqrt{-1 + \frac{b x}{a}}} - \frac{3 i \sqrt{a} x^{\frac{3}{2}}}{4 \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{2} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + \frac{i b x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{a^{\frac{3}{2}} \sqrt{x}}{4 b \sqrt{1 - \frac{b x}{a}}} + \frac{3 \sqrt{a} x^{\frac{3}{2}}}{4 \sqrt{1 - \frac{b x}{a}}} + \frac{a^{2} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} - \frac{b x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a**(3/2)*sqrt(x)/(4*b*sqrt(-1 + b*x/a)) - 3*I*sqrt(a)*x**(3/2)/(4*sqrt(-1 + b*x/a)) - I*a**2*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(3/2)) + I*b*x**(5/2)/(2*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-a**(3/2)*sqrt(x)/(4*b*sqrt(1 - b*x/a)) + 3*sqrt(a)*x**(3/2)/(4*sqrt(1 - b*x/a)) + a**2*asin(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(3/2)) - b*x**(5/2)/(2*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
500,1,119,0,1.959400," ","integrate((-b*x+a)**(1/2)/x**(1/2),x)","\begin{cases} - \frac{i \sqrt{a} \sqrt{x}}{\sqrt{-1 + \frac{b x}{a}}} - \frac{i a \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{\sqrt{b}} + \frac{i b x^{\frac{3}{2}}}{\sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\sqrt{a} \sqrt{x} \sqrt{1 - \frac{b x}{a}} + \frac{a \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*sqrt(a)*sqrt(x)/sqrt(-1 + b*x/a) - I*a*acosh(sqrt(b)*sqrt(x)/sqrt(a))/sqrt(b) + I*b*x**(3/2)/(sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (sqrt(a)*sqrt(x)*sqrt(1 - b*x/a) + a*asin(sqrt(b)*sqrt(x)/sqrt(a))/sqrt(b), True))","A",0
501,1,148,0,1.700861," ","integrate((-b*x+a)**(1/2)/x**(3/2),x)","\begin{cases} \frac{2 i \sqrt{a}}{\sqrt{x} \sqrt{-1 + \frac{b x}{a}}} + 2 i \sqrt{b} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} - \frac{2 i b \sqrt{x}}{\sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{2 \sqrt{a}}{\sqrt{x} \sqrt{1 - \frac{b x}{a}}} - 2 \sqrt{b} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} + \frac{2 b \sqrt{x}}{\sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*sqrt(a)/(sqrt(x)*sqrt(-1 + b*x/a)) + 2*I*sqrt(b)*acosh(sqrt(b)*sqrt(x)/sqrt(a)) - 2*I*b*sqrt(x)/(sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-2*sqrt(a)/(sqrt(x)*sqrt(1 - b*x/a)) - 2*sqrt(b)*asin(sqrt(b)*sqrt(x)/sqrt(a)) + 2*b*sqrt(x)/(sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
502,1,88,0,1.549017," ","integrate((-b*x+a)**(1/2)/x**(5/2),x)","\begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{3 x} + \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}}{3 a} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 i \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{3 x} + \frac{2 i b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{3 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(b)*sqrt(a/(b*x) - 1)/(3*x) + 2*b**(3/2)*sqrt(a/(b*x) - 1)/(3*a), Abs(a/(b*x)) > 1), (-2*I*sqrt(b)*sqrt(-a/(b*x) + 1)/(3*x) + 2*I*b**(3/2)*sqrt(-a/(b*x) + 1)/(3*a), True))","B",0
503,1,241,0,5.006231," ","integrate((-b*x+a)**(1/2)/x**(7/2),x)","\begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{5 x^{2}} + \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}}{15 a x} + \frac{4 b^{\frac{5}{2}} \sqrt{\frac{a}{b x} - 1}}{15 a^{2}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{6 i a^{3} b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{x \left(- 15 a^{3} b x + 15 a^{2} b^{2} x^{2}\right)} - \frac{8 i a^{2} b^{\frac{5}{2}} \sqrt{- \frac{a}{b x} + 1}}{- 15 a^{3} b x + 15 a^{2} b^{2} x^{2}} - \frac{2 i a b^{\frac{7}{2}} x \sqrt{- \frac{a}{b x} + 1}}{- 15 a^{3} b x + 15 a^{2} b^{2} x^{2}} + \frac{4 i b^{\frac{9}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{- 15 a^{3} b x + 15 a^{2} b^{2} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(b)*sqrt(a/(b*x) - 1)/(5*x**2) + 2*b**(3/2)*sqrt(a/(b*x) - 1)/(15*a*x) + 4*b**(5/2)*sqrt(a/(b*x) - 1)/(15*a**2), Abs(a/(b*x)) > 1), (6*I*a**3*b**(3/2)*sqrt(-a/(b*x) + 1)/(x*(-15*a**3*b*x + 15*a**2*b**2*x**2)) - 8*I*a**2*b**(5/2)*sqrt(-a/(b*x) + 1)/(-15*a**3*b*x + 15*a**2*b**2*x**2) - 2*I*a*b**(7/2)*x*sqrt(-a/(b*x) + 1)/(-15*a**3*b*x + 15*a**2*b**2*x**2) + 4*I*b**(9/2)*x**2*sqrt(-a/(b*x) + 1)/(-15*a**3*b*x + 15*a**2*b**2*x**2), True))","A",0
504,1,707,0,26.812890," ","integrate((-b*x+a)**(1/2)/x**(9/2),x)","\begin{cases} \frac{30 a^{5} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} - 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} - \frac{66 a^{4} b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} - 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} + \frac{34 a^{3} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} - 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} - \frac{6 a^{2} b^{\frac{15}{2}} x^{3} \sqrt{\frac{a}{b x} - 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} + \frac{24 a b^{\frac{17}{2}} x^{4} \sqrt{\frac{a}{b x} - 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} - \frac{16 b^{\frac{19}{2}} x^{5} \sqrt{\frac{a}{b x} - 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{30 i a^{5} b^{\frac{9}{2}} \sqrt{- \frac{a}{b x} + 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} - \frac{66 i a^{4} b^{\frac{11}{2}} x \sqrt{- \frac{a}{b x} + 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} + \frac{34 i a^{3} b^{\frac{13}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} - \frac{6 i a^{2} b^{\frac{15}{2}} x^{3} \sqrt{- \frac{a}{b x} + 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} + \frac{24 i a b^{\frac{17}{2}} x^{4} \sqrt{- \frac{a}{b x} + 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} - \frac{16 i b^{\frac{19}{2}} x^{5} \sqrt{- \frac{a}{b x} + 1}}{- 105 a^{5} b^{4} x^{3} + 210 a^{4} b^{5} x^{4} - 105 a^{3} b^{6} x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*a**5*b**(9/2)*sqrt(a/(b*x) - 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) - 66*a**4*b**(11/2)*x*sqrt(a/(b*x) - 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) + 34*a**3*b**(13/2)*x**2*sqrt(a/(b*x) - 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) - 6*a**2*b**(15/2)*x**3*sqrt(a/(b*x) - 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) + 24*a*b**(17/2)*x**4*sqrt(a/(b*x) - 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) - 16*b**(19/2)*x**5*sqrt(a/(b*x) - 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5), Abs(a/(b*x)) > 1), (30*I*a**5*b**(9/2)*sqrt(-a/(b*x) + 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) - 66*I*a**4*b**(11/2)*x*sqrt(-a/(b*x) + 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) + 34*I*a**3*b**(13/2)*x**2*sqrt(-a/(b*x) + 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) - 6*I*a**2*b**(15/2)*x**3*sqrt(-a/(b*x) + 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) + 24*I*a*b**(17/2)*x**4*sqrt(-a/(b*x) + 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5) - 16*I*b**(19/2)*x**5*sqrt(-a/(b*x) + 1)/(-105*a**5*b**4*x**3 + 210*a**4*b**5*x**4 - 105*a**3*b**6*x**5), True))","B",0
505,1,117,0,10.124051," ","integrate(x**(5/2)*(b*x+2)**(1/2),x)","\frac{b x^{\frac{9}{2}}}{4 \sqrt{b x + 2}} + \frac{7 x^{\frac{7}{2}}}{12 \sqrt{b x + 2}} - \frac{x^{\frac{5}{2}}}{24 b \sqrt{b x + 2}} + \frac{5 x^{\frac{3}{2}}}{24 b^{2} \sqrt{b x + 2}} + \frac{5 \sqrt{x}}{4 b^{3} \sqrt{b x + 2}} - \frac{5 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{7}{2}}}"," ",0,"b*x**(9/2)/(4*sqrt(b*x + 2)) + 7*x**(7/2)/(12*sqrt(b*x + 2)) - x**(5/2)/(24*b*sqrt(b*x + 2)) + 5*x**(3/2)/(24*b**2*sqrt(b*x + 2)) + 5*sqrt(x)/(4*b**3*sqrt(b*x + 2)) - 5*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(7/2))","A",0
506,1,90,0,5.223283," ","integrate(x**(3/2)*(b*x+2)**(1/2),x)","\frac{b x^{\frac{7}{2}}}{3 \sqrt{b x + 2}} + \frac{5 x^{\frac{5}{2}}}{6 \sqrt{b x + 2}} - \frac{x^{\frac{3}{2}}}{6 b \sqrt{b x + 2}} - \frac{\sqrt{x}}{b^{2} \sqrt{b x + 2}} + \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}}"," ",0,"b*x**(7/2)/(3*sqrt(b*x + 2)) + 5*x**(5/2)/(6*sqrt(b*x + 2)) - x**(3/2)/(6*b*sqrt(b*x + 2)) - sqrt(x)/(b**2*sqrt(b*x + 2)) + asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2)","A",0
507,1,71,0,2.912189," ","integrate(x**(1/2)*(b*x+2)**(1/2),x)","\frac{b x^{\frac{5}{2}}}{2 \sqrt{b x + 2}} + \frac{3 x^{\frac{3}{2}}}{2 \sqrt{b x + 2}} + \frac{\sqrt{x}}{b \sqrt{b x + 2}} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}}"," ",0,"b*x**(5/2)/(2*sqrt(b*x + 2)) + 3*x**(3/2)/(2*sqrt(b*x + 2)) + sqrt(x)/(b*sqrt(b*x + 2)) - asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2)","A",0
508,1,37,0,1.648130," ","integrate((b*x+2)**(1/2)/x**(1/2),x)","\sqrt{x} \sqrt{b x + 2} + \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}}"," ",0,"sqrt(x)*sqrt(b*x + 2) + 2*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b)","A",0
509,1,48,0,1.429161," ","integrate((b*x+2)**(1/2)/x**(3/2),x)","- 2 \sqrt{b} \sqrt{1 + \frac{2}{b x}} - \sqrt{b} \log{\left(\frac{1}{b x} \right)} + 2 \sqrt{b} \log{\left(\sqrt{1 + \frac{2}{b x}} + 1 \right)}"," ",0,"-2*sqrt(b)*sqrt(1 + 2/(b*x)) - sqrt(b)*log(1/(b*x)) + 2*sqrt(b)*log(sqrt(1 + 2/(b*x)) + 1)","A",0
510,1,37,0,1.451398," ","integrate((b*x+2)**(1/2)/x**(5/2),x)","- \frac{b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{3} - \frac{2 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}{3 x}"," ",0,"-b**(3/2)*sqrt(1 + 2/(b*x))/3 - 2*sqrt(b)*sqrt(1 + 2/(b*x))/(3*x)","B",0
511,1,56,0,4.716724," ","integrate((b*x+2)**(1/2)/x**(7/2),x)","\frac{b^{\frac{5}{2}} \sqrt{1 + \frac{2}{b x}}}{15} - \frac{b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{15 x} - \frac{2 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}{5 x^{2}}"," ",0,"b**(5/2)*sqrt(1 + 2/(b*x))/15 - b**(3/2)*sqrt(1 + 2/(b*x))/(15*x) - 2*sqrt(b)*sqrt(1 + 2/(b*x))/(5*x**2)","A",0
512,1,270,0,13.796272," ","integrate((b*x+2)**(1/2)/x**(9/2),x)","- \frac{2 b^{\frac{19}{2}} x^{5} \sqrt{1 + \frac{2}{b x}}}{105 b^{6} x^{5} + 420 b^{5} x^{4} + 420 b^{4} x^{3}} - \frac{6 b^{\frac{17}{2}} x^{4} \sqrt{1 + \frac{2}{b x}}}{105 b^{6} x^{5} + 420 b^{5} x^{4} + 420 b^{4} x^{3}} - \frac{3 b^{\frac{15}{2}} x^{3} \sqrt{1 + \frac{2}{b x}}}{105 b^{6} x^{5} + 420 b^{5} x^{4} + 420 b^{4} x^{3}} - \frac{34 b^{\frac{13}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{105 b^{6} x^{5} + 420 b^{5} x^{4} + 420 b^{4} x^{3}} - \frac{132 b^{\frac{11}{2}} x \sqrt{1 + \frac{2}{b x}}}{105 b^{6} x^{5} + 420 b^{5} x^{4} + 420 b^{4} x^{3}} - \frac{120 b^{\frac{9}{2}} \sqrt{1 + \frac{2}{b x}}}{105 b^{6} x^{5} + 420 b^{5} x^{4} + 420 b^{4} x^{3}}"," ",0,"-2*b**(19/2)*x**5*sqrt(1 + 2/(b*x))/(105*b**6*x**5 + 420*b**5*x**4 + 420*b**4*x**3) - 6*b**(17/2)*x**4*sqrt(1 + 2/(b*x))/(105*b**6*x**5 + 420*b**5*x**4 + 420*b**4*x**3) - 3*b**(15/2)*x**3*sqrt(1 + 2/(b*x))/(105*b**6*x**5 + 420*b**5*x**4 + 420*b**4*x**3) - 34*b**(13/2)*x**2*sqrt(1 + 2/(b*x))/(105*b**6*x**5 + 420*b**5*x**4 + 420*b**4*x**3) - 132*b**(11/2)*x*sqrt(1 + 2/(b*x))/(105*b**6*x**5 + 420*b**5*x**4 + 420*b**4*x**3) - 120*b**(9/2)*sqrt(1 + 2/(b*x))/(105*b**6*x**5 + 420*b**5*x**4 + 420*b**4*x**3)","B",0
513,1,252,0,9.916113," ","integrate(x**(5/2)*(-b*x+2)**(1/2),x)","\begin{cases} \frac{i b x^{\frac{9}{2}}}{4 \sqrt{b x - 2}} - \frac{7 i x^{\frac{7}{2}}}{12 \sqrt{b x - 2}} - \frac{i x^{\frac{5}{2}}}{24 b \sqrt{b x - 2}} - \frac{5 i x^{\frac{3}{2}}}{24 b^{2} \sqrt{b x - 2}} + \frac{5 i \sqrt{x}}{4 b^{3} \sqrt{b x - 2}} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{7}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b x^{\frac{9}{2}}}{4 \sqrt{- b x + 2}} + \frac{7 x^{\frac{7}{2}}}{12 \sqrt{- b x + 2}} + \frac{x^{\frac{5}{2}}}{24 b \sqrt{- b x + 2}} + \frac{5 x^{\frac{3}{2}}}{24 b^{2} \sqrt{- b x + 2}} - \frac{5 \sqrt{x}}{4 b^{3} \sqrt{- b x + 2}} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b*x**(9/2)/(4*sqrt(b*x - 2)) - 7*I*x**(7/2)/(12*sqrt(b*x - 2)) - I*x**(5/2)/(24*b*sqrt(b*x - 2)) - 5*I*x**(3/2)/(24*b**2*sqrt(b*x - 2)) + 5*I*sqrt(x)/(4*b**3*sqrt(b*x - 2)) - 5*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(7/2)), Abs(b*x)/2 > 1), (-b*x**(9/2)/(4*sqrt(-b*x + 2)) + 7*x**(7/2)/(12*sqrt(-b*x + 2)) + x**(5/2)/(24*b*sqrt(-b*x + 2)) + 5*x**(3/2)/(24*b**2*sqrt(-b*x + 2)) - 5*sqrt(x)/(4*b**3*sqrt(-b*x + 2)) + 5*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(7/2)), True))","A",0
514,1,196,0,5.294173," ","integrate(x**(3/2)*(-b*x+2)**(1/2),x)","\begin{cases} \frac{i b x^{\frac{7}{2}}}{3 \sqrt{b x - 2}} - \frac{5 i x^{\frac{5}{2}}}{6 \sqrt{b x - 2}} - \frac{i x^{\frac{3}{2}}}{6 b \sqrt{b x - 2}} + \frac{i \sqrt{x}}{b^{2} \sqrt{b x - 2}} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b x^{\frac{7}{2}}}{3 \sqrt{- b x + 2}} + \frac{5 x^{\frac{5}{2}}}{6 \sqrt{- b x + 2}} + \frac{x^{\frac{3}{2}}}{6 b \sqrt{- b x + 2}} - \frac{\sqrt{x}}{b^{2} \sqrt{- b x + 2}} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b*x**(7/2)/(3*sqrt(b*x - 2)) - 5*I*x**(5/2)/(6*sqrt(b*x - 2)) - I*x**(3/2)/(6*b*sqrt(b*x - 2)) + I*sqrt(x)/(b**2*sqrt(b*x - 2)) - I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2), Abs(b*x)/2 > 1), (-b*x**(7/2)/(3*sqrt(-b*x + 2)) + 5*x**(5/2)/(6*sqrt(-b*x + 2)) + x**(3/2)/(6*b*sqrt(-b*x + 2)) - sqrt(x)/(b**2*sqrt(-b*x + 2)) + asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2), True))","A",0
515,1,156,0,2.941776," ","integrate(x**(1/2)*(-b*x+2)**(1/2),x)","\begin{cases} \frac{i b x^{\frac{5}{2}}}{2 \sqrt{b x - 2}} - \frac{3 i x^{\frac{3}{2}}}{2 \sqrt{b x - 2}} + \frac{i \sqrt{x}}{b \sqrt{b x - 2}} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b x^{\frac{5}{2}}}{2 \sqrt{- b x + 2}} + \frac{3 x^{\frac{3}{2}}}{2 \sqrt{- b x + 2}} - \frac{\sqrt{x}}{b \sqrt{- b x + 2}} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b*x**(5/2)/(2*sqrt(b*x - 2)) - 3*I*x**(3/2)/(2*sqrt(b*x - 2)) + I*sqrt(x)/(b*sqrt(b*x - 2)) - I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), Abs(b*x)/2 > 1), (-b*x**(5/2)/(2*sqrt(-b*x + 2)) + 3*x**(3/2)/(2*sqrt(-b*x + 2)) - sqrt(x)/(b*sqrt(-b*x + 2)) + asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), True))","A",0
516,1,121,0,1.710570," ","integrate((-b*x+2)**(1/2)/x**(1/2),x)","\begin{cases} \frac{i b x^{\frac{3}{2}}}{\sqrt{b x - 2}} - \frac{2 i \sqrt{x}}{\sqrt{b x - 2}} - \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b x^{\frac{3}{2}}}{\sqrt{- b x + 2}} + \frac{2 \sqrt{x}}{\sqrt{- b x + 2}} + \frac{2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b*x**(3/2)/sqrt(b*x - 2) - 2*I*sqrt(x)/sqrt(b*x - 2) - 2*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), Abs(b*x)/2 > 1), (-b*x**(3/2)/sqrt(-b*x + 2) + 2*sqrt(x)/sqrt(-b*x + 2) + 2*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), True))","A",0
517,1,136,0,1.580066," ","integrate((-b*x+2)**(1/2)/x**(3/2),x)","\begin{cases} - 2 \sqrt{b} \sqrt{-1 + \frac{2}{b x}} - i \sqrt{b} \log{\left(\frac{1}{b x} \right)} + 2 i \sqrt{b} \log{\left(\frac{1}{\sqrt{b} \sqrt{x}} \right)} - 2 \sqrt{b} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\- 2 i \sqrt{b} \sqrt{1 - \frac{2}{b x}} - i \sqrt{b} \log{\left(\frac{1}{b x} \right)} + 2 i \sqrt{b} \log{\left(\sqrt{1 - \frac{2}{b x}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(b)*sqrt(-1 + 2/(b*x)) - I*sqrt(b)*log(1/(b*x)) + 2*I*sqrt(b)*log(1/(sqrt(b)*sqrt(x))) - 2*sqrt(b)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2), 2/Abs(b*x) > 1), (-2*I*sqrt(b)*sqrt(1 - 2/(b*x)) - I*sqrt(b)*log(1/(b*x)) + 2*I*sqrt(b)*log(sqrt(1 - 2/(b*x)) + 1), True))","C",0
518,1,82,0,1.505796," ","integrate((-b*x+2)**(1/2)/x**(5/2),x)","\begin{cases} \frac{b^{\frac{3}{2}} \sqrt{-1 + \frac{2}{b x}}}{3} - \frac{2 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}}{3 x} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{3} - \frac{2 i \sqrt{b} \sqrt{1 - \frac{2}{b x}}}{3 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(3/2)*sqrt(-1 + 2/(b*x))/3 - 2*sqrt(b)*sqrt(-1 + 2/(b*x))/(3*x), 2/Abs(b*x) > 1), (I*b**(3/2)*sqrt(1 - 2/(b*x))/3 - 2*I*sqrt(b)*sqrt(1 - 2/(b*x))/(3*x), True))","B",0
519,1,194,0,4.909466," ","integrate((-b*x+2)**(1/2)/x**(7/2),x)","\begin{cases} \frac{b^{\frac{5}{2}} \sqrt{-1 + \frac{2}{b x}}}{15} + \frac{b^{\frac{3}{2}} \sqrt{-1 + \frac{2}{b x}}}{15 x} - \frac{2 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}}{5 x^{2}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\- \frac{i b^{\frac{9}{2}} x^{2} \sqrt{1 - \frac{2}{b x}}}{- 15 b^{2} x^{2} + 30 b x} + \frac{i b^{\frac{7}{2}} x \sqrt{1 - \frac{2}{b x}}}{- 15 b^{2} x^{2} + 30 b x} + \frac{8 i b^{\frac{5}{2}} \sqrt{1 - \frac{2}{b x}}}{- 15 b^{2} x^{2} + 30 b x} - \frac{12 i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{x \left(- 15 b^{2} x^{2} + 30 b x\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(5/2)*sqrt(-1 + 2/(b*x))/15 + b**(3/2)*sqrt(-1 + 2/(b*x))/(15*x) - 2*sqrt(b)*sqrt(-1 + 2/(b*x))/(5*x**2), 2/Abs(b*x) > 1), (-I*b**(9/2)*x**2*sqrt(1 - 2/(b*x))/(-15*b**2*x**2 + 30*b*x) + I*b**(7/2)*x*sqrt(1 - 2/(b*x))/(-15*b**2*x**2 + 30*b*x) + 8*I*b**(5/2)*sqrt(1 - 2/(b*x))/(-15*b**2*x**2 + 30*b*x) - 12*I*b**(3/2)*sqrt(1 - 2/(b*x))/(x*(-15*b**2*x**2 + 30*b*x)), True))","A",0
520,1,554,0,24.597785," ","integrate((-b*x+2)**(1/2)/x**(9/2),x)","\begin{cases} - \frac{2 b^{\frac{19}{2}} x^{5} \sqrt{-1 + \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} + \frac{6 b^{\frac{17}{2}} x^{4} \sqrt{-1 + \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} - \frac{3 b^{\frac{15}{2}} x^{3} \sqrt{-1 + \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} + \frac{34 b^{\frac{13}{2}} x^{2} \sqrt{-1 + \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} - \frac{132 b^{\frac{11}{2}} x \sqrt{-1 + \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} + \frac{120 b^{\frac{9}{2}} \sqrt{-1 + \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\- \frac{2 i b^{\frac{19}{2}} x^{5} \sqrt{1 - \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} + \frac{6 i b^{\frac{17}{2}} x^{4} \sqrt{1 - \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} - \frac{3 i b^{\frac{15}{2}} x^{3} \sqrt{1 - \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} + \frac{34 i b^{\frac{13}{2}} x^{2} \sqrt{1 - \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} - \frac{132 i b^{\frac{11}{2}} x \sqrt{1 - \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} + \frac{120 i b^{\frac{9}{2}} \sqrt{1 - \frac{2}{b x}}}{- 105 b^{6} x^{5} + 420 b^{5} x^{4} - 420 b^{4} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*b**(19/2)*x**5*sqrt(-1 + 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) + 6*b**(17/2)*x**4*sqrt(-1 + 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) - 3*b**(15/2)*x**3*sqrt(-1 + 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) + 34*b**(13/2)*x**2*sqrt(-1 + 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) - 132*b**(11/2)*x*sqrt(-1 + 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) + 120*b**(9/2)*sqrt(-1 + 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3), 2/Abs(b*x) > 1), (-2*I*b**(19/2)*x**5*sqrt(1 - 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) + 6*I*b**(17/2)*x**4*sqrt(1 - 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) - 3*I*b**(15/2)*x**3*sqrt(1 - 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) + 34*I*b**(13/2)*x**2*sqrt(1 - 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) - 132*I*b**(11/2)*x*sqrt(1 - 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3) + 120*I*b**(9/2)*sqrt(1 - 2/(b*x))/(-105*b**6*x**5 + 420*b**5*x**4 - 420*b**4*x**3), True))","B",0
521,1,178,0,17.714059," ","integrate(x**(5/2)*(b*x+a)**(3/2),x)","\frac{3 a^{\frac{9}{2}} \sqrt{x}}{128 b^{3} \sqrt{1 + \frac{b x}{a}}} + \frac{a^{\frac{7}{2}} x^{\frac{3}{2}}}{128 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{a^{\frac{5}{2}} x^{\frac{5}{2}}}{320 b \sqrt{1 + \frac{b x}{a}}} + \frac{23 a^{\frac{3}{2}} x^{\frac{7}{2}}}{80 \sqrt{1 + \frac{b x}{a}}} + \frac{19 \sqrt{a} b x^{\frac{9}{2}}}{40 \sqrt{1 + \frac{b x}{a}}} - \frac{3 a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{128 b^{\frac{7}{2}}} + \frac{b^{2} x^{\frac{11}{2}}}{5 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"3*a**(9/2)*sqrt(x)/(128*b**3*sqrt(1 + b*x/a)) + a**(7/2)*x**(3/2)/(128*b**2*sqrt(1 + b*x/a)) - a**(5/2)*x**(5/2)/(320*b*sqrt(1 + b*x/a)) + 23*a**(3/2)*x**(7/2)/(80*sqrt(1 + b*x/a)) + 19*sqrt(a)*b*x**(9/2)/(40*sqrt(1 + b*x/a)) - 3*a**5*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(128*b**(7/2)) + b**2*x**(11/2)/(5*sqrt(a)*sqrt(1 + b*x/a))","A",0
522,1,153,0,9.278677," ","integrate(x**(3/2)*(b*x+a)**(3/2),x)","- \frac{3 a^{\frac{7}{2}} \sqrt{x}}{64 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{a^{\frac{5}{2}} x^{\frac{3}{2}}}{64 b \sqrt{1 + \frac{b x}{a}}} + \frac{13 a^{\frac{3}{2}} x^{\frac{5}{2}}}{32 \sqrt{1 + \frac{b x}{a}}} + \frac{5 \sqrt{a} b x^{\frac{7}{2}}}{8 \sqrt{1 + \frac{b x}{a}}} + \frac{3 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{5}{2}}} + \frac{b^{2} x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-3*a**(7/2)*sqrt(x)/(64*b**2*sqrt(1 + b*x/a)) - a**(5/2)*x**(3/2)/(64*b*sqrt(1 + b*x/a)) + 13*a**(3/2)*x**(5/2)/(32*sqrt(1 + b*x/a)) + 5*sqrt(a)*b*x**(7/2)/(8*sqrt(1 + b*x/a)) + 3*a**4*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(5/2)) + b**2*x**(9/2)/(4*sqrt(a)*sqrt(1 + b*x/a))","A",0
523,1,124,0,5.590401," ","integrate((b*x+a)**(3/2)*x**(1/2),x)","\frac{a^{\frac{5}{2}} \sqrt{x}}{8 b \sqrt{1 + \frac{b x}{a}}} + \frac{17 a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 \sqrt{1 + \frac{b x}{a}}} + \frac{11 \sqrt{a} b x^{\frac{5}{2}}}{12 \sqrt{1 + \frac{b x}{a}}} - \frac{a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{b^{2} x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"a**(5/2)*sqrt(x)/(8*b*sqrt(1 + b*x/a)) + 17*a**(3/2)*x**(3/2)/(24*sqrt(1 + b*x/a)) + 11*sqrt(a)*b*x**(5/2)/(12*sqrt(1 + b*x/a)) - a**3*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(3/2)) + b**2*x**(7/2)/(3*sqrt(a)*sqrt(1 + b*x/a))","A",0
524,1,75,0,3.173064," ","integrate((b*x+a)**(3/2)/x**(1/2),x)","\frac{5 a^{\frac{3}{2}} \sqrt{x} \sqrt{1 + \frac{b x}{a}}}{4} + \frac{\sqrt{a} b x^{\frac{3}{2}} \sqrt{1 + \frac{b x}{a}}}{2} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 \sqrt{b}}"," ",0,"5*a**(3/2)*sqrt(x)*sqrt(1 + b*x/a)/4 + sqrt(a)*b*x**(3/2)*sqrt(1 + b*x/a)/2 + 3*a**2*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(4*sqrt(b))","A",0
525,1,92,0,2.722349," ","integrate((b*x+a)**(3/2)/x**(3/2),x)","- \frac{2 a^{\frac{3}{2}}}{\sqrt{x} \sqrt{1 + \frac{b x}{a}}} - \frac{\sqrt{a} b \sqrt{x}}{\sqrt{1 + \frac{b x}{a}}} + 3 a \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} + \frac{b^{2} x^{\frac{3}{2}}}{\sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-2*a**(3/2)/(sqrt(x)*sqrt(1 + b*x/a)) - sqrt(a)*b*sqrt(x)/sqrt(1 + b*x/a) + 3*a*sqrt(b)*asinh(sqrt(b)*sqrt(x)/sqrt(a)) + b**2*x**(3/2)/(sqrt(a)*sqrt(1 + b*x/a))","A",0
526,1,71,0,3.036308," ","integrate((b*x+a)**(3/2)/x**(5/2),x)","- \frac{2 a \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 x} - \frac{8 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{3} - b^{\frac{3}{2}} \log{\left(\frac{a}{b x} \right)} + 2 b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a}{b x} + 1} + 1 \right)}"," ",0,"-2*a*sqrt(b)*sqrt(a/(b*x) + 1)/(3*x) - 8*b**(3/2)*sqrt(a/(b*x) + 1)/3 - b**(3/2)*log(a/(b*x)) + 2*b**(3/2)*log(sqrt(a/(b*x) + 1) + 1)","A",0
527,1,376,0,17.692944," ","integrate(x**(5/2)*(-b*x+a)**(3/2),x)","\begin{cases} \frac{3 i a^{\frac{9}{2}} \sqrt{x}}{128 b^{3} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{7}{2}} x^{\frac{3}{2}}}{128 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{5}{2}} x^{\frac{5}{2}}}{320 b \sqrt{-1 + \frac{b x}{a}}} - \frac{23 i a^{\frac{3}{2}} x^{\frac{7}{2}}}{80 \sqrt{-1 + \frac{b x}{a}}} + \frac{19 i \sqrt{a} b x^{\frac{9}{2}}}{40 \sqrt{-1 + \frac{b x}{a}}} - \frac{3 i a^{5} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{128 b^{\frac{7}{2}}} - \frac{i b^{2} x^{\frac{11}{2}}}{5 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{3 a^{\frac{9}{2}} \sqrt{x}}{128 b^{3} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{7}{2}} x^{\frac{3}{2}}}{128 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{5}{2}} x^{\frac{5}{2}}}{320 b \sqrt{1 - \frac{b x}{a}}} + \frac{23 a^{\frac{3}{2}} x^{\frac{7}{2}}}{80 \sqrt{1 - \frac{b x}{a}}} - \frac{19 \sqrt{a} b x^{\frac{9}{2}}}{40 \sqrt{1 - \frac{b x}{a}}} + \frac{3 a^{5} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{128 b^{\frac{7}{2}}} + \frac{b^{2} x^{\frac{11}{2}}}{5 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*I*a**(9/2)*sqrt(x)/(128*b**3*sqrt(-1 + b*x/a)) - I*a**(7/2)*x**(3/2)/(128*b**2*sqrt(-1 + b*x/a)) - I*a**(5/2)*x**(5/2)/(320*b*sqrt(-1 + b*x/a)) - 23*I*a**(3/2)*x**(7/2)/(80*sqrt(-1 + b*x/a)) + 19*I*sqrt(a)*b*x**(9/2)/(40*sqrt(-1 + b*x/a)) - 3*I*a**5*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(128*b**(7/2)) - I*b**2*x**(11/2)/(5*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-3*a**(9/2)*sqrt(x)/(128*b**3*sqrt(1 - b*x/a)) + a**(7/2)*x**(3/2)/(128*b**2*sqrt(1 - b*x/a)) + a**(5/2)*x**(5/2)/(320*b*sqrt(1 - b*x/a)) + 23*a**(3/2)*x**(7/2)/(80*sqrt(1 - b*x/a)) - 19*sqrt(a)*b*x**(9/2)/(40*sqrt(1 - b*x/a)) + 3*a**5*asin(sqrt(b)*sqrt(x)/sqrt(a))/(128*b**(7/2)) + b**2*x**(11/2)/(5*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
528,1,323,0,9.059867," ","integrate(x**(3/2)*(-b*x+a)**(3/2),x)","\begin{cases} \frac{3 i a^{\frac{7}{2}} \sqrt{x}}{64 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{5}{2}} x^{\frac{3}{2}}}{64 b \sqrt{-1 + \frac{b x}{a}}} - \frac{13 i a^{\frac{3}{2}} x^{\frac{5}{2}}}{32 \sqrt{-1 + \frac{b x}{a}}} + \frac{5 i \sqrt{a} b x^{\frac{7}{2}}}{8 \sqrt{-1 + \frac{b x}{a}}} - \frac{3 i a^{4} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{5}{2}}} - \frac{i b^{2} x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{3 a^{\frac{7}{2}} \sqrt{x}}{64 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{5}{2}} x^{\frac{3}{2}}}{64 b \sqrt{1 - \frac{b x}{a}}} + \frac{13 a^{\frac{3}{2}} x^{\frac{5}{2}}}{32 \sqrt{1 - \frac{b x}{a}}} - \frac{5 \sqrt{a} b x^{\frac{7}{2}}}{8 \sqrt{1 - \frac{b x}{a}}} + \frac{3 a^{4} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{5}{2}}} + \frac{b^{2} x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*I*a**(7/2)*sqrt(x)/(64*b**2*sqrt(-1 + b*x/a)) - I*a**(5/2)*x**(3/2)/(64*b*sqrt(-1 + b*x/a)) - 13*I*a**(3/2)*x**(5/2)/(32*sqrt(-1 + b*x/a)) + 5*I*sqrt(a)*b*x**(7/2)/(8*sqrt(-1 + b*x/a)) - 3*I*a**4*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(5/2)) - I*b**2*x**(9/2)/(4*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-3*a**(7/2)*sqrt(x)/(64*b**2*sqrt(1 - b*x/a)) + a**(5/2)*x**(3/2)/(64*b*sqrt(1 - b*x/a)) + 13*a**(3/2)*x**(5/2)/(32*sqrt(1 - b*x/a)) - 5*sqrt(a)*b*x**(7/2)/(8*sqrt(1 - b*x/a)) + 3*a**4*asin(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(5/2)) + b**2*x**(9/2)/(4*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
529,1,264,0,5.537259," ","integrate((-b*x+a)**(3/2)*x**(1/2),x)","\begin{cases} \frac{i a^{\frac{5}{2}} \sqrt{x}}{8 b \sqrt{-1 + \frac{b x}{a}}} - \frac{17 i a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 \sqrt{-1 + \frac{b x}{a}}} + \frac{11 i \sqrt{a} b x^{\frac{5}{2}}}{12 \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{3} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} - \frac{i b^{2} x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{a^{\frac{5}{2}} \sqrt{x}}{8 b \sqrt{1 - \frac{b x}{a}}} + \frac{17 a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 \sqrt{1 - \frac{b x}{a}}} - \frac{11 \sqrt{a} b x^{\frac{5}{2}}}{12 \sqrt{1 - \frac{b x}{a}}} + \frac{a^{3} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{b^{2} x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a**(5/2)*sqrt(x)/(8*b*sqrt(-1 + b*x/a)) - 17*I*a**(3/2)*x**(3/2)/(24*sqrt(-1 + b*x/a)) + 11*I*sqrt(a)*b*x**(5/2)/(12*sqrt(-1 + b*x/a)) - I*a**3*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(3/2)) - I*b**2*x**(7/2)/(3*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-a**(5/2)*sqrt(x)/(8*b*sqrt(1 - b*x/a)) + 17*a**(3/2)*x**(3/2)/(24*sqrt(1 - b*x/a)) - 11*sqrt(a)*b*x**(5/2)/(12*sqrt(1 - b*x/a)) + a**3*asin(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(3/2)) + b**2*x**(7/2)/(3*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
530,1,190,0,3.211844," ","integrate((-b*x+a)**(3/2)/x**(1/2),x)","\begin{cases} - \frac{5 i a^{\frac{3}{2}} \sqrt{x}}{4 \sqrt{-1 + \frac{b x}{a}}} + \frac{7 i \sqrt{a} b x^{\frac{3}{2}}}{4 \sqrt{-1 + \frac{b x}{a}}} - \frac{3 i a^{2} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 \sqrt{b}} - \frac{i b^{2} x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{5 a^{\frac{3}{2}} \sqrt{x} \sqrt{1 - \frac{b x}{a}}}{4} - \frac{\sqrt{a} b x^{\frac{3}{2}} \sqrt{1 - \frac{b x}{a}}}{2} + \frac{3 a^{2} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 \sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*a**(3/2)*sqrt(x)/(4*sqrt(-1 + b*x/a)) + 7*I*sqrt(a)*b*x**(3/2)/(4*sqrt(-1 + b*x/a)) - 3*I*a**2*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(4*sqrt(b)) - I*b**2*x**(5/2)/(2*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (5*a**(3/2)*sqrt(x)*sqrt(1 - b*x/a)/4 - sqrt(a)*b*x**(3/2)*sqrt(1 - b*x/a)/2 + 3*a**2*asin(sqrt(b)*sqrt(x)/sqrt(a))/(4*sqrt(b)), True))","A",0
531,1,197,0,2.880765," ","integrate((-b*x+a)**(3/2)/x**(3/2),x)","\begin{cases} \frac{2 i a^{\frac{3}{2}}}{\sqrt{x} \sqrt{-1 + \frac{b x}{a}}} - \frac{i \sqrt{a} b \sqrt{x}}{\sqrt{-1 + \frac{b x}{a}}} + 3 i a \sqrt{b} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} - \frac{i b^{2} x^{\frac{3}{2}}}{\sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{2 a^{\frac{3}{2}}}{\sqrt{x} \sqrt{1 - \frac{b x}{a}}} + \frac{\sqrt{a} b \sqrt{x}}{\sqrt{1 - \frac{b x}{a}}} - 3 a \sqrt{b} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} + \frac{b^{2} x^{\frac{3}{2}}}{\sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*a**(3/2)/(sqrt(x)*sqrt(-1 + b*x/a)) - I*sqrt(a)*b*sqrt(x)/sqrt(-1 + b*x/a) + 3*I*a*sqrt(b)*acosh(sqrt(b)*sqrt(x)/sqrt(a)) - I*b**2*x**(3/2)/(sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-2*a**(3/2)/(sqrt(x)*sqrt(1 - b*x/a)) + sqrt(a)*b*sqrt(x)/sqrt(1 - b*x/a) - 3*a*sqrt(b)*asin(sqrt(b)*sqrt(x)/sqrt(a)) + b**2*x**(3/2)/(sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
532,1,187,0,3.240649," ","integrate((-b*x+a)**(3/2)/x**(5/2),x)","\begin{cases} - \frac{2 a \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{3 x} + \frac{8 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}}{3} - 2 i b^{\frac{3}{2}} \log{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + i b^{\frac{3}{2}} \log{\left(\frac{a}{b x} \right)} + 2 b^{\frac{3}{2}} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 i a \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{3 x} + \frac{8 i b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{3} + i b^{\frac{3}{2}} \log{\left(\frac{a}{b x} \right)} - 2 i b^{\frac{3}{2}} \log{\left(\sqrt{- \frac{a}{b x} + 1} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*sqrt(b)*sqrt(a/(b*x) - 1)/(3*x) + 8*b**(3/2)*sqrt(a/(b*x) - 1)/3 - 2*I*b**(3/2)*log(sqrt(a)/(sqrt(b)*sqrt(x))) + I*b**(3/2)*log(a/(b*x)) + 2*b**(3/2)*asin(sqrt(b)*sqrt(x)/sqrt(a)), Abs(a/(b*x)) > 1), (-2*I*a*sqrt(b)*sqrt(-a/(b*x) + 1)/(3*x) + 8*I*b**(3/2)*sqrt(-a/(b*x) + 1)/3 + I*b**(3/2)*log(a/(b*x)) - 2*I*b**(3/2)*log(sqrt(-a/(b*x) + 1) + 1), True))","C",0
533,1,136,0,15.670537," ","integrate(x**(5/2)*(b*x+2)**(3/2),x)","\frac{b^{2} x^{\frac{11}{2}}}{5 \sqrt{b x + 2}} + \frac{19 b x^{\frac{9}{2}}}{20 \sqrt{b x + 2}} + \frac{23 x^{\frac{7}{2}}}{20 \sqrt{b x + 2}} - \frac{x^{\frac{5}{2}}}{40 b \sqrt{b x + 2}} + \frac{x^{\frac{3}{2}}}{8 b^{2} \sqrt{b x + 2}} + \frac{3 \sqrt{x}}{4 b^{3} \sqrt{b x + 2}} - \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{7}{2}}}"," ",0,"b**2*x**(11/2)/(5*sqrt(b*x + 2)) + 19*b*x**(9/2)/(20*sqrt(b*x + 2)) + 23*x**(7/2)/(20*sqrt(b*x + 2)) - x**(5/2)/(40*b*sqrt(b*x + 2)) + x**(3/2)/(8*b**2*sqrt(b*x + 2)) + 3*sqrt(x)/(4*b**3*sqrt(b*x + 2)) - 3*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(7/2))","A",0
534,1,117,0,7.858106," ","integrate(x**(3/2)*(b*x+2)**(3/2),x)","\frac{b^{2} x^{\frac{9}{2}}}{4 \sqrt{b x + 2}} + \frac{5 b x^{\frac{7}{2}}}{4 \sqrt{b x + 2}} + \frac{13 x^{\frac{5}{2}}}{8 \sqrt{b x + 2}} - \frac{x^{\frac{3}{2}}}{8 b \sqrt{b x + 2}} - \frac{3 \sqrt{x}}{4 b^{2} \sqrt{b x + 2}} + \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{5}{2}}}"," ",0,"b**2*x**(9/2)/(4*sqrt(b*x + 2)) + 5*b*x**(7/2)/(4*sqrt(b*x + 2)) + 13*x**(5/2)/(8*sqrt(b*x + 2)) - x**(3/2)/(8*b*sqrt(b*x + 2)) - 3*sqrt(x)/(4*b**2*sqrt(b*x + 2)) + 3*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(5/2))","A",0
535,1,92,0,4.809366," ","integrate((b*x+2)**(3/2)*x**(1/2),x)","\frac{b^{2} x^{\frac{7}{2}}}{3 \sqrt{b x + 2}} + \frac{11 b x^{\frac{5}{2}}}{6 \sqrt{b x + 2}} + \frac{17 x^{\frac{3}{2}}}{6 \sqrt{b x + 2}} + \frac{\sqrt{x}}{b \sqrt{b x + 2}} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}}"," ",0,"b**2*x**(7/2)/(3*sqrt(b*x + 2)) + 11*b*x**(5/2)/(6*sqrt(b*x + 2)) + 17*x**(3/2)/(6*sqrt(b*x + 2)) + sqrt(x)/(b*sqrt(b*x + 2)) - asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2)","A",0
536,1,76,0,2.816227," ","integrate((b*x+2)**(3/2)/x**(1/2),x)","\frac{b^{2} x^{\frac{5}{2}}}{2 \sqrt{b x + 2}} + \frac{7 b x^{\frac{3}{2}}}{2 \sqrt{b x + 2}} + \frac{5 \sqrt{x}}{\sqrt{b x + 2}} + \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}}"," ",0,"b**2*x**(5/2)/(2*sqrt(b*x + 2)) + 7*b*x**(3/2)/(2*sqrt(b*x + 2)) + 5*sqrt(x)/sqrt(b*x + 2) + 3*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b)","A",0
537,1,73,0,2.442130," ","integrate((b*x+2)**(3/2)/x**(3/2),x)","6 \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} + \frac{b^{2} x^{\frac{3}{2}}}{\sqrt{b x + 2}} - \frac{2 b \sqrt{x}}{\sqrt{b x + 2}} - \frac{8}{\sqrt{x} \sqrt{b x + 2}}"," ",0,"6*sqrt(b)*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2) + b**2*x**(3/2)/sqrt(b*x + 2) - 2*b*sqrt(x)/sqrt(b*x + 2) - 8/(sqrt(x)*sqrt(b*x + 2))","A",0
538,1,70,0,2.811793," ","integrate((b*x+2)**(3/2)/x**(5/2),x)","- \frac{8 b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{3} - b^{\frac{3}{2}} \log{\left(\frac{1}{b x} \right)} + 2 b^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{2}{b x}} + 1 \right)} - \frac{4 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}{3 x}"," ",0,"-8*b**(3/2)*sqrt(1 + 2/(b*x))/3 - b**(3/2)*log(1/(b*x)) + 2*b**(3/2)*log(sqrt(1 + 2/(b*x)) + 1) - 4*sqrt(b)*sqrt(1 + 2/(b*x))/(3*x)","A",0
539,1,291,0,15.279382," ","integrate(x**(5/2)*(-b*x+2)**(3/2),x)","\begin{cases} - \frac{i b^{2} x^{\frac{11}{2}}}{5 \sqrt{b x - 2}} + \frac{19 i b x^{\frac{9}{2}}}{20 \sqrt{b x - 2}} - \frac{23 i x^{\frac{7}{2}}}{20 \sqrt{b x - 2}} - \frac{i x^{\frac{5}{2}}}{40 b \sqrt{b x - 2}} - \frac{i x^{\frac{3}{2}}}{8 b^{2} \sqrt{b x - 2}} + \frac{3 i \sqrt{x}}{4 b^{3} \sqrt{b x - 2}} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{7}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{b^{2} x^{\frac{11}{2}}}{5 \sqrt{- b x + 2}} - \frac{19 b x^{\frac{9}{2}}}{20 \sqrt{- b x + 2}} + \frac{23 x^{\frac{7}{2}}}{20 \sqrt{- b x + 2}} + \frac{x^{\frac{5}{2}}}{40 b \sqrt{- b x + 2}} + \frac{x^{\frac{3}{2}}}{8 b^{2} \sqrt{- b x + 2}} - \frac{3 \sqrt{x}}{4 b^{3} \sqrt{- b x + 2}} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*b**2*x**(11/2)/(5*sqrt(b*x - 2)) + 19*I*b*x**(9/2)/(20*sqrt(b*x - 2)) - 23*I*x**(7/2)/(20*sqrt(b*x - 2)) - I*x**(5/2)/(40*b*sqrt(b*x - 2)) - I*x**(3/2)/(8*b**2*sqrt(b*x - 2)) + 3*I*sqrt(x)/(4*b**3*sqrt(b*x - 2)) - 3*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(7/2)), Abs(b*x)/2 > 1), (b**2*x**(11/2)/(5*sqrt(-b*x + 2)) - 19*b*x**(9/2)/(20*sqrt(-b*x + 2)) + 23*x**(7/2)/(20*sqrt(-b*x + 2)) + x**(5/2)/(40*b*sqrt(-b*x + 2)) + x**(3/2)/(8*b**2*sqrt(-b*x + 2)) - 3*sqrt(x)/(4*b**3*sqrt(-b*x + 2)) + 3*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(7/2)), True))","A",0
540,1,252,0,7.725881," ","integrate(x**(3/2)*(-b*x+2)**(3/2),x)","\begin{cases} - \frac{i b^{2} x^{\frac{9}{2}}}{4 \sqrt{b x - 2}} + \frac{5 i b x^{\frac{7}{2}}}{4 \sqrt{b x - 2}} - \frac{13 i x^{\frac{5}{2}}}{8 \sqrt{b x - 2}} - \frac{i x^{\frac{3}{2}}}{8 b \sqrt{b x - 2}} + \frac{3 i \sqrt{x}}{4 b^{2} \sqrt{b x - 2}} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{5}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{b^{2} x^{\frac{9}{2}}}{4 \sqrt{- b x + 2}} - \frac{5 b x^{\frac{7}{2}}}{4 \sqrt{- b x + 2}} + \frac{13 x^{\frac{5}{2}}}{8 \sqrt{- b x + 2}} + \frac{x^{\frac{3}{2}}}{8 b \sqrt{- b x + 2}} - \frac{3 \sqrt{x}}{4 b^{2} \sqrt{- b x + 2}} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*b**2*x**(9/2)/(4*sqrt(b*x - 2)) + 5*I*b*x**(7/2)/(4*sqrt(b*x - 2)) - 13*I*x**(5/2)/(8*sqrt(b*x - 2)) - I*x**(3/2)/(8*b*sqrt(b*x - 2)) + 3*I*sqrt(x)/(4*b**2*sqrt(b*x - 2)) - 3*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(5/2)), Abs(b*x)/2 > 1), (b**2*x**(9/2)/(4*sqrt(-b*x + 2)) - 5*b*x**(7/2)/(4*sqrt(-b*x + 2)) + 13*x**(5/2)/(8*sqrt(-b*x + 2)) + x**(3/2)/(8*b*sqrt(-b*x + 2)) - 3*sqrt(x)/(4*b**2*sqrt(-b*x + 2)) + 3*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(5/2)), True))","A",0
541,1,199,0,4.780104," ","integrate((-b*x+2)**(3/2)*x**(1/2),x)","\begin{cases} - \frac{i b^{2} x^{\frac{7}{2}}}{3 \sqrt{b x - 2}} + \frac{11 i b x^{\frac{5}{2}}}{6 \sqrt{b x - 2}} - \frac{17 i x^{\frac{3}{2}}}{6 \sqrt{b x - 2}} + \frac{i \sqrt{x}}{b \sqrt{b x - 2}} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{b^{2} x^{\frac{7}{2}}}{3 \sqrt{- b x + 2}} - \frac{11 b x^{\frac{5}{2}}}{6 \sqrt{- b x + 2}} + \frac{17 x^{\frac{3}{2}}}{6 \sqrt{- b x + 2}} - \frac{\sqrt{x}}{b \sqrt{- b x + 2}} + \frac{\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*b**2*x**(7/2)/(3*sqrt(b*x - 2)) + 11*I*b*x**(5/2)/(6*sqrt(b*x - 2)) - 17*I*x**(3/2)/(6*sqrt(b*x - 2)) + I*sqrt(x)/(b*sqrt(b*x - 2)) - I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), Abs(b*x)/2 > 1), (b**2*x**(7/2)/(3*sqrt(-b*x + 2)) - 11*b*x**(5/2)/(6*sqrt(-b*x + 2)) + 17*x**(3/2)/(6*sqrt(-b*x + 2)) - sqrt(x)/(b*sqrt(-b*x + 2)) + asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), True))","A",0
542,1,167,0,2.863290," ","integrate((-b*x+2)**(3/2)/x**(1/2),x)","\begin{cases} - \frac{i b^{2} x^{\frac{5}{2}}}{2 \sqrt{b x - 2}} + \frac{7 i b x^{\frac{3}{2}}}{2 \sqrt{b x - 2}} - \frac{5 i \sqrt{x}}{\sqrt{b x - 2}} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{b^{2} x^{\frac{5}{2}}}{2 \sqrt{- b x + 2}} - \frac{7 b x^{\frac{3}{2}}}{2 \sqrt{- b x + 2}} + \frac{5 \sqrt{x}}{\sqrt{- b x + 2}} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*b**2*x**(5/2)/(2*sqrt(b*x - 2)) + 7*I*b*x**(3/2)/(2*sqrt(b*x - 2)) - 5*I*sqrt(x)/sqrt(b*x - 2) - 3*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), Abs(b*x)/2 > 1), (b**2*x**(5/2)/(2*sqrt(-b*x + 2)) - 7*b*x**(3/2)/(2*sqrt(-b*x + 2)) + 5*sqrt(x)/sqrt(-b*x + 2) + 3*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), True))","A",0
543,1,160,0,2.492738," ","integrate((-b*x+2)**(3/2)/x**(3/2),x)","\begin{cases} 6 i \sqrt{b} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} - \frac{i b^{2} x^{\frac{3}{2}}}{\sqrt{b x - 2}} - \frac{2 i b \sqrt{x}}{\sqrt{b x - 2}} + \frac{8 i}{\sqrt{x} \sqrt{b x - 2}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- 6 \sqrt{b} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} + \frac{b^{2} x^{\frac{3}{2}}}{\sqrt{- b x + 2}} + \frac{2 b \sqrt{x}}{\sqrt{- b x + 2}} - \frac{8}{\sqrt{x} \sqrt{- b x + 2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*I*sqrt(b)*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2) - I*b**2*x**(3/2)/sqrt(b*x - 2) - 2*I*b*sqrt(x)/sqrt(b*x - 2) + 8*I/(sqrt(x)*sqrt(b*x - 2)), Abs(b*x)/2 > 1), (-6*sqrt(b)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2) + b**2*x**(3/2)/sqrt(-b*x + 2) + 2*b*sqrt(x)/sqrt(-b*x + 2) - 8/(sqrt(x)*sqrt(-b*x + 2)), True))","A",0
544,1,182,0,2.922782," ","integrate((-b*x+2)**(3/2)/x**(5/2),x)","\begin{cases} \frac{8 b^{\frac{3}{2}} \sqrt{-1 + \frac{2}{b x}}}{3} + i b^{\frac{3}{2}} \log{\left(\frac{1}{b x} \right)} - 2 i b^{\frac{3}{2}} \log{\left(\frac{1}{\sqrt{b} \sqrt{x}} \right)} + 2 b^{\frac{3}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} - \frac{4 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}}{3 x} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{8 i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{3} + i b^{\frac{3}{2}} \log{\left(\frac{1}{b x} \right)} - 2 i b^{\frac{3}{2}} \log{\left(\sqrt{1 - \frac{2}{b x}} + 1 \right)} - \frac{4 i \sqrt{b} \sqrt{1 - \frac{2}{b x}}}{3 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*b**(3/2)*sqrt(-1 + 2/(b*x))/3 + I*b**(3/2)*log(1/(b*x)) - 2*I*b**(3/2)*log(1/(sqrt(b)*sqrt(x))) + 2*b**(3/2)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2) - 4*sqrt(b)*sqrt(-1 + 2/(b*x))/(3*x), 2/Abs(b*x) > 1), (8*I*b**(3/2)*sqrt(1 - 2/(b*x))/3 + I*b**(3/2)*log(1/(b*x)) - 2*I*b**(3/2)*log(sqrt(1 - 2/(b*x)) + 1) - 4*I*sqrt(b)*sqrt(1 - 2/(b*x))/(3*x), True))","C",0
545,1,207,0,25.936150," ","integrate(x**(5/2)*(b*x+a)**(5/2),x)","\frac{5 a^{\frac{11}{2}} \sqrt{x}}{512 b^{3} \sqrt{1 + \frac{b x}{a}}} + \frac{5 a^{\frac{9}{2}} x^{\frac{3}{2}}}{1536 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{a^{\frac{7}{2}} x^{\frac{5}{2}}}{768 b \sqrt{1 + \frac{b x}{a}}} + \frac{55 a^{\frac{5}{2}} x^{\frac{7}{2}}}{192 \sqrt{1 + \frac{b x}{a}}} + \frac{67 a^{\frac{3}{2}} b x^{\frac{9}{2}}}{96 \sqrt{1 + \frac{b x}{a}}} + \frac{7 \sqrt{a} b^{2} x^{\frac{11}{2}}}{12 \sqrt{1 + \frac{b x}{a}}} - \frac{5 a^{6} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{512 b^{\frac{7}{2}}} + \frac{b^{3} x^{\frac{13}{2}}}{6 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"5*a**(11/2)*sqrt(x)/(512*b**3*sqrt(1 + b*x/a)) + 5*a**(9/2)*x**(3/2)/(1536*b**2*sqrt(1 + b*x/a)) - a**(7/2)*x**(5/2)/(768*b*sqrt(1 + b*x/a)) + 55*a**(5/2)*x**(7/2)/(192*sqrt(1 + b*x/a)) + 67*a**(3/2)*b*x**(9/2)/(96*sqrt(1 + b*x/a)) + 7*sqrt(a)*b**2*x**(11/2)/(12*sqrt(1 + b*x/a)) - 5*a**6*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(512*b**(7/2)) + b**3*x**(13/2)/(6*sqrt(a)*sqrt(1 + b*x/a))","A",0
546,1,180,0,16.411006," ","integrate(x**(3/2)*(b*x+a)**(5/2),x)","- \frac{3 a^{\frac{9}{2}} \sqrt{x}}{128 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{a^{\frac{7}{2}} x^{\frac{3}{2}}}{128 b \sqrt{1 + \frac{b x}{a}}} + \frac{129 a^{\frac{5}{2}} x^{\frac{5}{2}}}{320 \sqrt{1 + \frac{b x}{a}}} + \frac{73 a^{\frac{3}{2}} b x^{\frac{7}{2}}}{80 \sqrt{1 + \frac{b x}{a}}} + \frac{29 \sqrt{a} b^{2} x^{\frac{9}{2}}}{40 \sqrt{1 + \frac{b x}{a}}} + \frac{3 a^{5} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} + \frac{b^{3} x^{\frac{11}{2}}}{5 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-3*a**(9/2)*sqrt(x)/(128*b**2*sqrt(1 + b*x/a)) - a**(7/2)*x**(3/2)/(128*b*sqrt(1 + b*x/a)) + 129*a**(5/2)*x**(5/2)/(320*sqrt(1 + b*x/a)) + 73*a**(3/2)*b*x**(7/2)/(80*sqrt(1 + b*x/a)) + 29*sqrt(a)*b**2*x**(9/2)/(40*sqrt(1 + b*x/a)) + 3*a**5*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(128*b**(5/2)) + b**3*x**(11/2)/(5*sqrt(a)*sqrt(1 + b*x/a))","A",0
547,1,155,0,9.860260," ","integrate((b*x+a)**(5/2)*x**(1/2),x)","\frac{5 a^{\frac{7}{2}} \sqrt{x}}{64 b \sqrt{1 + \frac{b x}{a}}} + \frac{133 a^{\frac{5}{2}} x^{\frac{3}{2}}}{192 \sqrt{1 + \frac{b x}{a}}} + \frac{127 a^{\frac{3}{2}} b x^{\frac{5}{2}}}{96 \sqrt{1 + \frac{b x}{a}}} + \frac{23 \sqrt{a} b^{2} x^{\frac{7}{2}}}{24 \sqrt{1 + \frac{b x}{a}}} - \frac{5 a^{4} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{3}{2}}} + \frac{b^{3} x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"5*a**(7/2)*sqrt(x)/(64*b*sqrt(1 + b*x/a)) + 133*a**(5/2)*x**(3/2)/(192*sqrt(1 + b*x/a)) + 127*a**(3/2)*b*x**(5/2)/(96*sqrt(1 + b*x/a)) + 23*sqrt(a)*b**2*x**(7/2)/(24*sqrt(1 + b*x/a)) - 5*a**4*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(3/2)) + b**3*x**(9/2)/(4*sqrt(a)*sqrt(1 + b*x/a))","A",0
548,1,102,0,6.229161," ","integrate((b*x+a)**(5/2)/x**(1/2),x)","\frac{11 a^{\frac{5}{2}} \sqrt{x} \sqrt{1 + \frac{b x}{a}}}{8} + \frac{13 a^{\frac{3}{2}} b x^{\frac{3}{2}} \sqrt{1 + \frac{b x}{a}}}{12} + \frac{\sqrt{a} b^{2} x^{\frac{5}{2}} \sqrt{1 + \frac{b x}{a}}}{3} + \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 \sqrt{b}}"," ",0,"11*a**(5/2)*sqrt(x)*sqrt(1 + b*x/a)/8 + 13*a**(3/2)*b*x**(3/2)*sqrt(1 + b*x/a)/12 + sqrt(a)*b**2*x**(5/2)*sqrt(1 + b*x/a)/3 + 5*a**3*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(8*sqrt(b))","A",0
549,1,126,0,6.147514," ","integrate((b*x+a)**(5/2)/x**(3/2),x)","- \frac{2 a^{\frac{5}{2}}}{\sqrt{x} \sqrt{1 + \frac{b x}{a}}} + \frac{a^{\frac{3}{2}} b \sqrt{x}}{4 \sqrt{1 + \frac{b x}{a}}} + \frac{11 \sqrt{a} b^{2} x^{\frac{3}{2}}}{4 \sqrt{1 + \frac{b x}{a}}} + \frac{15 a^{2} \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4} + \frac{b^{3} x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-2*a**(5/2)/(sqrt(x)*sqrt(1 + b*x/a)) + a**(3/2)*b*sqrt(x)/(4*sqrt(1 + b*x/a)) + 11*sqrt(a)*b**2*x**(3/2)/(4*sqrt(1 + b*x/a)) + 15*a**2*sqrt(b)*asinh(sqrt(b)*sqrt(x)/sqrt(a))/4 + b**3*x**(5/2)/(2*sqrt(a)*sqrt(1 + b*x/a))","A",0
550,1,99,0,5.622032," ","integrate((b*x+a)**(5/2)/x**(5/2),x)","- \frac{2 a^{2} \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 x} - \frac{14 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{3} - \frac{5 a b^{\frac{3}{2}} \log{\left(\frac{a}{b x} \right)}}{2} + 5 a b^{\frac{3}{2}} \log{\left(\sqrt{\frac{a}{b x} + 1} + 1 \right)} + b^{\frac{5}{2}} x \sqrt{\frac{a}{b x} + 1}"," ",0,"-2*a**2*sqrt(b)*sqrt(a/(b*x) + 1)/(3*x) - 14*a*b**(3/2)*sqrt(a/(b*x) + 1)/3 - 5*a*b**(3/2)*log(a/(b*x))/2 + 5*a*b**(3/2)*log(sqrt(a/(b*x) + 1) + 1) + b**(5/2)*x*sqrt(a/(b*x) + 1)","A",0
551,1,435,0,25.959908," ","integrate(x**(5/2)*(-b*x+a)**(5/2),x)","\begin{cases} \frac{5 i a^{\frac{11}{2}} \sqrt{x}}{512 b^{3} \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{\frac{9}{2}} x^{\frac{3}{2}}}{1536 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{7}{2}} x^{\frac{5}{2}}}{768 b \sqrt{-1 + \frac{b x}{a}}} - \frac{55 i a^{\frac{5}{2}} x^{\frac{7}{2}}}{192 \sqrt{-1 + \frac{b x}{a}}} + \frac{67 i a^{\frac{3}{2}} b x^{\frac{9}{2}}}{96 \sqrt{-1 + \frac{b x}{a}}} - \frac{7 i \sqrt{a} b^{2} x^{\frac{11}{2}}}{12 \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{6} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{512 b^{\frac{7}{2}}} + \frac{i b^{3} x^{\frac{13}{2}}}{6 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{5 a^{\frac{11}{2}} \sqrt{x}}{512 b^{3} \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{\frac{9}{2}} x^{\frac{3}{2}}}{1536 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{7}{2}} x^{\frac{5}{2}}}{768 b \sqrt{1 - \frac{b x}{a}}} + \frac{55 a^{\frac{5}{2}} x^{\frac{7}{2}}}{192 \sqrt{1 - \frac{b x}{a}}} - \frac{67 a^{\frac{3}{2}} b x^{\frac{9}{2}}}{96 \sqrt{1 - \frac{b x}{a}}} + \frac{7 \sqrt{a} b^{2} x^{\frac{11}{2}}}{12 \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{6} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{512 b^{\frac{7}{2}}} - \frac{b^{3} x^{\frac{13}{2}}}{6 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*I*a**(11/2)*sqrt(x)/(512*b**3*sqrt(-1 + b*x/a)) - 5*I*a**(9/2)*x**(3/2)/(1536*b**2*sqrt(-1 + b*x/a)) - I*a**(7/2)*x**(5/2)/(768*b*sqrt(-1 + b*x/a)) - 55*I*a**(5/2)*x**(7/2)/(192*sqrt(-1 + b*x/a)) + 67*I*a**(3/2)*b*x**(9/2)/(96*sqrt(-1 + b*x/a)) - 7*I*sqrt(a)*b**2*x**(11/2)/(12*sqrt(-1 + b*x/a)) - 5*I*a**6*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(512*b**(7/2)) + I*b**3*x**(13/2)/(6*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-5*a**(11/2)*sqrt(x)/(512*b**3*sqrt(1 - b*x/a)) + 5*a**(9/2)*x**(3/2)/(1536*b**2*sqrt(1 - b*x/a)) + a**(7/2)*x**(5/2)/(768*b*sqrt(1 - b*x/a)) + 55*a**(5/2)*x**(7/2)/(192*sqrt(1 - b*x/a)) - 67*a**(3/2)*b*x**(9/2)/(96*sqrt(1 - b*x/a)) + 7*sqrt(a)*b**2*x**(11/2)/(12*sqrt(1 - b*x/a)) + 5*a**6*asin(sqrt(b)*sqrt(x)/sqrt(a))/(512*b**(7/2)) - b**3*x**(13/2)/(6*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
552,1,379,0,16.397904," ","integrate(x**(3/2)*(-b*x+a)**(5/2),x)","\begin{cases} \frac{3 i a^{\frac{9}{2}} \sqrt{x}}{128 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i a^{\frac{7}{2}} x^{\frac{3}{2}}}{128 b \sqrt{-1 + \frac{b x}{a}}} - \frac{129 i a^{\frac{5}{2}} x^{\frac{5}{2}}}{320 \sqrt{-1 + \frac{b x}{a}}} + \frac{73 i a^{\frac{3}{2}} b x^{\frac{7}{2}}}{80 \sqrt{-1 + \frac{b x}{a}}} - \frac{29 i \sqrt{a} b^{2} x^{\frac{9}{2}}}{40 \sqrt{-1 + \frac{b x}{a}}} - \frac{3 i a^{5} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} + \frac{i b^{3} x^{\frac{11}{2}}}{5 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{3 a^{\frac{9}{2}} \sqrt{x}}{128 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{a^{\frac{7}{2}} x^{\frac{3}{2}}}{128 b \sqrt{1 - \frac{b x}{a}}} + \frac{129 a^{\frac{5}{2}} x^{\frac{5}{2}}}{320 \sqrt{1 - \frac{b x}{a}}} - \frac{73 a^{\frac{3}{2}} b x^{\frac{7}{2}}}{80 \sqrt{1 - \frac{b x}{a}}} + \frac{29 \sqrt{a} b^{2} x^{\frac{9}{2}}}{40 \sqrt{1 - \frac{b x}{a}}} + \frac{3 a^{5} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} - \frac{b^{3} x^{\frac{11}{2}}}{5 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*I*a**(9/2)*sqrt(x)/(128*b**2*sqrt(-1 + b*x/a)) - I*a**(7/2)*x**(3/2)/(128*b*sqrt(-1 + b*x/a)) - 129*I*a**(5/2)*x**(5/2)/(320*sqrt(-1 + b*x/a)) + 73*I*a**(3/2)*b*x**(7/2)/(80*sqrt(-1 + b*x/a)) - 29*I*sqrt(a)*b**2*x**(9/2)/(40*sqrt(-1 + b*x/a)) - 3*I*a**5*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(128*b**(5/2)) + I*b**3*x**(11/2)/(5*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-3*a**(9/2)*sqrt(x)/(128*b**2*sqrt(1 - b*x/a)) + a**(7/2)*x**(3/2)/(128*b*sqrt(1 - b*x/a)) + 129*a**(5/2)*x**(5/2)/(320*sqrt(1 - b*x/a)) - 73*a**(3/2)*b*x**(7/2)/(80*sqrt(1 - b*x/a)) + 29*sqrt(a)*b**2*x**(9/2)/(40*sqrt(1 - b*x/a)) + 3*a**5*asin(sqrt(b)*sqrt(x)/sqrt(a))/(128*b**(5/2)) - b**3*x**(11/2)/(5*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
553,1,326,0,9.807303," ","integrate((-b*x+a)**(5/2)*x**(1/2),x)","\begin{cases} \frac{5 i a^{\frac{7}{2}} \sqrt{x}}{64 b \sqrt{-1 + \frac{b x}{a}}} - \frac{133 i a^{\frac{5}{2}} x^{\frac{3}{2}}}{192 \sqrt{-1 + \frac{b x}{a}}} + \frac{127 i a^{\frac{3}{2}} b x^{\frac{5}{2}}}{96 \sqrt{-1 + \frac{b x}{a}}} - \frac{23 i \sqrt{a} b^{2} x^{\frac{7}{2}}}{24 \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{4} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{3}{2}}} + \frac{i b^{3} x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{5 a^{\frac{7}{2}} \sqrt{x}}{64 b \sqrt{1 - \frac{b x}{a}}} + \frac{133 a^{\frac{5}{2}} x^{\frac{3}{2}}}{192 \sqrt{1 - \frac{b x}{a}}} - \frac{127 a^{\frac{3}{2}} b x^{\frac{5}{2}}}{96 \sqrt{1 - \frac{b x}{a}}} + \frac{23 \sqrt{a} b^{2} x^{\frac{7}{2}}}{24 \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{4} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{64 b^{\frac{3}{2}}} - \frac{b^{3} x^{\frac{9}{2}}}{4 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*I*a**(7/2)*sqrt(x)/(64*b*sqrt(-1 + b*x/a)) - 133*I*a**(5/2)*x**(3/2)/(192*sqrt(-1 + b*x/a)) + 127*I*a**(3/2)*b*x**(5/2)/(96*sqrt(-1 + b*x/a)) - 23*I*sqrt(a)*b**2*x**(7/2)/(24*sqrt(-1 + b*x/a)) - 5*I*a**4*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(3/2)) + I*b**3*x**(9/2)/(4*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-5*a**(7/2)*sqrt(x)/(64*b*sqrt(1 - b*x/a)) + 133*a**(5/2)*x**(3/2)/(192*sqrt(1 - b*x/a)) - 127*a**(3/2)*b*x**(5/2)/(96*sqrt(1 - b*x/a)) + 23*sqrt(a)*b**2*x**(7/2)/(24*sqrt(1 - b*x/a)) + 5*a**4*asin(sqrt(b)*sqrt(x)/sqrt(a))/(64*b**(3/2)) - b**3*x**(9/2)/(4*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
554,1,246,0,6.228000," ","integrate((-b*x+a)**(5/2)/x**(1/2),x)","\begin{cases} - \frac{11 i a^{\frac{5}{2}} \sqrt{x}}{8 \sqrt{-1 + \frac{b x}{a}}} + \frac{59 i a^{\frac{3}{2}} b x^{\frac{3}{2}}}{24 \sqrt{-1 + \frac{b x}{a}}} - \frac{17 i \sqrt{a} b^{2} x^{\frac{5}{2}}}{12 \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{3} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 \sqrt{b}} + \frac{i b^{3} x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{11 a^{\frac{5}{2}} \sqrt{x} \sqrt{1 - \frac{b x}{a}}}{8} - \frac{13 a^{\frac{3}{2}} b x^{\frac{3}{2}} \sqrt{1 - \frac{b x}{a}}}{12} + \frac{\sqrt{a} b^{2} x^{\frac{5}{2}} \sqrt{1 - \frac{b x}{a}}}{3} + \frac{5 a^{3} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 \sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-11*I*a**(5/2)*sqrt(x)/(8*sqrt(-1 + b*x/a)) + 59*I*a**(3/2)*b*x**(3/2)/(24*sqrt(-1 + b*x/a)) - 17*I*sqrt(a)*b**2*x**(5/2)/(12*sqrt(-1 + b*x/a)) - 5*I*a**3*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(8*sqrt(b)) + I*b**3*x**(7/2)/(3*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (11*a**(5/2)*sqrt(x)*sqrt(1 - b*x/a)/8 - 13*a**(3/2)*b*x**(3/2)*sqrt(1 - b*x/a)/12 + sqrt(a)*b**2*x**(5/2)*sqrt(1 - b*x/a)/3 + 5*a**3*asin(sqrt(b)*sqrt(x)/sqrt(a))/(8*sqrt(b)), True))","A",0
555,1,267,0,6.221921," ","integrate((-b*x+a)**(5/2)/x**(3/2),x)","\begin{cases} \frac{2 i a^{\frac{5}{2}}}{\sqrt{x} \sqrt{-1 + \frac{b x}{a}}} + \frac{i a^{\frac{3}{2}} b \sqrt{x}}{4 \sqrt{-1 + \frac{b x}{a}}} - \frac{11 i \sqrt{a} b^{2} x^{\frac{3}{2}}}{4 \sqrt{-1 + \frac{b x}{a}}} + \frac{15 i a^{2} \sqrt{b} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4} + \frac{i b^{3} x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{2 a^{\frac{5}{2}}}{\sqrt{x} \sqrt{1 - \frac{b x}{a}}} - \frac{a^{\frac{3}{2}} b \sqrt{x}}{4 \sqrt{1 - \frac{b x}{a}}} + \frac{11 \sqrt{a} b^{2} x^{\frac{3}{2}}}{4 \sqrt{1 - \frac{b x}{a}}} - \frac{15 a^{2} \sqrt{b} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4} - \frac{b^{3} x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*a**(5/2)/(sqrt(x)*sqrt(-1 + b*x/a)) + I*a**(3/2)*b*sqrt(x)/(4*sqrt(-1 + b*x/a)) - 11*I*sqrt(a)*b**2*x**(3/2)/(4*sqrt(-1 + b*x/a)) + 15*I*a**2*sqrt(b)*acosh(sqrt(b)*sqrt(x)/sqrt(a))/4 + I*b**3*x**(5/2)/(2*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-2*a**(5/2)/(sqrt(x)*sqrt(1 - b*x/a)) - a**(3/2)*b*sqrt(x)/(4*sqrt(1 - b*x/a)) + 11*sqrt(a)*b**2*x**(3/2)/(4*sqrt(1 - b*x/a)) - 15*a**2*sqrt(b)*asin(sqrt(b)*sqrt(x)/sqrt(a))/4 - b**3*x**(5/2)/(2*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
556,1,245,0,5.845328," ","integrate((-b*x+a)**(5/2)/x**(5/2),x)","\begin{cases} - \frac{2 a^{2} \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{3 x} + \frac{14 a b^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}}{3} - 5 i a b^{\frac{3}{2}} \log{\left(\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right)} + \frac{5 i a b^{\frac{3}{2}} \log{\left(\frac{a}{b x} \right)}}{2} + 5 a b^{\frac{3}{2}} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)} + b^{\frac{5}{2}} x \sqrt{\frac{a}{b x} - 1} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 i a^{2} \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{3 x} + \frac{14 i a b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{3} + \frac{5 i a b^{\frac{3}{2}} \log{\left(\frac{a}{b x} \right)}}{2} - 5 i a b^{\frac{3}{2}} \log{\left(\sqrt{- \frac{a}{b x} + 1} + 1 \right)} + i b^{\frac{5}{2}} x \sqrt{- \frac{a}{b x} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*sqrt(b)*sqrt(a/(b*x) - 1)/(3*x) + 14*a*b**(3/2)*sqrt(a/(b*x) - 1)/3 - 5*I*a*b**(3/2)*log(sqrt(a)/(sqrt(b)*sqrt(x))) + 5*I*a*b**(3/2)*log(a/(b*x))/2 + 5*a*b**(3/2)*asin(sqrt(b)*sqrt(x)/sqrt(a)) + b**(5/2)*x*sqrt(a/(b*x) - 1), Abs(a/(b*x)) > 1), (-2*I*a**2*sqrt(b)*sqrt(-a/(b*x) + 1)/(3*x) + 14*I*a*b**(3/2)*sqrt(-a/(b*x) + 1)/3 + 5*I*a*b**(3/2)*log(a/(b*x))/2 - 5*I*a*b**(3/2)*log(sqrt(-a/(b*x) + 1) + 1) + I*b**(5/2)*x*sqrt(-a/(b*x) + 1), True))","C",0
557,1,158,0,22.959770," ","integrate(x**(5/2)*(b*x+2)**(5/2),x)","\frac{b^{3} x^{\frac{13}{2}}}{6 \sqrt{b x + 2}} + \frac{7 b^{2} x^{\frac{11}{2}}}{6 \sqrt{b x + 2}} + \frac{67 b x^{\frac{9}{2}}}{24 \sqrt{b x + 2}} + \frac{55 x^{\frac{7}{2}}}{24 \sqrt{b x + 2}} - \frac{x^{\frac{5}{2}}}{48 b \sqrt{b x + 2}} + \frac{5 x^{\frac{3}{2}}}{48 b^{2} \sqrt{b x + 2}} + \frac{5 \sqrt{x}}{8 b^{3} \sqrt{b x + 2}} - \frac{5 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{8 b^{\frac{7}{2}}}"," ",0,"b**3*x**(13/2)/(6*sqrt(b*x + 2)) + 7*b**2*x**(11/2)/(6*sqrt(b*x + 2)) + 67*b*x**(9/2)/(24*sqrt(b*x + 2)) + 55*x**(7/2)/(24*sqrt(b*x + 2)) - x**(5/2)/(48*b*sqrt(b*x + 2)) + 5*x**(3/2)/(48*b**2*sqrt(b*x + 2)) + 5*sqrt(x)/(8*b**3*sqrt(b*x + 2)) - 5*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(8*b**(7/2))","A",0
558,1,138,0,14.422673," ","integrate(x**(3/2)*(b*x+2)**(5/2),x)","\frac{b^{3} x^{\frac{11}{2}}}{5 \sqrt{b x + 2}} + \frac{29 b^{2} x^{\frac{9}{2}}}{20 \sqrt{b x + 2}} + \frac{73 b x^{\frac{7}{2}}}{20 \sqrt{b x + 2}} + \frac{129 x^{\frac{5}{2}}}{40 \sqrt{b x + 2}} - \frac{x^{\frac{3}{2}}}{8 b \sqrt{b x + 2}} - \frac{3 \sqrt{x}}{4 b^{2} \sqrt{b x + 2}} + \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{5}{2}}}"," ",0,"b**3*x**(11/2)/(5*sqrt(b*x + 2)) + 29*b**2*x**(9/2)/(20*sqrt(b*x + 2)) + 73*b*x**(7/2)/(20*sqrt(b*x + 2)) + 129*x**(5/2)/(40*sqrt(b*x + 2)) - x**(3/2)/(8*b*sqrt(b*x + 2)) - 3*sqrt(x)/(4*b**2*sqrt(b*x + 2)) + 3*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(5/2))","A",0
559,1,119,0,8.611044," ","integrate((b*x+2)**(5/2)*x**(1/2),x)","\frac{b^{3} x^{\frac{9}{2}}}{4 \sqrt{b x + 2}} + \frac{23 b^{2} x^{\frac{7}{2}}}{12 \sqrt{b x + 2}} + \frac{127 b x^{\frac{5}{2}}}{24 \sqrt{b x + 2}} + \frac{133 x^{\frac{3}{2}}}{24 \sqrt{b x + 2}} + \frac{5 \sqrt{x}}{4 b \sqrt{b x + 2}} - \frac{5 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{3}{2}}}"," ",0,"b**3*x**(9/2)/(4*sqrt(b*x + 2)) + 23*b**2*x**(7/2)/(12*sqrt(b*x + 2)) + 127*b*x**(5/2)/(24*sqrt(b*x + 2)) + 133*x**(3/2)/(24*sqrt(b*x + 2)) + 5*sqrt(x)/(4*b*sqrt(b*x + 2)) - 5*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(3/2))","A",0
560,1,97,0,5.458410," ","integrate((b*x+2)**(5/2)/x**(1/2),x)","\frac{b^{3} x^{\frac{7}{2}}}{3 \sqrt{b x + 2}} + \frac{17 b^{2} x^{\frac{5}{2}}}{6 \sqrt{b x + 2}} + \frac{59 b x^{\frac{3}{2}}}{6 \sqrt{b x + 2}} + \frac{11 \sqrt{x}}{\sqrt{b x + 2}} + \frac{5 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}}"," ",0,"b**3*x**(7/2)/(3*sqrt(b*x + 2)) + 17*b**2*x**(5/2)/(6*sqrt(b*x + 2)) + 59*b*x**(3/2)/(6*sqrt(b*x + 2)) + 11*sqrt(x)/sqrt(b*x + 2) + 5*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b)","A",0
561,1,94,0,5.602245," ","integrate((b*x+2)**(5/2)/x**(3/2),x)","15 \sqrt{b} \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} + \frac{b^{3} x^{\frac{5}{2}}}{2 \sqrt{b x + 2}} + \frac{11 b^{2} x^{\frac{3}{2}}}{2 \sqrt{b x + 2}} + \frac{b \sqrt{x}}{\sqrt{b x + 2}} - \frac{16}{\sqrt{x} \sqrt{b x + 2}}"," ",0,"15*sqrt(b)*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2) + b**3*x**(5/2)/(2*sqrt(b*x + 2)) + 11*b**2*x**(3/2)/(2*sqrt(b*x + 2)) + b*sqrt(x)/sqrt(b*x + 2) - 16/(sqrt(x)*sqrt(b*x + 2))","A",0
562,1,88,0,5.152023," ","integrate((b*x+2)**(5/2)/x**(5/2),x)","b^{\frac{5}{2}} x \sqrt{1 + \frac{2}{b x}} - \frac{28 b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{3} - 5 b^{\frac{3}{2}} \log{\left(\frac{1}{b x} \right)} + 10 b^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{2}{b x}} + 1 \right)} - \frac{8 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}{3 x}"," ",0,"b**(5/2)*x*sqrt(1 + 2/(b*x)) - 28*b**(3/2)*sqrt(1 + 2/(b*x))/3 - 5*b**(3/2)*log(1/(b*x)) + 10*b**(3/2)*log(sqrt(1 + 2/(b*x)) + 1) - 8*sqrt(b)*sqrt(1 + 2/(b*x))/(3*x)","A",0
563,1,337,0,22.838200," ","integrate(x**(5/2)*(-b*x+2)**(5/2),x)","\begin{cases} \frac{i b^{3} x^{\frac{13}{2}}}{6 \sqrt{b x - 2}} - \frac{7 i b^{2} x^{\frac{11}{2}}}{6 \sqrt{b x - 2}} + \frac{67 i b x^{\frac{9}{2}}}{24 \sqrt{b x - 2}} - \frac{55 i x^{\frac{7}{2}}}{24 \sqrt{b x - 2}} - \frac{i x^{\frac{5}{2}}}{48 b \sqrt{b x - 2}} - \frac{5 i x^{\frac{3}{2}}}{48 b^{2} \sqrt{b x - 2}} + \frac{5 i \sqrt{x}}{8 b^{3} \sqrt{b x - 2}} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{8 b^{\frac{7}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b^{3} x^{\frac{13}{2}}}{6 \sqrt{- b x + 2}} + \frac{7 b^{2} x^{\frac{11}{2}}}{6 \sqrt{- b x + 2}} - \frac{67 b x^{\frac{9}{2}}}{24 \sqrt{- b x + 2}} + \frac{55 x^{\frac{7}{2}}}{24 \sqrt{- b x + 2}} + \frac{x^{\frac{5}{2}}}{48 b \sqrt{- b x + 2}} + \frac{5 x^{\frac{3}{2}}}{48 b^{2} \sqrt{- b x + 2}} - \frac{5 \sqrt{x}}{8 b^{3} \sqrt{- b x + 2}} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{8 b^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b**3*x**(13/2)/(6*sqrt(b*x - 2)) - 7*I*b**2*x**(11/2)/(6*sqrt(b*x - 2)) + 67*I*b*x**(9/2)/(24*sqrt(b*x - 2)) - 55*I*x**(7/2)/(24*sqrt(b*x - 2)) - I*x**(5/2)/(48*b*sqrt(b*x - 2)) - 5*I*x**(3/2)/(48*b**2*sqrt(b*x - 2)) + 5*I*sqrt(x)/(8*b**3*sqrt(b*x - 2)) - 5*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(8*b**(7/2)), Abs(b*x)/2 > 1), (-b**3*x**(13/2)/(6*sqrt(-b*x + 2)) + 7*b**2*x**(11/2)/(6*sqrt(-b*x + 2)) - 67*b*x**(9/2)/(24*sqrt(-b*x + 2)) + 55*x**(7/2)/(24*sqrt(-b*x + 2)) + x**(5/2)/(48*b*sqrt(-b*x + 2)) + 5*x**(3/2)/(48*b**2*sqrt(-b*x + 2)) - 5*sqrt(x)/(8*b**3*sqrt(-b*x + 2)) + 5*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(8*b**(7/2)), True))","A",0
564,1,294,0,14.297817," ","integrate(x**(3/2)*(-b*x+2)**(5/2),x)","\begin{cases} \frac{i b^{3} x^{\frac{11}{2}}}{5 \sqrt{b x - 2}} - \frac{29 i b^{2} x^{\frac{9}{2}}}{20 \sqrt{b x - 2}} + \frac{73 i b x^{\frac{7}{2}}}{20 \sqrt{b x - 2}} - \frac{129 i x^{\frac{5}{2}}}{40 \sqrt{b x - 2}} - \frac{i x^{\frac{3}{2}}}{8 b \sqrt{b x - 2}} + \frac{3 i \sqrt{x}}{4 b^{2} \sqrt{b x - 2}} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{5}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b^{3} x^{\frac{11}{2}}}{5 \sqrt{- b x + 2}} + \frac{29 b^{2} x^{\frac{9}{2}}}{20 \sqrt{- b x + 2}} - \frac{73 b x^{\frac{7}{2}}}{20 \sqrt{- b x + 2}} + \frac{129 x^{\frac{5}{2}}}{40 \sqrt{- b x + 2}} + \frac{x^{\frac{3}{2}}}{8 b \sqrt{- b x + 2}} - \frac{3 \sqrt{x}}{4 b^{2} \sqrt{- b x + 2}} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b**3*x**(11/2)/(5*sqrt(b*x - 2)) - 29*I*b**2*x**(9/2)/(20*sqrt(b*x - 2)) + 73*I*b*x**(7/2)/(20*sqrt(b*x - 2)) - 129*I*x**(5/2)/(40*sqrt(b*x - 2)) - I*x**(3/2)/(8*b*sqrt(b*x - 2)) + 3*I*sqrt(x)/(4*b**2*sqrt(b*x - 2)) - 3*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(5/2)), Abs(b*x)/2 > 1), (-b**3*x**(11/2)/(5*sqrt(-b*x + 2)) + 29*b**2*x**(9/2)/(20*sqrt(-b*x + 2)) - 73*b*x**(7/2)/(20*sqrt(-b*x + 2)) + 129*x**(5/2)/(40*sqrt(-b*x + 2)) + x**(3/2)/(8*b*sqrt(-b*x + 2)) - 3*sqrt(x)/(4*b**2*sqrt(-b*x + 2)) + 3*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(5/2)), True))","A",0
565,1,255,0,8.591526," ","integrate((-b*x+2)**(5/2)*x**(1/2),x)","\begin{cases} \frac{i b^{3} x^{\frac{9}{2}}}{4 \sqrt{b x - 2}} - \frac{23 i b^{2} x^{\frac{7}{2}}}{12 \sqrt{b x - 2}} + \frac{127 i b x^{\frac{5}{2}}}{24 \sqrt{b x - 2}} - \frac{133 i x^{\frac{3}{2}}}{24 \sqrt{b x - 2}} + \frac{5 i \sqrt{x}}{4 b \sqrt{b x - 2}} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{3}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b^{3} x^{\frac{9}{2}}}{4 \sqrt{- b x + 2}} + \frac{23 b^{2} x^{\frac{7}{2}}}{12 \sqrt{- b x + 2}} - \frac{127 b x^{\frac{5}{2}}}{24 \sqrt{- b x + 2}} + \frac{133 x^{\frac{3}{2}}}{24 \sqrt{- b x + 2}} - \frac{5 \sqrt{x}}{4 b \sqrt{- b x + 2}} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{4 b^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b**3*x**(9/2)/(4*sqrt(b*x - 2)) - 23*I*b**2*x**(7/2)/(12*sqrt(b*x - 2)) + 127*I*b*x**(5/2)/(24*sqrt(b*x - 2)) - 133*I*x**(3/2)/(24*sqrt(b*x - 2)) + 5*I*sqrt(x)/(4*b*sqrt(b*x - 2)) - 5*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(3/2)), Abs(b*x)/2 > 1), (-b**3*x**(9/2)/(4*sqrt(-b*x + 2)) + 23*b**2*x**(7/2)/(12*sqrt(-b*x + 2)) - 127*b*x**(5/2)/(24*sqrt(-b*x + 2)) + 133*x**(3/2)/(24*sqrt(-b*x + 2)) - 5*sqrt(x)/(4*b*sqrt(-b*x + 2)) + 5*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(4*b**(3/2)), True))","A",0
566,1,209,0,5.522004," ","integrate((-b*x+2)**(5/2)/x**(1/2),x)","\begin{cases} \frac{i b^{3} x^{\frac{7}{2}}}{3 \sqrt{b x - 2}} - \frac{17 i b^{2} x^{\frac{5}{2}}}{6 \sqrt{b x - 2}} + \frac{59 i b x^{\frac{3}{2}}}{6 \sqrt{b x - 2}} - \frac{11 i \sqrt{x}}{\sqrt{b x - 2}} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{b^{3} x^{\frac{7}{2}}}{3 \sqrt{- b x + 2}} + \frac{17 b^{2} x^{\frac{5}{2}}}{6 \sqrt{- b x + 2}} - \frac{59 b x^{\frac{3}{2}}}{6 \sqrt{- b x + 2}} + \frac{11 \sqrt{x}}{\sqrt{- b x + 2}} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b**3*x**(7/2)/(3*sqrt(b*x - 2)) - 17*I*b**2*x**(5/2)/(6*sqrt(b*x - 2)) + 59*I*b*x**(3/2)/(6*sqrt(b*x - 2)) - 11*I*sqrt(x)/sqrt(b*x - 2) - 5*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), Abs(b*x)/2 > 1), (-b**3*x**(7/2)/(3*sqrt(-b*x + 2)) + 17*b**2*x**(5/2)/(6*sqrt(-b*x + 2)) - 59*b*x**(3/2)/(6*sqrt(-b*x + 2)) + 11*sqrt(x)/sqrt(-b*x + 2) + 5*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), True))","A",0
567,1,202,0,5.619140," ","integrate((-b*x+2)**(5/2)/x**(3/2),x)","\begin{cases} 15 i \sqrt{b} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} + \frac{i b^{3} x^{\frac{5}{2}}}{2 \sqrt{b x - 2}} - \frac{11 i b^{2} x^{\frac{3}{2}}}{2 \sqrt{b x - 2}} + \frac{i b \sqrt{x}}{\sqrt{b x - 2}} + \frac{16 i}{\sqrt{x} \sqrt{b x - 2}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- 15 \sqrt{b} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} - \frac{b^{3} x^{\frac{5}{2}}}{2 \sqrt{- b x + 2}} + \frac{11 b^{2} x^{\frac{3}{2}}}{2 \sqrt{- b x + 2}} - \frac{b \sqrt{x}}{\sqrt{- b x + 2}} - \frac{16}{\sqrt{x} \sqrt{- b x + 2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*I*sqrt(b)*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2) + I*b**3*x**(5/2)/(2*sqrt(b*x - 2)) - 11*I*b**2*x**(3/2)/(2*sqrt(b*x - 2)) + I*b*sqrt(x)/sqrt(b*x - 2) + 16*I/(sqrt(x)*sqrt(b*x - 2)), Abs(b*x)/2 > 1), (-15*sqrt(b)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2) - b**3*x**(5/2)/(2*sqrt(-b*x + 2)) + 11*b**2*x**(3/2)/(2*sqrt(-b*x + 2)) - b*sqrt(x)/sqrt(-b*x + 2) - 16/(sqrt(x)*sqrt(-b*x + 2)), True))","A",0
568,1,221,0,5.346282," ","integrate((-b*x+2)**(5/2)/x**(5/2),x)","\begin{cases} b^{\frac{5}{2}} x \sqrt{-1 + \frac{2}{b x}} + \frac{28 b^{\frac{3}{2}} \sqrt{-1 + \frac{2}{b x}}}{3} + 5 i b^{\frac{3}{2}} \log{\left(\frac{1}{b x} \right)} - 10 i b^{\frac{3}{2}} \log{\left(\frac{1}{\sqrt{b} \sqrt{x}} \right)} + 10 b^{\frac{3}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)} - \frac{8 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}}{3 x} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\i b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}} + \frac{28 i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{3} + 5 i b^{\frac{3}{2}} \log{\left(\frac{1}{b x} \right)} - 10 i b^{\frac{3}{2}} \log{\left(\sqrt{1 - \frac{2}{b x}} + 1 \right)} - \frac{8 i \sqrt{b} \sqrt{1 - \frac{2}{b x}}}{3 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((b**(5/2)*x*sqrt(-1 + 2/(b*x)) + 28*b**(3/2)*sqrt(-1 + 2/(b*x))/3 + 5*I*b**(3/2)*log(1/(b*x)) - 10*I*b**(3/2)*log(1/(sqrt(b)*sqrt(x))) + 10*b**(3/2)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2) - 8*sqrt(b)*sqrt(-1 + 2/(b*x))/(3*x), 2/Abs(b*x) > 1), (I*b**(5/2)*x*sqrt(1 - 2/(b*x)) + 28*I*b**(3/2)*sqrt(1 - 2/(b*x))/3 + 5*I*b**(3/2)*log(1/(b*x)) - 10*I*b**(3/2)*log(sqrt(1 - 2/(b*x)) + 1) - 8*I*sqrt(b)*sqrt(1 - 2/(b*x))/(3*x), True))","C",0
569,1,128,0,8.520542," ","integrate(x**(5/2)/(b*x+a)**(1/2),x)","\frac{5 a^{\frac{5}{2}} \sqrt{x}}{8 b^{3} \sqrt{1 + \frac{b x}{a}}} + \frac{5 a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{\sqrt{a} x^{\frac{5}{2}}}{12 b \sqrt{1 + \frac{b x}{a}}} - \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}}} + \frac{x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"5*a**(5/2)*sqrt(x)/(8*b**3*sqrt(1 + b*x/a)) + 5*a**(3/2)*x**(3/2)/(24*b**2*sqrt(1 + b*x/a)) - sqrt(a)*x**(5/2)/(12*b*sqrt(1 + b*x/a)) - 5*a**3*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(7/2)) + x**(7/2)/(3*sqrt(a)*sqrt(1 + b*x/a))","A",0
570,1,100,0,4.300797," ","integrate(x**(3/2)/(b*x+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} \sqrt{x}}{4 b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{\sqrt{a} x^{\frac{3}{2}}}{4 b \sqrt{1 + \frac{b x}{a}}} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}}} + \frac{x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-3*a**(3/2)*sqrt(x)/(4*b**2*sqrt(1 + b*x/a)) - sqrt(a)*x**(3/2)/(4*b*sqrt(1 + b*x/a)) + 3*a**2*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(5/2)) + x**(5/2)/(2*sqrt(a)*sqrt(1 + b*x/a))","A",0
571,1,44,0,2.186742," ","integrate(x**(1/2)/(b*x+a)**(1/2),x)","\frac{\sqrt{a} \sqrt{x} \sqrt{1 + \frac{b x}{a}}}{b} - \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}}"," ",0,"sqrt(a)*sqrt(x)*sqrt(1 + b*x/a)/b - a*asinh(sqrt(b)*sqrt(x)/sqrt(a))/b**(3/2)","A",0
572,1,22,0,1.096530," ","integrate(1/x**(1/2)/(b*x+a)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"2*asinh(sqrt(b)*sqrt(x)/sqrt(a))/sqrt(b)","A",0
573,1,19,0,0.912799," ","integrate(1/x**(3/2)/(b*x+a)**(1/2),x)","- \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{a}"," ",0,"-2*sqrt(b)*sqrt(a/(b*x) + 1)/a","A",0
574,1,42,0,1.920204," ","integrate(1/x**(5/2)/(b*x+a)**(1/2),x)","- \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 a x} + \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a^{2}}"," ",0,"-2*sqrt(b)*sqrt(a/(b*x) + 1)/(3*a*x) + 4*b**(3/2)*sqrt(a/(b*x) + 1)/(3*a**2)","A",0
575,1,287,0,6.249355," ","integrate(1/x**(7/2)/(b*x+a)**(1/2),x)","- \frac{6 a^{4} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x^{3} + 15 a^{3} b^{6} x^{4}} - \frac{4 a^{3} b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x^{3} + 15 a^{3} b^{6} x^{4}} - \frac{6 a^{2} b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x^{3} + 15 a^{3} b^{6} x^{4}} - \frac{24 a b^{\frac{15}{2}} x^{3} \sqrt{\frac{a}{b x} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x^{3} + 15 a^{3} b^{6} x^{4}} - \frac{16 b^{\frac{17}{2}} x^{4} \sqrt{\frac{a}{b x} + 1}}{15 a^{5} b^{4} x^{2} + 30 a^{4} b^{5} x^{3} + 15 a^{3} b^{6} x^{4}}"," ",0,"-6*a**4*b**(9/2)*sqrt(a/(b*x) + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x**3 + 15*a**3*b**6*x**4) - 4*a**3*b**(11/2)*x*sqrt(a/(b*x) + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x**3 + 15*a**3*b**6*x**4) - 6*a**2*b**(13/2)*x**2*sqrt(a/(b*x) + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x**3 + 15*a**3*b**6*x**4) - 24*a*b**(15/2)*x**3*sqrt(a/(b*x) + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x**3 + 15*a**3*b**6*x**4) - 16*b**(17/2)*x**4*sqrt(a/(b*x) + 1)/(15*a**5*b**4*x**2 + 30*a**4*b**5*x**3 + 15*a**3*b**6*x**4)","B",0
576,1,488,0,16.137064," ","integrate(1/x**(9/2)/(b*x+a)**(1/2),x)","- \frac{10 a^{6} b^{\frac{19}{2}} \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}} - \frac{18 a^{5} b^{\frac{21}{2}} x \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}} - \frac{10 a^{4} b^{\frac{23}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}} + \frac{10 a^{3} b^{\frac{25}{2}} x^{3} \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}} + \frac{60 a^{2} b^{\frac{27}{2}} x^{4} \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}} + \frac{80 a b^{\frac{29}{2}} x^{5} \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}} + \frac{32 b^{\frac{31}{2}} x^{6} \sqrt{\frac{a}{b x} + 1}}{35 a^{7} b^{9} x^{3} + 105 a^{6} b^{10} x^{4} + 105 a^{5} b^{11} x^{5} + 35 a^{4} b^{12} x^{6}}"," ",0,"-10*a**6*b**(19/2)*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6) - 18*a**5*b**(21/2)*x*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6) - 10*a**4*b**(23/2)*x**2*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6) + 10*a**3*b**(25/2)*x**3*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6) + 60*a**2*b**(27/2)*x**4*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6) + 80*a*b**(29/2)*x**5*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6) + 32*b**(31/2)*x**6*sqrt(a/(b*x) + 1)/(35*a**7*b**9*x**3 + 105*a**6*b**10*x**4 + 105*a**5*b**11*x**5 + 35*a**4*b**12*x**6)","B",0
577,1,105,0,8.139471," ","integrate(x**(5/2)/(b*x+a)**(3/2),x)","- \frac{15 a^{\frac{3}{2}} \sqrt{x}}{4 b^{3} \sqrt{1 + \frac{b x}{a}}} - \frac{5 \sqrt{a} x^{\frac{3}{2}}}{4 b^{2} \sqrt{1 + \frac{b x}{a}}} + \frac{15 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{7}{2}}} + \frac{x^{\frac{5}{2}}}{2 \sqrt{a} b \sqrt{1 + \frac{b x}{a}}}"," ",0,"-15*a**(3/2)*sqrt(x)/(4*b**3*sqrt(1 + b*x/a)) - 5*sqrt(a)*x**(3/2)/(4*b**2*sqrt(1 + b*x/a)) + 15*a**2*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(7/2)) + x**(5/2)/(2*sqrt(a)*b*sqrt(1 + b*x/a))","A",0
578,1,71,0,3.677774," ","integrate(x**(3/2)/(b*x+a)**(3/2),x)","\frac{3 \sqrt{a} \sqrt{x}}{b^{2} \sqrt{1 + \frac{b x}{a}}} - \frac{3 a \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{5}{2}}} + \frac{x^{\frac{3}{2}}}{\sqrt{a} b \sqrt{1 + \frac{b x}{a}}}"," ",0,"3*sqrt(a)*sqrt(x)/(b**2*sqrt(1 + b*x/a)) - 3*a*asinh(sqrt(b)*sqrt(x)/sqrt(a))/b**(5/2) + x**(3/2)/(sqrt(a)*b*sqrt(1 + b*x/a))","A",0
579,1,46,0,1.779857," ","integrate(x**(1/2)/(b*x+a)**(3/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} - \frac{2 \sqrt{x}}{\sqrt{a} b \sqrt{1 + \frac{b x}{a}}}"," ",0,"2*asinh(sqrt(b)*sqrt(x)/sqrt(a))/b**(3/2) - 2*sqrt(x)/(sqrt(a)*b*sqrt(1 + b*x/a))","A",0
580,1,17,0,0.879021," ","integrate(1/(b*x+a)**(3/2)/x**(1/2),x)","\frac{2}{a \sqrt{b} \sqrt{\frac{a}{b x} + 1}}"," ",0,"2/(a*sqrt(b)*sqrt(a/(b*x) + 1))","A",0
581,1,41,0,1.597938," ","integrate(1/x**(3/2)/(b*x+a)**(3/2),x)","- \frac{2}{a \sqrt{b} x \sqrt{\frac{a}{b x} + 1}} - \frac{4 \sqrt{b}}{a^{2} \sqrt{\frac{a}{b x} + 1}}"," ",0,"-2/(a*sqrt(b)*x*sqrt(a/(b*x) + 1)) - 4*sqrt(b)/(a**2*sqrt(a/(b*x) + 1))","A",0
582,1,219,0,3.983146," ","integrate(1/x**(5/2)/(b*x+a)**(3/2),x)","- \frac{2 a^{3} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{3}} + \frac{6 a^{2} b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{3}} + \frac{24 a b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{3}} + \frac{16 b^{\frac{15}{2}} x^{3} \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} + 3 a^{3} b^{6} x^{3}}"," ",0,"-2*a**3*b**(9/2)*sqrt(a/(b*x) + 1)/(3*a**5*b**4*x + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**3) + 6*a**2*b**(11/2)*x*sqrt(a/(b*x) + 1)/(3*a**5*b**4*x + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**3) + 24*a*b**(13/2)*x**2*sqrt(a/(b*x) + 1)/(3*a**5*b**4*x + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**3) + 16*b**(15/2)*x**3*sqrt(a/(b*x) + 1)/(3*a**5*b**4*x + 6*a**4*b**5*x**2 + 3*a**3*b**6*x**3)","B",0
583,1,348,0,11.154285," ","integrate(1/x**(7/2)/(b*x+a)**(3/2),x)","- \frac{2 a^{5} b^{\frac{19}{2}} \sqrt{\frac{a}{b x} + 1}}{5 a^{7} b^{9} x^{2} + 15 a^{6} b^{10} x^{3} + 15 a^{5} b^{11} x^{4} + 5 a^{4} b^{12} x^{5}} - \frac{10 a^{3} b^{\frac{23}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{5 a^{7} b^{9} x^{2} + 15 a^{6} b^{10} x^{3} + 15 a^{5} b^{11} x^{4} + 5 a^{4} b^{12} x^{5}} - \frac{60 a^{2} b^{\frac{25}{2}} x^{3} \sqrt{\frac{a}{b x} + 1}}{5 a^{7} b^{9} x^{2} + 15 a^{6} b^{10} x^{3} + 15 a^{5} b^{11} x^{4} + 5 a^{4} b^{12} x^{5}} - \frac{80 a b^{\frac{27}{2}} x^{4} \sqrt{\frac{a}{b x} + 1}}{5 a^{7} b^{9} x^{2} + 15 a^{6} b^{10} x^{3} + 15 a^{5} b^{11} x^{4} + 5 a^{4} b^{12} x^{5}} - \frac{32 b^{\frac{29}{2}} x^{5} \sqrt{\frac{a}{b x} + 1}}{5 a^{7} b^{9} x^{2} + 15 a^{6} b^{10} x^{3} + 15 a^{5} b^{11} x^{4} + 5 a^{4} b^{12} x^{5}}"," ",0,"-2*a**5*b**(19/2)*sqrt(a/(b*x) + 1)/(5*a**7*b**9*x**2 + 15*a**6*b**10*x**3 + 15*a**5*b**11*x**4 + 5*a**4*b**12*x**5) - 10*a**3*b**(23/2)*x**2*sqrt(a/(b*x) + 1)/(5*a**7*b**9*x**2 + 15*a**6*b**10*x**3 + 15*a**5*b**11*x**4 + 5*a**4*b**12*x**5) - 60*a**2*b**(25/2)*x**3*sqrt(a/(b*x) + 1)/(5*a**7*b**9*x**2 + 15*a**6*b**10*x**3 + 15*a**5*b**11*x**4 + 5*a**4*b**12*x**5) - 80*a*b**(27/2)*x**4*sqrt(a/(b*x) + 1)/(5*a**7*b**9*x**2 + 15*a**6*b**10*x**3 + 15*a**5*b**11*x**4 + 5*a**4*b**12*x**5) - 32*b**(29/2)*x**5*sqrt(a/(b*x) + 1)/(5*a**7*b**9*x**2 + 15*a**6*b**10*x**3 + 15*a**5*b**11*x**4 + 5*a**4*b**12*x**5)","B",0
584,1,396,0,7.609899," ","integrate(x**(5/2)/(b*x+a)**(5/2),x)","- \frac{15 a^{\frac{81}{2}} b^{22} x^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 + \frac{b x}{a}}} - \frac{15 a^{\frac{79}{2}} b^{23} x^{\frac{53}{2}} \sqrt{1 + \frac{b x}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 + \frac{b x}{a}}} + \frac{15 a^{40} b^{\frac{45}{2}} x^{26}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 + \frac{b x}{a}}} + \frac{20 a^{39} b^{\frac{47}{2}} x^{27}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 + \frac{b x}{a}}} + \frac{3 a^{38} b^{\frac{49}{2}} x^{28}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 + \frac{b x}{a}}}"," ",0,"-15*a**(81/2)*b**22*x**(51/2)*sqrt(1 + b*x/a)*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 + b*x/a) + 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 + b*x/a)) - 15*a**(79/2)*b**23*x**(53/2)*sqrt(1 + b*x/a)*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 + b*x/a) + 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 + b*x/a)) + 15*a**40*b**(45/2)*x**26/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 + b*x/a) + 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 + b*x/a)) + 20*a**39*b**(47/2)*x**27/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 + b*x/a) + 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 + b*x/a)) + 3*a**38*b**(49/2)*x**28/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 + b*x/a) + 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 + b*x/a))","B",0
585,1,328,0,4.026754," ","integrate(x**(3/2)/(b*x+a)**(5/2),x)","\frac{6 a^{\frac{39}{2}} b^{11} x^{\frac{27}{2}} \sqrt{1 + \frac{b x}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 + \frac{b x}{a}}} + \frac{6 a^{\frac{37}{2}} b^{12} x^{\frac{29}{2}} \sqrt{1 + \frac{b x}{a}} \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 + \frac{b x}{a}}} - \frac{6 a^{19} b^{\frac{23}{2}} x^{14}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 + \frac{b x}{a}}} - \frac{8 a^{18} b^{\frac{25}{2}} x^{15}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 + \frac{b x}{a}}}"," ",0,"6*a**(39/2)*b**11*x**(27/2)*sqrt(1 + b*x/a)*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 + b*x/a) + 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 + b*x/a)) + 6*a**(37/2)*b**12*x**(29/2)*sqrt(1 + b*x/a)*asinh(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 + b*x/a) + 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 + b*x/a)) - 6*a**19*b**(23/2)*x**14/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 + b*x/a) + 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 + b*x/a)) - 8*a**18*b**(25/2)*x**15/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 + b*x/a) + 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 + b*x/a))","B",0
586,1,42,0,1.427166," ","integrate(x**(1/2)/(b*x+a)**(5/2),x)","\frac{2 x^{\frac{3}{2}}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{b x}{a}} + 3 a^{\frac{3}{2}} b x \sqrt{1 + \frac{b x}{a}}}"," ",0,"2*x**(3/2)/(3*a**(5/2)*sqrt(1 + b*x/a) + 3*a**(3/2)*b*x*sqrt(1 + b*x/a))","B",0
587,1,92,0,1.895536," ","integrate(1/(b*x+a)**(5/2)/x**(1/2),x)","\frac{6 a}{3 a^{3} \sqrt{b} \sqrt{\frac{a}{b x} + 1} + 3 a^{2} b^{\frac{3}{2}} x \sqrt{\frac{a}{b x} + 1}} + \frac{4 b x}{3 a^{3} \sqrt{b} \sqrt{\frac{a}{b x} + 1} + 3 a^{2} b^{\frac{3}{2}} x \sqrt{\frac{a}{b x} + 1}}"," ",0,"6*a/(3*a**3*sqrt(b)*sqrt(a/(b*x) + 1) + 3*a**2*b**(3/2)*x*sqrt(a/(b*x) + 1)) + 4*b*x/(3*a**3*sqrt(b)*sqrt(a/(b*x) + 1) + 3*a**2*b**(3/2)*x*sqrt(a/(b*x) + 1))","B",0
588,1,153,0,3.972253," ","integrate(1/x**(3/2)/(b*x+a)**(5/2),x)","- \frac{6 a^{2} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} - \frac{24 a b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} - \frac{16 b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{3 a^{5} b^{4} + 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}}"," ",0,"-6*a**2*b**(9/2)*sqrt(a/(b*x) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x + 3*a**3*b**6*x**2) - 24*a*b**(11/2)*x*sqrt(a/(b*x) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x + 3*a**3*b**6*x**2) - 16*b**(13/2)*x**2*sqrt(a/(b*x) + 1)/(3*a**5*b**4 + 6*a**4*b**5*x + 3*a**3*b**6*x**2)","B",0
589,1,337,0,7.060992," ","integrate(1/x**(5/2)/(b*x+a)**(5/2),x)","- \frac{2 a^{4} b^{\frac{19}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{10 a^{3} b^{\frac{21}{2}} x \sqrt{\frac{a}{b x} + 1}}{3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{60 a^{2} b^{\frac{23}{2}} x^{2} \sqrt{\frac{a}{b x} + 1}}{3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{80 a b^{\frac{25}{2}} x^{3} \sqrt{\frac{a}{b x} + 1}}{3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{32 b^{\frac{27}{2}} x^{4} \sqrt{\frac{a}{b x} + 1}}{3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} + 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}}"," ",0,"-2*a**4*b**(19/2)*sqrt(a/(b*x) + 1)/(3*a**7*b**9*x + 9*a**6*b**10*x**2 + 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 10*a**3*b**(21/2)*x*sqrt(a/(b*x) + 1)/(3*a**7*b**9*x + 9*a**6*b**10*x**2 + 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 60*a**2*b**(23/2)*x**2*sqrt(a/(b*x) + 1)/(3*a**7*b**9*x + 9*a**6*b**10*x**2 + 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 80*a*b**(25/2)*x**3*sqrt(a/(b*x) + 1)/(3*a**7*b**9*x + 9*a**6*b**10*x**2 + 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 32*b**(27/2)*x**4*sqrt(a/(b*x) + 1)/(3*a**7*b**9*x + 9*a**6*b**10*x**2 + 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4)","B",0
590,1,270,0,8.432457," ","integrate(x**(5/2)/(-b*x+a)**(1/2),x)","\begin{cases} \frac{5 i a^{\frac{5}{2}} \sqrt{x}}{8 b^{3} \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i \sqrt{a} x^{\frac{5}{2}}}{12 b \sqrt{-1 + \frac{b x}{a}}} - \frac{5 i a^{3} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}}} - \frac{i x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{5 a^{\frac{5}{2}} \sqrt{x}}{8 b^{3} \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{\frac{3}{2}} x^{\frac{3}{2}}}{24 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{\sqrt{a} x^{\frac{5}{2}}}{12 b \sqrt{1 - \frac{b x}{a}}} + \frac{5 a^{3} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{8 b^{\frac{7}{2}}} + \frac{x^{\frac{7}{2}}}{3 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*I*a**(5/2)*sqrt(x)/(8*b**3*sqrt(-1 + b*x/a)) - 5*I*a**(3/2)*x**(3/2)/(24*b**2*sqrt(-1 + b*x/a)) - I*sqrt(a)*x**(5/2)/(12*b*sqrt(-1 + b*x/a)) - 5*I*a**3*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(7/2)) - I*x**(7/2)/(3*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-5*a**(5/2)*sqrt(x)/(8*b**3*sqrt(1 - b*x/a)) + 5*a**(3/2)*x**(3/2)/(24*b**2*sqrt(1 - b*x/a)) + sqrt(a)*x**(5/2)/(12*b*sqrt(1 - b*x/a)) + 5*a**3*asin(sqrt(b)*sqrt(x)/sqrt(a))/(8*b**(7/2)) + x**(7/2)/(3*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
591,1,214,0,4.295756," ","integrate(x**(3/2)/(-b*x+a)**(1/2),x)","\begin{cases} \frac{3 i a^{\frac{3}{2}} \sqrt{x}}{4 b^{2} \sqrt{-1 + \frac{b x}{a}}} - \frac{i \sqrt{a} x^{\frac{3}{2}}}{4 b \sqrt{-1 + \frac{b x}{a}}} - \frac{3 i a^{2} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}}} - \frac{i x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{3 a^{\frac{3}{2}} \sqrt{x}}{4 b^{2} \sqrt{1 - \frac{b x}{a}}} + \frac{\sqrt{a} x^{\frac{3}{2}}}{4 b \sqrt{1 - \frac{b x}{a}}} + \frac{3 a^{2} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{5}{2}}} + \frac{x^{\frac{5}{2}}}{2 \sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*I*a**(3/2)*sqrt(x)/(4*b**2*sqrt(-1 + b*x/a)) - I*sqrt(a)*x**(3/2)/(4*b*sqrt(-1 + b*x/a)) - 3*I*a**2*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(5/2)) - I*x**(5/2)/(2*sqrt(a)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-3*a**(3/2)*sqrt(x)/(4*b**2*sqrt(1 - b*x/a)) + sqrt(a)*x**(3/2)/(4*b*sqrt(1 - b*x/a)) + 3*a**2*asin(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(5/2)) + x**(5/2)/(2*sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
592,1,121,0,2.277595," ","integrate(x**(1/2)/(-b*x+a)**(1/2),x)","\begin{cases} - \frac{i \sqrt{a} \sqrt{x} \sqrt{-1 + \frac{b x}{a}}}{b} - \frac{i a \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{\sqrt{a} \sqrt{x}}{b \sqrt{1 - \frac{b x}{a}}} + \frac{a \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} + \frac{x^{\frac{3}{2}}}{\sqrt{a} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*sqrt(a)*sqrt(x)*sqrt(-1 + b*x/a)/b - I*a*acosh(sqrt(b)*sqrt(x)/sqrt(a))/b**(3/2), Abs(b*x/a) > 1), (-sqrt(a)*sqrt(x)/(b*sqrt(1 - b*x/a)) + a*asin(sqrt(b)*sqrt(x)/sqrt(a))/b**(3/2) + x**(3/2)/(sqrt(a)*sqrt(1 - b*x/a)), True))","A",0
593,1,54,0,1.152659," ","integrate(1/x**(1/2)/(-b*x+a)**(1/2),x)","\begin{cases} - \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{2 \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(b)*sqrt(x)/sqrt(a))/sqrt(b), Abs(b*x/a) > 1), (2*asin(sqrt(b)*sqrt(x)/sqrt(a))/sqrt(b), True))","A",0
594,1,46,0,0.969049," ","integrate(1/x**(3/2)/(-b*x+a)**(1/2),x)","\begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{a} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 i \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(b)*sqrt(a/(b*x) - 1)/a, Abs(a/(b*x)) > 1), (-2*I*sqrt(b)*sqrt(-a/(b*x) + 1)/a, True))","A",0
595,1,177,0,2.055245," ","integrate(1/x**(5/2)/(-b*x+a)**(1/2),x)","\begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{3 a x} - \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}}{3 a^{2}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{2 i a^{2} b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{3} b x + 3 a^{2} b^{2} x^{2}} + \frac{2 i a b^{\frac{5}{2}} x \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{3} b x + 3 a^{2} b^{2} x^{2}} - \frac{4 i b^{\frac{7}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{3} b x + 3 a^{2} b^{2} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(b)*sqrt(a/(b*x) - 1)/(3*a*x) - 4*b**(3/2)*sqrt(a/(b*x) - 1)/(3*a**2), Abs(a/(b*x)) > 1), (2*I*a**2*b**(3/2)*sqrt(-a/(b*x) + 1)/(-3*a**3*b*x + 3*a**2*b**2*x**2) + 2*I*a*b**(5/2)*x*sqrt(-a/(b*x) + 1)/(-3*a**3*b*x + 3*a**2*b**2*x**2) - 4*I*b**(7/2)*x**2*sqrt(-a/(b*x) + 1)/(-3*a**3*b*x + 3*a**2*b**2*x**2), True))","A",0
596,1,224,0,8.030009," ","integrate(x**(5/2)/(-b*x+a)**(3/2),x)","\begin{cases} - \frac{15 i a^{\frac{3}{2}} \sqrt{x}}{4 b^{3} \sqrt{-1 + \frac{b x}{a}}} + \frac{5 i \sqrt{a} x^{\frac{3}{2}}}{4 b^{2} \sqrt{-1 + \frac{b x}{a}}} + \frac{15 i a^{2} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{7}{2}}} + \frac{i x^{\frac{5}{2}}}{2 \sqrt{a} b \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{15 a^{\frac{3}{2}} \sqrt{x}}{4 b^{3} \sqrt{1 - \frac{b x}{a}}} - \frac{5 \sqrt{a} x^{\frac{3}{2}}}{4 b^{2} \sqrt{1 - \frac{b x}{a}}} - \frac{15 a^{2} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{4 b^{\frac{7}{2}}} - \frac{x^{\frac{5}{2}}}{2 \sqrt{a} b \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*I*a**(3/2)*sqrt(x)/(4*b**3*sqrt(-1 + b*x/a)) + 5*I*sqrt(a)*x**(3/2)/(4*b**2*sqrt(-1 + b*x/a)) + 15*I*a**2*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(7/2)) + I*x**(5/2)/(2*sqrt(a)*b*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (15*a**(3/2)*sqrt(x)/(4*b**3*sqrt(1 - b*x/a)) - 5*sqrt(a)*x**(3/2)/(4*b**2*sqrt(1 - b*x/a)) - 15*a**2*asin(sqrt(b)*sqrt(x)/sqrt(a))/(4*b**(7/2)) - x**(5/2)/(2*sqrt(a)*b*sqrt(1 - b*x/a)), True))","A",0
597,1,155,0,3.704083," ","integrate(x**(3/2)/(-b*x+a)**(3/2),x)","\begin{cases} - \frac{3 i \sqrt{a} \sqrt{x}}{b^{2} \sqrt{-1 + \frac{b x}{a}}} + \frac{3 i a \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{5}{2}}} + \frac{i x^{\frac{3}{2}}}{\sqrt{a} b \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{3 \sqrt{a} \sqrt{x}}{b^{2} \sqrt{1 - \frac{b x}{a}}} - \frac{3 a \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{5}{2}}} - \frac{x^{\frac{3}{2}}}{\sqrt{a} b \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*sqrt(a)*sqrt(x)/(b**2*sqrt(-1 + b*x/a)) + 3*I*a*acosh(sqrt(b)*sqrt(x)/sqrt(a))/b**(5/2) + I*x**(3/2)/(sqrt(a)*b*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (3*sqrt(a)*sqrt(x)/(b**2*sqrt(1 - b*x/a)) - 3*a*asin(sqrt(b)*sqrt(x)/sqrt(a))/b**(5/2) - x**(3/2)/(sqrt(a)*b*sqrt(1 - b*x/a)), True))","A",0
598,1,102,0,1.891479," ","integrate(x**(1/2)/(-b*x+a)**(3/2),x)","\begin{cases} \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} - \frac{2 i \sqrt{x}}{\sqrt{a} b \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{2 \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} + \frac{2 \sqrt{x}}{\sqrt{a} b \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(sqrt(b)*sqrt(x)/sqrt(a))/b**(3/2) - 2*I*sqrt(x)/(sqrt(a)*b*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-2*asin(sqrt(b)*sqrt(x)/sqrt(a))/b**(3/2) + 2*sqrt(x)/(sqrt(a)*b*sqrt(1 - b*x/a)), True))","A",0
599,1,44,0,0.942953," ","integrate(1/(-b*x+a)**(3/2)/x**(1/2),x)","\begin{cases} \frac{2}{a \sqrt{b} \sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 i}{a \sqrt{b} \sqrt{- \frac{a}{b x} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(a*sqrt(b)*sqrt(a/(b*x) - 1)), Abs(a/(b*x)) > 1), (-2*I/(a*sqrt(b)*sqrt(-a/(b*x) + 1)), True))","A",0
600,1,112,0,1.678360," ","integrate(1/x**(3/2)/(-b*x+a)**(3/2),x)","\begin{cases} - \frac{2}{a \sqrt{b} x \sqrt{\frac{a}{b x} - 1}} + \frac{4 \sqrt{b}}{a^{2} \sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{2 i a b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{a^{3} b - a^{2} b^{2} x} + \frac{4 i b^{\frac{5}{2}} x \sqrt{- \frac{a}{b x} + 1}}{a^{3} b - a^{2} b^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(a*sqrt(b)*x*sqrt(a/(b*x) - 1)) + 4*sqrt(b)/(a**2*sqrt(a/(b*x) - 1)), Abs(a/(b*x)) > 1), (-2*I*a*b**(3/2)*sqrt(-a/(b*x) + 1)/(a**3*b - a**2*b**2*x) + 4*I*b**(5/2)*x*sqrt(-a/(b*x) + 1)/(a**3*b - a**2*b**2*x), True))","A",0
601,1,452,0,4.639610," ","integrate(1/x**(5/2)/(-b*x+a)**(3/2),x)","\begin{cases} \frac{2 a^{3} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} + \frac{6 a^{2} b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} - 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} - \frac{24 a b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} + \frac{16 b^{\frac{15}{2}} x^{3} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{2 i a^{3} b^{\frac{9}{2}} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} + \frac{6 i a^{2} b^{\frac{11}{2}} x \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} - \frac{24 i a b^{\frac{13}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} + \frac{16 i b^{\frac{15}{2}} x^{3} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{5} b^{4} x + 6 a^{4} b^{5} x^{2} - 3 a^{3} b^{6} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*b**(9/2)*sqrt(a/(b*x) - 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3) + 6*a**2*b**(11/2)*x*sqrt(a/(b*x) - 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3) - 24*a*b**(13/2)*x**2*sqrt(a/(b*x) - 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3) + 16*b**(15/2)*x**3*sqrt(a/(b*x) - 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3), Abs(a/(b*x)) > 1), (2*I*a**3*b**(9/2)*sqrt(-a/(b*x) + 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3) + 6*I*a**2*b**(11/2)*x*sqrt(-a/(b*x) + 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3) - 24*I*a*b**(13/2)*x**2*sqrt(-a/(b*x) + 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3) + 16*I*b**(15/2)*x**3*sqrt(-a/(b*x) + 1)/(-3*a**5*b**4*x + 6*a**4*b**5*x**2 - 3*a**3*b**6*x**3), True))","B",0
602,1,971,0,8.483429," ","integrate(x**(5/2)/(-b*x+a)**(5/2),x)","\begin{cases} - \frac{30 i a^{\frac{81}{2}} b^{22} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{15 \pi a^{\frac{81}{2}} b^{22} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{30 i a^{\frac{79}{2}} b^{23} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} - \frac{15 \pi a^{\frac{79}{2}} b^{23} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{30 i a^{40} b^{\frac{45}{2}} x^{26}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} - \frac{40 i a^{39} b^{\frac{47}{2}} x^{27}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{6 i a^{38} b^{\frac{49}{2}} x^{28}}{6 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{-1 + \frac{b x}{a}} - 6 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{15 a^{\frac{81}{2}} b^{22} x^{\frac{51}{2}} \sqrt{1 - \frac{b x}{a}} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 - \frac{b x}{a}}} - \frac{15 a^{\frac{79}{2}} b^{23} x^{\frac{53}{2}} \sqrt{1 - \frac{b x}{a}} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 - \frac{b x}{a}}} - \frac{15 a^{40} b^{\frac{45}{2}} x^{26}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 - \frac{b x}{a}}} + \frac{20 a^{39} b^{\frac{47}{2}} x^{27}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 - \frac{b x}{a}}} - \frac{3 a^{38} b^{\frac{49}{2}} x^{28}}{3 a^{\frac{79}{2}} b^{\frac{51}{2}} x^{\frac{51}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{77}{2}} b^{\frac{53}{2}} x^{\frac{53}{2}} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-30*I*a**(81/2)*b**22*x**(51/2)*sqrt(-1 + b*x/a)*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)) + 15*pi*a**(81/2)*b**22*x**(51/2)*sqrt(-1 + b*x/a)/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)) + 30*I*a**(79/2)*b**23*x**(53/2)*sqrt(-1 + b*x/a)*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)) - 15*pi*a**(79/2)*b**23*x**(53/2)*sqrt(-1 + b*x/a)/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)) + 30*I*a**40*b**(45/2)*x**26/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)) - 40*I*a**39*b**(47/2)*x**27/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)) + 6*I*a**38*b**(49/2)*x**28/(6*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(-1 + b*x/a) - 6*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (15*a**(81/2)*b**22*x**(51/2)*sqrt(1 - b*x/a)*asin(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 - b*x/a) - 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 - b*x/a)) - 15*a**(79/2)*b**23*x**(53/2)*sqrt(1 - b*x/a)*asin(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 - b*x/a) - 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 - b*x/a)) - 15*a**40*b**(45/2)*x**26/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 - b*x/a) - 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 - b*x/a)) + 20*a**39*b**(47/2)*x**27/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 - b*x/a) - 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 - b*x/a)) - 3*a**38*b**(49/2)*x**28/(3*a**(79/2)*b**(51/2)*x**(51/2)*sqrt(1 - b*x/a) - 3*a**(77/2)*b**(53/2)*x**(53/2)*sqrt(1 - b*x/a)), True))","B",0
603,1,833,0,4.495999," ","integrate(x**(3/2)/(-b*x+a)**(5/2),x)","\begin{cases} - \frac{6 i a^{\frac{39}{2}} b^{11} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{3 \pi a^{\frac{39}{2}} b^{11} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{6 i a^{\frac{37}{2}} b^{12} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}} \operatorname{acosh}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}} - \frac{3 \pi a^{\frac{37}{2}} b^{12} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}} + \frac{6 i a^{19} b^{\frac{23}{2}} x^{14}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}} - \frac{8 i a^{18} b^{\frac{25}{2}} x^{15}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{-1 + \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\\frac{6 a^{\frac{39}{2}} b^{11} x^{\frac{27}{2}} \sqrt{1 - \frac{b x}{a}} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 - \frac{b x}{a}}} - \frac{6 a^{\frac{37}{2}} b^{12} x^{\frac{29}{2}} \sqrt{1 - \frac{b x}{a}} \operatorname{asin}{\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right)}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 - \frac{b x}{a}}} - \frac{6 a^{19} b^{\frac{23}{2}} x^{14}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 - \frac{b x}{a}}} + \frac{8 a^{18} b^{\frac{25}{2}} x^{15}}{3 a^{\frac{39}{2}} b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{1 - \frac{b x}{a}} - 3 a^{\frac{37}{2}} b^{\frac{29}{2}} x^{\frac{29}{2}} \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*I*a**(39/2)*b**11*x**(27/2)*sqrt(-1 + b*x/a)*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(-1 + b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(-1 + b*x/a)) + 3*pi*a**(39/2)*b**11*x**(27/2)*sqrt(-1 + b*x/a)/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(-1 + b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(-1 + b*x/a)) + 6*I*a**(37/2)*b**12*x**(29/2)*sqrt(-1 + b*x/a)*acosh(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(-1 + b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(-1 + b*x/a)) - 3*pi*a**(37/2)*b**12*x**(29/2)*sqrt(-1 + b*x/a)/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(-1 + b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(-1 + b*x/a)) + 6*I*a**19*b**(23/2)*x**14/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(-1 + b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(-1 + b*x/a)) - 8*I*a**18*b**(25/2)*x**15/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(-1 + b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (6*a**(39/2)*b**11*x**(27/2)*sqrt(1 - b*x/a)*asin(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 - b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 - b*x/a)) - 6*a**(37/2)*b**12*x**(29/2)*sqrt(1 - b*x/a)*asin(sqrt(b)*sqrt(x)/sqrt(a))/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 - b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 - b*x/a)) - 6*a**19*b**(23/2)*x**14/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 - b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 - b*x/a)) + 8*a**18*b**(25/2)*x**15/(3*a**(39/2)*b**(27/2)*x**(27/2)*sqrt(1 - b*x/a) - 3*a**(37/2)*b**(29/2)*x**(29/2)*sqrt(1 - b*x/a)), True))","B",0
604,1,95,0,1.506650," ","integrate(x**(1/2)/(-b*x+a)**(5/2),x)","\begin{cases} \frac{2 i x^{\frac{3}{2}}}{- 3 a^{\frac{5}{2}} \sqrt{-1 + \frac{b x}{a}} + 3 a^{\frac{3}{2}} b x \sqrt{-1 + \frac{b x}{a}}} & \text{for}\: \left|{\frac{b x}{a}}\right| > 1 \\- \frac{2 x^{\frac{3}{2}}}{- 3 a^{\frac{5}{2}} \sqrt{1 - \frac{b x}{a}} + 3 a^{\frac{3}{2}} b x \sqrt{1 - \frac{b x}{a}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*x**(3/2)/(-3*a**(5/2)*sqrt(-1 + b*x/a) + 3*a**(3/2)*b*x*sqrt(-1 + b*x/a)), Abs(b*x/a) > 1), (-2*x**(3/2)/(-3*a**(5/2)*sqrt(1 - b*x/a) + 3*a**(3/2)*b*x*sqrt(1 - b*x/a)), True))","B",0
605,1,211,0,1.996044," ","integrate(1/(-b*x+a)**(5/2)/x**(1/2),x)","\begin{cases} \frac{6 i a}{3 i a^{3} \sqrt{b} \sqrt{\frac{a}{b x} - 1} - 3 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{a}{b x} - 1}} - \frac{4 i b x}{3 i a^{3} \sqrt{b} \sqrt{\frac{a}{b x} - 1} - 3 i a^{2} b^{\frac{3}{2}} x \sqrt{\frac{a}{b x} - 1}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{6 a b}{3 i a^{3} b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1} - 3 i a^{2} b^{\frac{5}{2}} x \sqrt{- \frac{a}{b x} + 1}} - \frac{4 b^{2} x}{3 i a^{3} b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1} - 3 i a^{2} b^{\frac{5}{2}} x \sqrt{- \frac{a}{b x} + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*I*a/(3*I*a**3*sqrt(b)*sqrt(a/(b*x) - 1) - 3*I*a**2*b**(3/2)*x*sqrt(a/(b*x) - 1)) - 4*I*b*x/(3*I*a**3*sqrt(b)*sqrt(a/(b*x) - 1) - 3*I*a**2*b**(3/2)*x*sqrt(a/(b*x) - 1)), Abs(a/(b*x)) > 1), (6*a*b/(3*I*a**3*b**(3/2)*sqrt(-a/(b*x) + 1) - 3*I*a**2*b**(5/2)*x*sqrt(-a/(b*x) + 1)) - 4*b**2*x/(3*I*a**3*b**(3/2)*sqrt(-a/(b*x) + 1) - 3*I*a**2*b**(5/2)*x*sqrt(-a/(b*x) + 1)), True))","C",0
606,1,314,0,4.265041," ","integrate(1/x**(3/2)/(-b*x+a)**(5/2),x)","\begin{cases} - \frac{6 a^{2} b^{\frac{9}{2}} \sqrt{\frac{a}{b x} - 1}}{3 a^{5} b^{4} - 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} + \frac{24 a b^{\frac{11}{2}} x \sqrt{\frac{a}{b x} - 1}}{3 a^{5} b^{4} - 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} - \frac{16 b^{\frac{13}{2}} x^{2} \sqrt{\frac{a}{b x} - 1}}{3 a^{5} b^{4} - 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\- \frac{6 i a^{2} b^{\frac{9}{2}} \sqrt{- \frac{a}{b x} + 1}}{3 a^{5} b^{4} - 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} + \frac{24 i a b^{\frac{11}{2}} x \sqrt{- \frac{a}{b x} + 1}}{3 a^{5} b^{4} - 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} - \frac{16 i b^{\frac{13}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{3 a^{5} b^{4} - 6 a^{4} b^{5} x + 3 a^{3} b^{6} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*a**2*b**(9/2)*sqrt(a/(b*x) - 1)/(3*a**5*b**4 - 6*a**4*b**5*x + 3*a**3*b**6*x**2) + 24*a*b**(11/2)*x*sqrt(a/(b*x) - 1)/(3*a**5*b**4 - 6*a**4*b**5*x + 3*a**3*b**6*x**2) - 16*b**(13/2)*x**2*sqrt(a/(b*x) - 1)/(3*a**5*b**4 - 6*a**4*b**5*x + 3*a**3*b**6*x**2), Abs(a/(b*x)) > 1), (-6*I*a**2*b**(9/2)*sqrt(-a/(b*x) + 1)/(3*a**5*b**4 - 6*a**4*b**5*x + 3*a**3*b**6*x**2) + 24*I*a*b**(11/2)*x*sqrt(-a/(b*x) + 1)/(3*a**5*b**4 - 6*a**4*b**5*x + 3*a**3*b**6*x**2) - 16*I*b**(13/2)*x**2*sqrt(-a/(b*x) + 1)/(3*a**5*b**4 - 6*a**4*b**5*x + 3*a**3*b**6*x**2), True))","B",0
607,1,688,0,13.450127," ","integrate(1/x**(5/2)/(-b*x+a)**(5/2),x)","\begin{cases} \frac{2 a^{4} b^{\frac{19}{2}} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{10 a^{3} b^{\frac{21}{2}} x \sqrt{\frac{a}{b x} - 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} - \frac{60 a^{2} b^{\frac{23}{2}} x^{2} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{80 a b^{\frac{25}{2}} x^{3} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} - \frac{32 b^{\frac{27}{2}} x^{4} \sqrt{\frac{a}{b x} - 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} & \text{for}\: \left|{\frac{a}{b x}}\right| > 1 \\\frac{2 i a^{4} b^{\frac{19}{2}} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{10 i a^{3} b^{\frac{21}{2}} x \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} - \frac{60 i a^{2} b^{\frac{23}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} + \frac{80 i a b^{\frac{25}{2}} x^{3} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} - \frac{32 i b^{\frac{27}{2}} x^{4} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{7} b^{9} x + 9 a^{6} b^{10} x^{2} - 9 a^{5} b^{11} x^{3} + 3 a^{4} b^{12} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**4*b**(19/2)*sqrt(a/(b*x) - 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 10*a**3*b**(21/2)*x*sqrt(a/(b*x) - 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) - 60*a**2*b**(23/2)*x**2*sqrt(a/(b*x) - 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 80*a*b**(25/2)*x**3*sqrt(a/(b*x) - 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) - 32*b**(27/2)*x**4*sqrt(a/(b*x) - 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4), Abs(a/(b*x)) > 1), (2*I*a**4*b**(19/2)*sqrt(-a/(b*x) + 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 10*I*a**3*b**(21/2)*x*sqrt(-a/(b*x) + 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) - 60*I*a**2*b**(23/2)*x**2*sqrt(-a/(b*x) + 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) + 80*I*a*b**(25/2)*x**3*sqrt(-a/(b*x) + 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4) - 32*I*b**(27/2)*x**4*sqrt(-a/(b*x) + 1)/(-3*a**7*b**9*x + 9*a**6*b**10*x**2 - 9*a**5*b**11*x**3 + 3*a**4*b**12*x**4), True))","B",0
608,1,95,0,7.397260," ","integrate(x**(5/2)/(b*x+2)**(1/2),x)","\frac{x^{\frac{7}{2}}}{3 \sqrt{b x + 2}} - \frac{x^{\frac{5}{2}}}{6 b \sqrt{b x + 2}} + \frac{5 x^{\frac{3}{2}}}{6 b^{2} \sqrt{b x + 2}} + \frac{5 \sqrt{x}}{b^{3} \sqrt{b x + 2}} - \frac{5 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{7}{2}}}"," ",0,"x**(7/2)/(3*sqrt(b*x + 2)) - x**(5/2)/(6*b*sqrt(b*x + 2)) + 5*x**(3/2)/(6*b**2*sqrt(b*x + 2)) + 5*sqrt(x)/(b**3*sqrt(b*x + 2)) - 5*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(7/2)","A",0
609,1,75,0,3.671218," ","integrate(x**(3/2)/(b*x+2)**(1/2),x)","\frac{x^{\frac{5}{2}}}{2 \sqrt{b x + 2}} - \frac{x^{\frac{3}{2}}}{2 b \sqrt{b x + 2}} - \frac{3 \sqrt{x}}{b^{2} \sqrt{b x + 2}} + \frac{3 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}}"," ",0,"x**(5/2)/(2*sqrt(b*x + 2)) - x**(3/2)/(2*b*sqrt(b*x + 2)) - 3*sqrt(x)/(b**2*sqrt(b*x + 2)) + 3*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2)","A",0
610,1,54,0,1.933753," ","integrate(x**(1/2)/(b*x+2)**(1/2),x)","\frac{x^{\frac{3}{2}}}{\sqrt{b x + 2}} + \frac{2 \sqrt{x}}{b \sqrt{b x + 2}} - \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}}"," ",0,"x**(3/2)/sqrt(b*x + 2) + 2*sqrt(x)/(b*sqrt(b*x + 2)) - 2*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2)","A",0
611,1,24,0,1.021577," ","integrate(1/x**(1/2)/(b*x+2)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}}"," ",0,"2*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b)","A",0
612,1,15,0,0.879474," ","integrate(1/x**(3/2)/(b*x+2)**(1/2),x)","- \sqrt{b} \sqrt{1 + \frac{2}{b x}}"," ",0,"-sqrt(b)*sqrt(1 + 2/(b*x))","A",0
613,1,34,0,1.873137," ","integrate(1/x**(5/2)/(b*x+2)**(1/2),x)","\frac{b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{3} - \frac{\sqrt{b} \sqrt{1 + \frac{2}{b x}}}{3 x}"," ",0,"b**(3/2)*sqrt(1 + 2/(b*x))/3 - sqrt(b)*sqrt(1 + 2/(b*x))/(3*x)","A",0
614,1,224,0,6.103588," ","integrate(1/x**(7/2)/(b*x+2)**(1/2),x)","- \frac{2 b^{\frac{17}{2}} x^{4} \sqrt{1 + \frac{2}{b x}}}{15 b^{6} x^{4} + 60 b^{5} x^{3} + 60 b^{4} x^{2}} - \frac{6 b^{\frac{15}{2}} x^{3} \sqrt{1 + \frac{2}{b x}}}{15 b^{6} x^{4} + 60 b^{5} x^{3} + 60 b^{4} x^{2}} - \frac{3 b^{\frac{13}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{15 b^{6} x^{4} + 60 b^{5} x^{3} + 60 b^{4} x^{2}} - \frac{4 b^{\frac{11}{2}} x \sqrt{1 + \frac{2}{b x}}}{15 b^{6} x^{4} + 60 b^{5} x^{3} + 60 b^{4} x^{2}} - \frac{12 b^{\frac{9}{2}} \sqrt{1 + \frac{2}{b x}}}{15 b^{6} x^{4} + 60 b^{5} x^{3} + 60 b^{4} x^{2}}"," ",0,"-2*b**(17/2)*x**4*sqrt(1 + 2/(b*x))/(15*b**6*x**4 + 60*b**5*x**3 + 60*b**4*x**2) - 6*b**(15/2)*x**3*sqrt(1 + 2/(b*x))/(15*b**6*x**4 + 60*b**5*x**3 + 60*b**4*x**2) - 3*b**(13/2)*x**2*sqrt(1 + 2/(b*x))/(15*b**6*x**4 + 60*b**5*x**3 + 60*b**4*x**2) - 4*b**(11/2)*x*sqrt(1 + 2/(b*x))/(15*b**6*x**4 + 60*b**5*x**3 + 60*b**4*x**2) - 12*b**(9/2)*sqrt(1 + 2/(b*x))/(15*b**6*x**4 + 60*b**5*x**3 + 60*b**4*x**2)","B",0
615,1,374,0,15.993104," ","integrate(1/x**(9/2)/(b*x+2)**(1/2),x)","\frac{2 b^{\frac{31}{2}} x^{6} \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}} + \frac{10 b^{\frac{29}{2}} x^{5} \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}} + \frac{15 b^{\frac{27}{2}} x^{4} \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}} + \frac{5 b^{\frac{25}{2}} x^{3} \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}} - \frac{10 b^{\frac{23}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}} - \frac{36 b^{\frac{21}{2}} x \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}} - \frac{40 b^{\frac{19}{2}} \sqrt{1 + \frac{2}{b x}}}{35 b^{12} x^{6} + 210 b^{11} x^{5} + 420 b^{10} x^{4} + 280 b^{9} x^{3}}"," ",0,"2*b**(31/2)*x**6*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3) + 10*b**(29/2)*x**5*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3) + 15*b**(27/2)*x**4*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3) + 5*b**(25/2)*x**3*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3) - 10*b**(23/2)*x**2*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3) - 36*b**(21/2)*x*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3) - 40*b**(19/2)*sqrt(1 + 2/(b*x))/(35*b**12*x**6 + 210*b**11*x**5 + 420*b**10*x**4 + 280*b**9*x**3)","B",0
616,1,80,0,7.099116," ","integrate(x**(5/2)/(b*x+2)**(3/2),x)","\frac{x^{\frac{5}{2}}}{2 b \sqrt{b x + 2}} - \frac{5 x^{\frac{3}{2}}}{2 b^{2} \sqrt{b x + 2}} - \frac{15 \sqrt{x}}{b^{3} \sqrt{b x + 2}} + \frac{15 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{7}{2}}}"," ",0,"x**(5/2)/(2*b*sqrt(b*x + 2)) - 5*x**(3/2)/(2*b**2*sqrt(b*x + 2)) - 15*sqrt(x)/(b**3*sqrt(b*x + 2)) + 15*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(7/2)","A",0
617,1,58,0,3.064880," ","integrate(x**(3/2)/(b*x+2)**(3/2),x)","\frac{x^{\frac{3}{2}}}{b \sqrt{b x + 2}} + \frac{6 \sqrt{x}}{b^{2} \sqrt{b x + 2}} - \frac{6 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}}"," ",0,"x**(3/2)/(b*sqrt(b*x + 2)) + 6*sqrt(x)/(b**2*sqrt(b*x + 2)) - 6*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2)","A",0
618,1,41,0,1.564603," ","integrate(x**(1/2)/(b*x+2)**(3/2),x)","- \frac{2 \sqrt{x}}{b \sqrt{b x + 2}} + \frac{2 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}}"," ",0,"-2*sqrt(x)/(b*sqrt(b*x + 2)) + 2*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2)","A",0
619,1,15,0,0.862000," ","integrate(1/(b*x+2)**(3/2)/x**(1/2),x)","\frac{1}{\sqrt{b} \sqrt{1 + \frac{2}{b x}}}"," ",0,"1/(sqrt(b)*sqrt(1 + 2/(b*x)))","A",0
620,1,34,0,1.543042," ","integrate(1/x**(3/2)/(b*x+2)**(3/2),x)","- \frac{\sqrt{b}}{\sqrt{1 + \frac{2}{b x}}} - \frac{1}{\sqrt{b} x \sqrt{1 + \frac{2}{b x}}}"," ",0,"-sqrt(b)/sqrt(1 + 2/(b*x)) - 1/(sqrt(b)*x*sqrt(1 + 2/(b*x)))","A",0
621,1,170,0,3.856680," ","integrate(1/x**(5/2)/(b*x+2)**(3/2),x)","\frac{2 b^{\frac{15}{2}} x^{3} \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{3} + 12 b^{5} x^{2} + 12 b^{4} x} + \frac{6 b^{\frac{13}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{3} + 12 b^{5} x^{2} + 12 b^{4} x} + \frac{3 b^{\frac{11}{2}} x \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{3} + 12 b^{5} x^{2} + 12 b^{4} x} - \frac{2 b^{\frac{9}{2}} \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{3} + 12 b^{5} x^{2} + 12 b^{4} x}"," ",0,"2*b**(15/2)*x**3*sqrt(1 + 2/(b*x))/(3*b**6*x**3 + 12*b**5*x**2 + 12*b**4*x) + 6*b**(13/2)*x**2*sqrt(1 + 2/(b*x))/(3*b**6*x**3 + 12*b**5*x**2 + 12*b**4*x) + 3*b**(11/2)*x*sqrt(1 + 2/(b*x))/(3*b**6*x**3 + 12*b**5*x**2 + 12*b**4*x) - 2*b**(9/2)*sqrt(1 + 2/(b*x))/(3*b**6*x**3 + 12*b**5*x**2 + 12*b**4*x)","B",0
622,1,269,0,10.971258," ","integrate(1/x**(7/2)/(b*x+2)**(3/2),x)","- \frac{2 b^{\frac{29}{2}} x^{5} \sqrt{1 + \frac{2}{b x}}}{5 b^{12} x^{5} + 30 b^{11} x^{4} + 60 b^{10} x^{3} + 40 b^{9} x^{2}} - \frac{10 b^{\frac{27}{2}} x^{4} \sqrt{1 + \frac{2}{b x}}}{5 b^{12} x^{5} + 30 b^{11} x^{4} + 60 b^{10} x^{3} + 40 b^{9} x^{2}} - \frac{15 b^{\frac{25}{2}} x^{3} \sqrt{1 + \frac{2}{b x}}}{5 b^{12} x^{5} + 30 b^{11} x^{4} + 60 b^{10} x^{3} + 40 b^{9} x^{2}} - \frac{5 b^{\frac{23}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{5 b^{12} x^{5} + 30 b^{11} x^{4} + 60 b^{10} x^{3} + 40 b^{9} x^{2}} - \frac{4 b^{\frac{19}{2}} \sqrt{1 + \frac{2}{b x}}}{5 b^{12} x^{5} + 30 b^{11} x^{4} + 60 b^{10} x^{3} + 40 b^{9} x^{2}}"," ",0,"-2*b**(29/2)*x**5*sqrt(1 + 2/(b*x))/(5*b**12*x**5 + 30*b**11*x**4 + 60*b**10*x**3 + 40*b**9*x**2) - 10*b**(27/2)*x**4*sqrt(1 + 2/(b*x))/(5*b**12*x**5 + 30*b**11*x**4 + 60*b**10*x**3 + 40*b**9*x**2) - 15*b**(25/2)*x**3*sqrt(1 + 2/(b*x))/(5*b**12*x**5 + 30*b**11*x**4 + 60*b**10*x**3 + 40*b**9*x**2) - 5*b**(23/2)*x**2*sqrt(1 + 2/(b*x))/(5*b**12*x**5 + 30*b**11*x**4 + 60*b**10*x**3 + 40*b**9*x**2) - 4*b**(19/2)*sqrt(1 + 2/(b*x))/(5*b**12*x**5 + 30*b**11*x**4 + 60*b**10*x**3 + 40*b**9*x**2)","B",0
623,1,308,0,6.617080," ","integrate(x**(5/2)/(b*x+2)**(5/2),x)","\frac{3 b^{\frac{23}{2}} x^{15}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x + 2} + 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x + 2}} + \frac{40 b^{\frac{21}{2}} x^{14}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x + 2} + 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x + 2}} + \frac{60 b^{\frac{19}{2}} x^{13}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x + 2} + 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x + 2}} - \frac{30 b^{10} x^{\frac{27}{2}} \sqrt{b x + 2} \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x + 2} + 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x + 2}} - \frac{60 b^{9} x^{\frac{25}{2}} \sqrt{b x + 2} \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x + 2} + 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x + 2}}"," ",0,"3*b**(23/2)*x**15/(3*b**(27/2)*x**(27/2)*sqrt(b*x + 2) + 6*b**(25/2)*x**(25/2)*sqrt(b*x + 2)) + 40*b**(21/2)*x**14/(3*b**(27/2)*x**(27/2)*sqrt(b*x + 2) + 6*b**(25/2)*x**(25/2)*sqrt(b*x + 2)) + 60*b**(19/2)*x**13/(3*b**(27/2)*x**(27/2)*sqrt(b*x + 2) + 6*b**(25/2)*x**(25/2)*sqrt(b*x + 2)) - 30*b**10*x**(27/2)*sqrt(b*x + 2)*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(27/2)*x**(27/2)*sqrt(b*x + 2) + 6*b**(25/2)*x**(25/2)*sqrt(b*x + 2)) - 60*b**9*x**(25/2)*sqrt(b*x + 2)*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(27/2)*x**(27/2)*sqrt(b*x + 2) + 6*b**(25/2)*x**(25/2)*sqrt(b*x + 2))","B",0
624,1,257,0,3.577839," ","integrate(x**(3/2)/(b*x+2)**(5/2),x)","- \frac{8 b^{\frac{11}{2}} x^{8}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x + 2} + 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x + 2}} - \frac{12 b^{\frac{9}{2}} x^{7}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x + 2} + 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x + 2}} + \frac{6 b^{5} x^{\frac{15}{2}} \sqrt{b x + 2} \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x + 2} + 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x + 2}} + \frac{12 b^{4} x^{\frac{13}{2}} \sqrt{b x + 2} \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x + 2} + 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x + 2}}"," ",0,"-8*b**(11/2)*x**8/(3*b**(15/2)*x**(15/2)*sqrt(b*x + 2) + 6*b**(13/2)*x**(13/2)*sqrt(b*x + 2)) - 12*b**(9/2)*x**7/(3*b**(15/2)*x**(15/2)*sqrt(b*x + 2) + 6*b**(13/2)*x**(13/2)*sqrt(b*x + 2)) + 6*b**5*x**(15/2)*sqrt(b*x + 2)*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(15/2)*x**(15/2)*sqrt(b*x + 2) + 6*b**(13/2)*x**(13/2)*sqrt(b*x + 2)) + 12*b**4*x**(13/2)*sqrt(b*x + 2)*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(15/2)*x**(15/2)*sqrt(b*x + 2) + 6*b**(13/2)*x**(13/2)*sqrt(b*x + 2))","B",0
625,1,27,0,1.403714," ","integrate(x**(1/2)/(b*x+2)**(5/2),x)","\frac{x^{\frac{3}{2}}}{3 b x \sqrt{b x + 2} + 6 \sqrt{b x + 2}}"," ",0,"x**(3/2)/(3*b*x*sqrt(b*x + 2) + 6*sqrt(b*x + 2))","A",0
626,1,75,0,1.841958," ","integrate(1/(b*x+2)**(5/2)/x**(1/2),x)","\frac{b x}{3 b^{\frac{3}{2}} x \sqrt{1 + \frac{2}{b x}} + 6 \sqrt{b} \sqrt{1 + \frac{2}{b x}}} + \frac{3}{3 b^{\frac{3}{2}} x \sqrt{1 + \frac{2}{b x}} + 6 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}"," ",0,"b*x/(3*b**(3/2)*x*sqrt(1 + 2/(b*x)) + 6*sqrt(b)*sqrt(1 + 2/(b*x))) + 3/(3*b**(3/2)*x*sqrt(1 + 2/(b*x)) + 6*sqrt(b)*sqrt(1 + 2/(b*x)))","B",0
627,1,117,0,3.888646," ","integrate(1/x**(3/2)/(b*x+2)**(5/2),x)","- \frac{2 b^{\frac{13}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{2} + 12 b^{5} x + 12 b^{4}} - \frac{6 b^{\frac{11}{2}} x \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{2} + 12 b^{5} x + 12 b^{4}} - \frac{3 b^{\frac{9}{2}} \sqrt{1 + \frac{2}{b x}}}{3 b^{6} x^{2} + 12 b^{5} x + 12 b^{4}}"," ",0,"-2*b**(13/2)*x**2*sqrt(1 + 2/(b*x))/(3*b**6*x**2 + 12*b**5*x + 12*b**4) - 6*b**(11/2)*x*sqrt(1 + 2/(b*x))/(3*b**6*x**2 + 12*b**5*x + 12*b**4) - 3*b**(9/2)*sqrt(1 + 2/(b*x))/(3*b**6*x**2 + 12*b**5*x + 12*b**4)","B",0
628,1,257,0,6.852692," ","integrate(1/x**(5/2)/(b*x+2)**(5/2),x)","\frac{2 b^{\frac{27}{2}} x^{4} \sqrt{1 + \frac{2}{b x}}}{3 b^{12} x^{4} + 18 b^{11} x^{3} + 36 b^{10} x^{2} + 24 b^{9} x} + \frac{10 b^{\frac{25}{2}} x^{3} \sqrt{1 + \frac{2}{b x}}}{3 b^{12} x^{4} + 18 b^{11} x^{3} + 36 b^{10} x^{2} + 24 b^{9} x} + \frac{15 b^{\frac{23}{2}} x^{2} \sqrt{1 + \frac{2}{b x}}}{3 b^{12} x^{4} + 18 b^{11} x^{3} + 36 b^{10} x^{2} + 24 b^{9} x} + \frac{5 b^{\frac{21}{2}} x \sqrt{1 + \frac{2}{b x}}}{3 b^{12} x^{4} + 18 b^{11} x^{3} + 36 b^{10} x^{2} + 24 b^{9} x} - \frac{2 b^{\frac{19}{2}} \sqrt{1 + \frac{2}{b x}}}{3 b^{12} x^{4} + 18 b^{11} x^{3} + 36 b^{10} x^{2} + 24 b^{9} x}"," ",0,"2*b**(27/2)*x**4*sqrt(1 + 2/(b*x))/(3*b**12*x**4 + 18*b**11*x**3 + 36*b**10*x**2 + 24*b**9*x) + 10*b**(25/2)*x**3*sqrt(1 + 2/(b*x))/(3*b**12*x**4 + 18*b**11*x**3 + 36*b**10*x**2 + 24*b**9*x) + 15*b**(23/2)*x**2*sqrt(1 + 2/(b*x))/(3*b**12*x**4 + 18*b**11*x**3 + 36*b**10*x**2 + 24*b**9*x) + 5*b**(21/2)*x*sqrt(1 + 2/(b*x))/(3*b**12*x**4 + 18*b**11*x**3 + 36*b**10*x**2 + 24*b**9*x) - 2*b**(19/2)*sqrt(1 + 2/(b*x))/(3*b**12*x**4 + 18*b**11*x**3 + 36*b**10*x**2 + 24*b**9*x)","B",0
629,1,206,0,7.510970," ","integrate(x**(5/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \frac{i x^{\frac{7}{2}}}{3 \sqrt{b x - 2}} - \frac{i x^{\frac{5}{2}}}{6 b \sqrt{b x - 2}} - \frac{5 i x^{\frac{3}{2}}}{6 b^{2} \sqrt{b x - 2}} + \frac{5 i \sqrt{x}}{b^{3} \sqrt{b x - 2}} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{7}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{x^{\frac{7}{2}}}{3 \sqrt{- b x + 2}} + \frac{x^{\frac{5}{2}}}{6 b \sqrt{- b x + 2}} + \frac{5 x^{\frac{3}{2}}}{6 b^{2} \sqrt{- b x + 2}} - \frac{5 \sqrt{x}}{b^{3} \sqrt{- b x + 2}} + \frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**(7/2)/(3*sqrt(b*x - 2)) - I*x**(5/2)/(6*b*sqrt(b*x - 2)) - 5*I*x**(3/2)/(6*b**2*sqrt(b*x - 2)) + 5*I*sqrt(x)/(b**3*sqrt(b*x - 2)) - 5*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(7/2), Abs(b*x)/2 > 1), (x**(7/2)/(3*sqrt(-b*x + 2)) + x**(5/2)/(6*b*sqrt(-b*x + 2)) + 5*x**(3/2)/(6*b**2*sqrt(-b*x + 2)) - 5*sqrt(x)/(b**3*sqrt(-b*x + 2)) + 5*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(7/2), True))","A",0
630,1,163,0,3.590877," ","integrate(x**(3/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \frac{i x^{\frac{5}{2}}}{2 \sqrt{b x - 2}} - \frac{i x^{\frac{3}{2}}}{2 b \sqrt{b x - 2}} + \frac{3 i \sqrt{x}}{b^{2} \sqrt{b x - 2}} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{x^{\frac{5}{2}}}{2 \sqrt{- b x + 2}} + \frac{x^{\frac{3}{2}}}{2 b \sqrt{- b x + 2}} - \frac{3 \sqrt{x}}{b^{2} \sqrt{- b x + 2}} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**(5/2)/(2*sqrt(b*x - 2)) - I*x**(3/2)/(2*b*sqrt(b*x - 2)) + 3*I*sqrt(x)/(b**2*sqrt(b*x - 2)) - 3*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2), Abs(b*x)/2 > 1), (x**(5/2)/(2*sqrt(-b*x + 2)) + x**(3/2)/(2*b*sqrt(-b*x + 2)) - 3*sqrt(x)/(b**2*sqrt(-b*x + 2)) + 3*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2), True))","A",0
631,1,121,0,1.966439," ","integrate(x**(1/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \frac{i x^{\frac{3}{2}}}{\sqrt{b x - 2}} + \frac{2 i \sqrt{x}}{b \sqrt{b x - 2}} - \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{x^{\frac{3}{2}}}{\sqrt{- b x + 2}} - \frac{2 \sqrt{x}}{b \sqrt{- b x + 2}} + \frac{2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x**(3/2)/sqrt(b*x - 2) + 2*I*sqrt(x)/(b*sqrt(b*x - 2)) - 2*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), Abs(b*x)/2 > 1), (x**(3/2)/sqrt(-b*x + 2) - 2*sqrt(x)/(b*sqrt(-b*x + 2)) + 2*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), True))","A",0
632,1,58,0,1.080696," ","integrate(1/x**(1/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), Abs(b*x)/2 > 1), (2*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/sqrt(b), True))","A",0
633,1,39,0,0.934258," ","integrate(1/x**(3/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \sqrt{b} \sqrt{-1 + \frac{2}{b x}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\- i \sqrt{b} \sqrt{1 - \frac{2}{b x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(b)*sqrt(-1 + 2/(b*x)), 2/Abs(b*x) > 1), (-I*sqrt(b)*sqrt(1 - 2/(b*x)), True))","A",0
634,1,139,0,1.957159," ","integrate(1/x**(5/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \frac{b^{\frac{3}{2}} \sqrt{-1 + \frac{2}{b x}}}{3} - \frac{\sqrt{b} \sqrt{-1 + \frac{2}{b x}}}{3 x} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{i b^{\frac{7}{2}} x^{2} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{2} x^{2} + 6 b x} - \frac{i b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}}}{- 3 b^{2} x^{2} + 6 b x} - \frac{2 i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{2} x^{2} + 6 b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**(3/2)*sqrt(-1 + 2/(b*x))/3 - sqrt(b)*sqrt(-1 + 2/(b*x))/(3*x), 2/Abs(b*x) > 1), (I*b**(7/2)*x**2*sqrt(1 - 2/(b*x))/(-3*b**2*x**2 + 6*b*x) - I*b**(5/2)*x*sqrt(1 - 2/(b*x))/(-3*b**2*x**2 + 6*b*x) - 2*I*b**(3/2)*sqrt(1 - 2/(b*x))/(-3*b**2*x**2 + 6*b*x), True))","A",0
635,1,173,0,7.025855," ","integrate(x**(5/2)/(-b*x+2)**(3/2),x)","\begin{cases} \frac{i x^{\frac{5}{2}}}{2 b \sqrt{b x - 2}} + \frac{5 i x^{\frac{3}{2}}}{2 b^{2} \sqrt{b x - 2}} - \frac{15 i \sqrt{x}}{b^{3} \sqrt{b x - 2}} + \frac{15 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{7}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{x^{\frac{5}{2}}}{2 b \sqrt{- b x + 2}} - \frac{5 x^{\frac{3}{2}}}{2 b^{2} \sqrt{- b x + 2}} + \frac{15 \sqrt{x}}{b^{3} \sqrt{- b x + 2}} - \frac{15 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**(5/2)/(2*b*sqrt(b*x - 2)) + 5*I*x**(3/2)/(2*b**2*sqrt(b*x - 2)) - 15*I*sqrt(x)/(b**3*sqrt(b*x - 2)) + 15*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(7/2), Abs(b*x)/2 > 1), (-x**(5/2)/(2*b*sqrt(-b*x + 2)) - 5*x**(3/2)/(2*b**2*sqrt(-b*x + 2)) + 15*sqrt(x)/(b**3*sqrt(-b*x + 2)) - 15*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(7/2), True))","A",0
636,1,128,0,3.199265," ","integrate(x**(3/2)/(-b*x+2)**(3/2),x)","\begin{cases} \frac{i x^{\frac{3}{2}}}{b \sqrt{b x - 2}} - \frac{6 i \sqrt{x}}{b^{2} \sqrt{b x - 2}} + \frac{6 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{x^{\frac{3}{2}}}{b \sqrt{- b x + 2}} + \frac{6 \sqrt{x}}{b^{2} \sqrt{- b x + 2}} - \frac{6 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**(3/2)/(b*sqrt(b*x - 2)) - 6*I*sqrt(x)/(b**2*sqrt(b*x - 2)) + 6*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2), Abs(b*x)/2 > 1), (-x**(3/2)/(b*sqrt(-b*x + 2)) + 6*sqrt(x)/(b**2*sqrt(-b*x + 2)) - 6*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(5/2), True))","A",0
637,1,92,0,1.692653," ","integrate(x**(1/2)/(-b*x+2)**(3/2),x)","\begin{cases} - \frac{2 i \sqrt{x}}{b \sqrt{b x - 2}} + \frac{2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{2 \sqrt{x}}{b \sqrt{- b x + 2}} - \frac{2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*sqrt(x)/(b*sqrt(b*x - 2)) + 2*I*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), Abs(b*x)/2 > 1), (2*sqrt(x)/(b*sqrt(-b*x + 2)) - 2*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b**(3/2), True))","A",0
638,1,39,0,0.931140," ","integrate(1/(-b*x+2)**(3/2)/x**(1/2),x)","\begin{cases} \frac{1}{\sqrt{b} \sqrt{-1 + \frac{2}{b x}}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\- \frac{i}{\sqrt{b} \sqrt{1 - \frac{2}{b x}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/(sqrt(b)*sqrt(-1 + 2/(b*x))), 2/Abs(b*x) > 1), (-I/(sqrt(b)*sqrt(1 - 2/(b*x))), True))","A",0
639,1,90,0,1.606046," ","integrate(1/x**(3/2)/(-b*x+2)**(3/2),x)","\begin{cases} \frac{\sqrt{b}}{\sqrt{-1 + \frac{2}{b x}}} - \frac{1}{\sqrt{b} x \sqrt{-1 + \frac{2}{b x}}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{i b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}}}{- b^{2} x + 2 b} - \frac{i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{- b^{2} x + 2 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(b)/sqrt(-1 + 2/(b*x)) - 1/(sqrt(b)*x*sqrt(-1 + 2/(b*x))), 2/Abs(b*x) > 1), (I*b**(5/2)*x*sqrt(1 - 2/(b*x))/(-b**2*x + 2*b) - I*b**(3/2)*sqrt(1 - 2/(b*x))/(-b**2*x + 2*b), True))","A",0
640,1,354,0,4.293051," ","integrate(1/x**(5/2)/(-b*x+2)**(3/2),x)","\begin{cases} \frac{2 b^{\frac{15}{2}} x^{3} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} - \frac{6 b^{\frac{13}{2}} x^{2} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} + \frac{3 b^{\frac{11}{2}} x \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} + \frac{2 b^{\frac{9}{2}} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{2 i b^{\frac{15}{2}} x^{3} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} - \frac{6 i b^{\frac{13}{2}} x^{2} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} + \frac{3 i b^{\frac{11}{2}} x \sqrt{1 - \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} + \frac{2 i b^{\frac{9}{2}} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{6} x^{3} + 12 b^{5} x^{2} - 12 b^{4} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(15/2)*x**3*sqrt(-1 + 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x) - 6*b**(13/2)*x**2*sqrt(-1 + 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x) + 3*b**(11/2)*x*sqrt(-1 + 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x) + 2*b**(9/2)*sqrt(-1 + 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x), 2/Abs(b*x) > 1), (2*I*b**(15/2)*x**3*sqrt(1 - 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x) - 6*I*b**(13/2)*x**2*sqrt(1 - 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x) + 3*I*b**(11/2)*x*sqrt(1 - 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x) + 2*I*b**(9/2)*sqrt(1 - 2/(b*x))/(-3*b**6*x**3 + 12*b**5*x**2 - 12*b**4*x), True))","B",0
641,1,753,0,6.803083," ","integrate(x**(5/2)/(-b*x+2)**(5/2),x)","\begin{cases} - \frac{3 i b^{\frac{23}{2}} x^{15}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} + \frac{40 i b^{\frac{21}{2}} x^{14}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} - \frac{60 i b^{\frac{19}{2}} x^{13}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} - \frac{30 i b^{10} x^{\frac{27}{2}} \sqrt{b x - 2} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} + \frac{15 \pi b^{10} x^{\frac{27}{2}} \sqrt{b x - 2}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} + \frac{60 i b^{9} x^{\frac{25}{2}} \sqrt{b x - 2} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} - \frac{30 \pi b^{9} x^{\frac{25}{2}} \sqrt{b x - 2}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{b x - 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{b x - 2}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\\frac{3 b^{\frac{23}{2}} x^{15}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{- b x + 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{- b x + 2}} - \frac{40 b^{\frac{21}{2}} x^{14}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{- b x + 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{- b x + 2}} + \frac{60 b^{\frac{19}{2}} x^{13}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{- b x + 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{- b x + 2}} + \frac{30 b^{10} x^{\frac{27}{2}} \sqrt{- b x + 2} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{- b x + 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{- b x + 2}} - \frac{60 b^{9} x^{\frac{25}{2}} \sqrt{- b x + 2} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{27}{2}} x^{\frac{27}{2}} \sqrt{- b x + 2} - 6 b^{\frac{25}{2}} x^{\frac{25}{2}} \sqrt{- b x + 2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*b**(23/2)*x**15/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)) + 40*I*b**(21/2)*x**14/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)) - 60*I*b**(19/2)*x**13/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)) - 30*I*b**10*x**(27/2)*sqrt(b*x - 2)*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)) + 15*pi*b**10*x**(27/2)*sqrt(b*x - 2)/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)) + 60*I*b**9*x**(25/2)*sqrt(b*x - 2)*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)) - 30*pi*b**9*x**(25/2)*sqrt(b*x - 2)/(3*b**(27/2)*x**(27/2)*sqrt(b*x - 2) - 6*b**(25/2)*x**(25/2)*sqrt(b*x - 2)), Abs(b*x)/2 > 1), (3*b**(23/2)*x**15/(3*b**(27/2)*x**(27/2)*sqrt(-b*x + 2) - 6*b**(25/2)*x**(25/2)*sqrt(-b*x + 2)) - 40*b**(21/2)*x**14/(3*b**(27/2)*x**(27/2)*sqrt(-b*x + 2) - 6*b**(25/2)*x**(25/2)*sqrt(-b*x + 2)) + 60*b**(19/2)*x**13/(3*b**(27/2)*x**(27/2)*sqrt(-b*x + 2) - 6*b**(25/2)*x**(25/2)*sqrt(-b*x + 2)) + 30*b**10*x**(27/2)*sqrt(-b*x + 2)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(27/2)*x**(27/2)*sqrt(-b*x + 2) - 6*b**(25/2)*x**(25/2)*sqrt(-b*x + 2)) - 60*b**9*x**(25/2)*sqrt(-b*x + 2)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(27/2)*x**(27/2)*sqrt(-b*x + 2) - 6*b**(25/2)*x**(25/2)*sqrt(-b*x + 2)), True))","B",0
642,1,649,0,3.700423," ","integrate(x**(3/2)/(-b*x+2)**(5/2),x)","\begin{cases} \frac{8 i b^{\frac{11}{2}} x^{8}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x - 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x - 2}} - \frac{12 i b^{\frac{9}{2}} x^{7}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x - 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x - 2}} - \frac{6 i b^{5} x^{\frac{15}{2}} \sqrt{b x - 2} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x - 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x - 2}} + \frac{3 \pi b^{5} x^{\frac{15}{2}} \sqrt{b x - 2}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x - 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x - 2}} + \frac{12 i b^{4} x^{\frac{13}{2}} \sqrt{b x - 2} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x - 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x - 2}} - \frac{6 \pi b^{4} x^{\frac{13}{2}} \sqrt{b x - 2}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{b x - 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{b x - 2}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{8 b^{\frac{11}{2}} x^{8}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{- b x + 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{- b x + 2}} + \frac{12 b^{\frac{9}{2}} x^{7}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{- b x + 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{- b x + 2}} + \frac{6 b^{5} x^{\frac{15}{2}} \sqrt{- b x + 2} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{- b x + 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{- b x + 2}} - \frac{12 b^{4} x^{\frac{13}{2}} \sqrt{- b x + 2} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{3 b^{\frac{15}{2}} x^{\frac{15}{2}} \sqrt{- b x + 2} - 6 b^{\frac{13}{2}} x^{\frac{13}{2}} \sqrt{- b x + 2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*I*b**(11/2)*x**8/(3*b**(15/2)*x**(15/2)*sqrt(b*x - 2) - 6*b**(13/2)*x**(13/2)*sqrt(b*x - 2)) - 12*I*b**(9/2)*x**7/(3*b**(15/2)*x**(15/2)*sqrt(b*x - 2) - 6*b**(13/2)*x**(13/2)*sqrt(b*x - 2)) - 6*I*b**5*x**(15/2)*sqrt(b*x - 2)*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(15/2)*x**(15/2)*sqrt(b*x - 2) - 6*b**(13/2)*x**(13/2)*sqrt(b*x - 2)) + 3*pi*b**5*x**(15/2)*sqrt(b*x - 2)/(3*b**(15/2)*x**(15/2)*sqrt(b*x - 2) - 6*b**(13/2)*x**(13/2)*sqrt(b*x - 2)) + 12*I*b**4*x**(13/2)*sqrt(b*x - 2)*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(15/2)*x**(15/2)*sqrt(b*x - 2) - 6*b**(13/2)*x**(13/2)*sqrt(b*x - 2)) - 6*pi*b**4*x**(13/2)*sqrt(b*x - 2)/(3*b**(15/2)*x**(15/2)*sqrt(b*x - 2) - 6*b**(13/2)*x**(13/2)*sqrt(b*x - 2)), Abs(b*x)/2 > 1), (-8*b**(11/2)*x**8/(3*b**(15/2)*x**(15/2)*sqrt(-b*x + 2) - 6*b**(13/2)*x**(13/2)*sqrt(-b*x + 2)) + 12*b**(9/2)*x**7/(3*b**(15/2)*x**(15/2)*sqrt(-b*x + 2) - 6*b**(13/2)*x**(13/2)*sqrt(-b*x + 2)) + 6*b**5*x**(15/2)*sqrt(-b*x + 2)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(15/2)*x**(15/2)*sqrt(-b*x + 2) - 6*b**(13/2)*x**(13/2)*sqrt(-b*x + 2)) - 12*b**4*x**(13/2)*sqrt(-b*x + 2)*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/(3*b**(15/2)*x**(15/2)*sqrt(-b*x + 2) - 6*b**(13/2)*x**(13/2)*sqrt(-b*x + 2)), True))","B",0
643,1,65,0,1.457904," ","integrate(x**(1/2)/(-b*x+2)**(5/2),x)","\begin{cases} \frac{i x^{\frac{3}{2}}}{3 b x \sqrt{b x - 2} - 6 \sqrt{b x - 2}} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{x^{\frac{3}{2}}}{3 b x \sqrt{- b x + 2} - 6 \sqrt{- b x + 2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*x**(3/2)/(3*b*x*sqrt(b*x - 2) - 6*sqrt(b*x - 2)), Abs(b*x)/2 > 1), (-x**(3/2)/(3*b*x*sqrt(-b*x + 2) - 6*sqrt(-b*x + 2)), True))","B",0
644,1,177,0,1.907815," ","integrate(1/(-b*x+2)**(5/2)/x**(1/2),x)","\begin{cases} \frac{i b x}{3 i b^{\frac{3}{2}} x \sqrt{-1 + \frac{2}{b x}} - 6 i \sqrt{b} \sqrt{-1 + \frac{2}{b x}}} - \frac{3 i}{3 i b^{\frac{3}{2}} x \sqrt{-1 + \frac{2}{b x}} - 6 i \sqrt{b} \sqrt{-1 + \frac{2}{b x}}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{b^{2} x}{3 i b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}} - 6 i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}} - \frac{3 b}{3 i b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}} - 6 i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b*x/(3*I*b**(3/2)*x*sqrt(-1 + 2/(b*x)) - 6*I*sqrt(b)*sqrt(-1 + 2/(b*x))) - 3*I/(3*I*b**(3/2)*x*sqrt(-1 + 2/(b*x)) - 6*I*sqrt(b)*sqrt(-1 + 2/(b*x))), 2/Abs(b*x) > 1), (b**2*x/(3*I*b**(5/2)*x*sqrt(1 - 2/(b*x)) - 6*I*b**(3/2)*sqrt(1 - 2/(b*x))) - 3*b/(3*I*b**(5/2)*x*sqrt(1 - 2/(b*x)) - 6*I*b**(3/2)*sqrt(1 - 2/(b*x))), True))","C",0
645,1,243,0,3.995142," ","integrate(1/x**(3/2)/(-b*x+2)**(5/2),x)","\begin{cases} - \frac{2 b^{\frac{13}{2}} x^{2} \sqrt{-1 + \frac{2}{b x}}}{3 b^{6} x^{2} - 12 b^{5} x + 12 b^{4}} + \frac{6 b^{\frac{11}{2}} x \sqrt{-1 + \frac{2}{b x}}}{3 b^{6} x^{2} - 12 b^{5} x + 12 b^{4}} - \frac{3 b^{\frac{9}{2}} \sqrt{-1 + \frac{2}{b x}}}{3 b^{6} x^{2} - 12 b^{5} x + 12 b^{4}} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\- \frac{2 i b^{\frac{13}{2}} x^{2} \sqrt{1 - \frac{2}{b x}}}{3 b^{6} x^{2} - 12 b^{5} x + 12 b^{4}} + \frac{6 i b^{\frac{11}{2}} x \sqrt{1 - \frac{2}{b x}}}{3 b^{6} x^{2} - 12 b^{5} x + 12 b^{4}} - \frac{3 i b^{\frac{9}{2}} \sqrt{1 - \frac{2}{b x}}}{3 b^{6} x^{2} - 12 b^{5} x + 12 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*b**(13/2)*x**2*sqrt(-1 + 2/(b*x))/(3*b**6*x**2 - 12*b**5*x + 12*b**4) + 6*b**(11/2)*x*sqrt(-1 + 2/(b*x))/(3*b**6*x**2 - 12*b**5*x + 12*b**4) - 3*b**(9/2)*sqrt(-1 + 2/(b*x))/(3*b**6*x**2 - 12*b**5*x + 12*b**4), 2/Abs(b*x) > 1), (-2*I*b**(13/2)*x**2*sqrt(1 - 2/(b*x))/(3*b**6*x**2 - 12*b**5*x + 12*b**4) + 6*I*b**(11/2)*x*sqrt(1 - 2/(b*x))/(3*b**6*x**2 - 12*b**5*x + 12*b**4) - 3*I*b**(9/2)*sqrt(1 - 2/(b*x))/(3*b**6*x**2 - 12*b**5*x + 12*b**4), True))","B",0
646,1,529,0,12.398149," ","integrate(1/x**(5/2)/(-b*x+2)**(5/2),x)","\begin{cases} \frac{2 b^{\frac{27}{2}} x^{4} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} - \frac{10 b^{\frac{25}{2}} x^{3} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} + \frac{15 b^{\frac{23}{2}} x^{2} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} - \frac{5 b^{\frac{21}{2}} x \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} - \frac{2 b^{\frac{19}{2}} \sqrt{-1 + \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} & \text{for}\: \frac{2}{\left|{b x}\right|} > 1 \\\frac{2 i b^{\frac{27}{2}} x^{4} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} - \frac{10 i b^{\frac{25}{2}} x^{3} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} + \frac{15 i b^{\frac{23}{2}} x^{2} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} - \frac{5 i b^{\frac{21}{2}} x \sqrt{1 - \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} - \frac{2 i b^{\frac{19}{2}} \sqrt{1 - \frac{2}{b x}}}{- 3 b^{12} x^{4} + 18 b^{11} x^{3} - 36 b^{10} x^{2} + 24 b^{9} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(27/2)*x**4*sqrt(-1 + 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) - 10*b**(25/2)*x**3*sqrt(-1 + 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) + 15*b**(23/2)*x**2*sqrt(-1 + 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) - 5*b**(21/2)*x*sqrt(-1 + 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) - 2*b**(19/2)*sqrt(-1 + 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x), 2/Abs(b*x) > 1), (2*I*b**(27/2)*x**4*sqrt(1 - 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) - 10*I*b**(25/2)*x**3*sqrt(1 - 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) + 15*I*b**(23/2)*x**2*sqrt(1 - 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) - 5*I*b**(21/2)*x*sqrt(1 - 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x) - 2*I*b**(19/2)*sqrt(1 - 2/(b*x))/(-3*b**12*x**4 + 18*b**11*x**3 - 36*b**10*x**2 + 24*b**9*x), True))","B",0
647,1,54,0,1.646357," ","integrate(x**(1/2)/(1-x)**(1/2),x)","\begin{cases} - i \sqrt{x} \sqrt{x - 1} - i \operatorname{acosh}{\left(\sqrt{x} \right)} & \text{for}\: \left|{x}\right| > 1 \\\frac{x^{\frac{3}{2}}}{\sqrt{1 - x}} - \frac{\sqrt{x}}{\sqrt{1 - x}} + \operatorname{asin}{\left(\sqrt{x} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*sqrt(x)*sqrt(x - 1) - I*acosh(sqrt(x)), Abs(x) > 1), (x**(3/2)/sqrt(1 - x) - sqrt(x)/sqrt(1 - x) + asin(sqrt(x)), True))","A",0
648,1,20,0,0.971172," ","integrate(1/(1-x)**(1/2)/x**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\sqrt{x} \right)} & \text{for}\: \left|{x}\right| > 1 \\2 \operatorname{asin}{\left(\sqrt{x} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(x)), Abs(x) > 1), (2*asin(sqrt(x)), True))","A",0
649,1,42,0,1.060054," ","integrate(1/x**(1/2)/(-b*x+1)**(1/2),x)","\begin{cases} - \frac{2 i \operatorname{acosh}{\left(\sqrt{b} \sqrt{x} \right)}}{\sqrt{b}} & \text{for}\: \left|{b x}\right| > 1 \\\frac{2 \operatorname{asin}{\left(\sqrt{b} \sqrt{x} \right)}}{\sqrt{b}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(b)*sqrt(x))/sqrt(b), Abs(b*x) > 1), (2*asin(sqrt(b)*sqrt(x))/sqrt(b), True))","A",0
650,1,19,0,2.008919," ","integrate(x**(5/3)*(b*x+a),x)","\frac{3 a x^{\frac{8}{3}}}{8} + \frac{3 b x^{\frac{11}{3}}}{11}"," ",0,"3*a*x**(8/3)/8 + 3*b*x**(11/3)/11","A",0
651,1,19,0,1.303998," ","integrate(x**(4/3)*(b*x+a),x)","\frac{3 a x^{\frac{7}{3}}}{7} + \frac{3 b x^{\frac{10}{3}}}{10}"," ",0,"3*a*x**(7/3)/7 + 3*b*x**(10/3)/10","A",0
652,1,19,0,0.445570," ","integrate(x**(2/3)*(b*x+a),x)","\frac{3 a x^{\frac{5}{3}}}{5} + \frac{3 b x^{\frac{8}{3}}}{8}"," ",0,"3*a*x**(5/3)/5 + 3*b*x**(8/3)/8","A",0
653,1,19,0,1.519745," ","integrate(x**(1/3)*(b*x+a),x)","\frac{3 a x^{\frac{4}{3}}}{4} + \frac{3 b x^{\frac{7}{3}}}{7}"," ",0,"3*a*x**(4/3)/4 + 3*b*x**(7/3)/7","A",0
654,1,19,0,1.659383," ","integrate((b*x+a)/x**(1/3),x)","\frac{3 a x^{\frac{2}{3}}}{2} + \frac{3 b x^{\frac{5}{3}}}{5}"," ",0,"3*a*x**(2/3)/2 + 3*b*x**(5/3)/5","A",0
655,1,17,0,1.493835," ","integrate((b*x+a)/x**(2/3),x)","3 a \sqrt[3]{x} + \frac{3 b x^{\frac{4}{3}}}{4}"," ",0,"3*a*x**(1/3) + 3*b*x**(4/3)/4","A",0
656,1,17,0,0.386709," ","integrate((b*x+a)/x**(4/3),x)","- \frac{3 a}{\sqrt[3]{x}} + \frac{3 b x^{\frac{2}{3}}}{2}"," ",0,"-3*a/x**(1/3) + 3*b*x**(2/3)/2","A",0
657,1,17,0,0.451084," ","integrate((b*x+a)/x**(5/3),x)","- \frac{3 a}{2 x^{\frac{2}{3}}} + 3 b \sqrt[3]{x}"," ",0,"-3*a/(2*x**(2/3)) + 3*b*x**(1/3)","A",0
658,1,34,0,3.747868," ","integrate(x**(5/3)*(b*x+a)**2,x)","\frac{3 a^{2} x^{\frac{8}{3}}}{8} + \frac{6 a b x^{\frac{11}{3}}}{11} + \frac{3 b^{2} x^{\frac{14}{3}}}{14}"," ",0,"3*a**2*x**(8/3)/8 + 6*a*b*x**(11/3)/11 + 3*b**2*x**(14/3)/14","A",0
659,1,34,0,2.645912," ","integrate(x**(4/3)*(b*x+a)**2,x)","\frac{3 a^{2} x^{\frac{7}{3}}}{7} + \frac{3 a b x^{\frac{10}{3}}}{5} + \frac{3 b^{2} x^{\frac{13}{3}}}{13}"," ",0,"3*a**2*x**(7/3)/7 + 3*a*b*x**(10/3)/5 + 3*b**2*x**(13/3)/13","A",0
660,1,34,0,1.061842," ","integrate(x**(2/3)*(b*x+a)**2,x)","\frac{3 a^{2} x^{\frac{5}{3}}}{5} + \frac{3 a b x^{\frac{8}{3}}}{4} + \frac{3 b^{2} x^{\frac{11}{3}}}{11}"," ",0,"3*a**2*x**(5/3)/5 + 3*a*b*x**(8/3)/4 + 3*b**2*x**(11/3)/11","A",0
661,1,2633,0,2.218392," ","integrate(x**(1/3)*(b*x+a)**2,x)","\begin{cases} \frac{27 a^{\frac{34}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{27 a^{\frac{34}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{72 a^{\frac{31}{3}} b \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{81 a^{\frac{31}{3}} b \left(\frac{a}{b} + x\right)}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{60 a^{\frac{28}{3}} b^{2} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{81 a^{\frac{28}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{60 a^{\frac{25}{3}} b^{3} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{27 a^{\frac{25}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{135 a^{\frac{22}{3}} b^{4} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{132 a^{\frac{19}{3}} b^{5} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{42 a^{\frac{16}{3}} b^{6} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\- \frac{27 a^{\frac{34}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{27 a^{\frac{34}{3}}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{72 a^{\frac{31}{3}} b \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{81 a^{\frac{31}{3}} b \left(\frac{a}{b} + x\right)}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{60 a^{\frac{28}{3}} b^{2} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{81 a^{\frac{28}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{60 a^{\frac{25}{3}} b^{3} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{27 a^{\frac{25}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{135 a^{\frac{22}{3}} b^{4} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{132 a^{\frac{19}{3}} b^{5} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{42 a^{\frac{16}{3}} b^{6} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6}}{- 140 a^{8} b^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} + 420 a^{7} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 420 a^{6} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 140 a^{5} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((27*a**(34/3)*(-1 + b*(a/b + x)/a)**(1/3)*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 27*a**(34/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 72*a**(31/3)*b*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 81*a**(31/3)*b*(a/b + x)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 60*a**(28/3)*b**2*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**2*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 81*a**(28/3)*b**2*(a/b + x)**2/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 60*a**(25/3)*b**3*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**3*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 27*a**(25/3)*b**3*(a/b + x)**3/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 135*a**(22/3)*b**4*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**4*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 132*a**(19/3)*b**5*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**5*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 42*a**(16/3)*b**6*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**6*exp(2*I*pi/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)), Abs(b*(a/b + x)/a) > 1), (-27*a**(34/3)*(1 - b*(a/b + x)/a)**(1/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 27*a**(34/3)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 72*a**(31/3)*b*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 81*a**(31/3)*b*(a/b + x)/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 60*a**(28/3)*b**2*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**2/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 81*a**(28/3)*b**2*(a/b + x)**2/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 60*a**(25/3)*b**3*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**3/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 27*a**(25/3)*b**3*(a/b + x)**3/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 135*a**(22/3)*b**4*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**4/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) + 132*a**(19/3)*b**5*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**5/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)) - 42*a**(16/3)*b**6*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**6/(-140*a**8*b**(4/3)*exp(2*I*pi/3) + 420*a**7*b**(7/3)*(a/b + x)*exp(2*I*pi/3) - 420*a**6*b**(10/3)*(a/b + x)**2*exp(2*I*pi/3) + 140*a**5*b**(13/3)*(a/b + x)**3*exp(2*I*pi/3)), True))","C",0
662,1,1765,0,2.045125," ","integrate((b*x+a)**2/x**(1/3),x)","\begin{cases} - \frac{27 a^{\frac{32}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{27 a^{\frac{32}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{63 a^{\frac{29}{3}} b \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{81 a^{\frac{29}{3}} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{42 a^{\frac{26}{3}} b^{2} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{81 a^{\frac{26}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{18 a^{\frac{23}{3}} b^{3} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{27 a^{\frac{23}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{27 a^{\frac{20}{3}} b^{4} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{15 a^{\frac{17}{3}} b^{5} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{5}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\- \frac{27 a^{\frac{32}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{27 a^{\frac{32}{3}} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{63 a^{\frac{29}{3}} b \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{81 a^{\frac{29}{3}} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{42 a^{\frac{26}{3}} b^{2} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{81 a^{\frac{26}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{18 a^{\frac{23}{3}} b^{3} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{27 a^{\frac{23}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{27 a^{\frac{20}{3}} b^{4} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{15 a^{\frac{17}{3}} b^{5} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}}}{- 40 a^{8} b^{\frac{2}{3}} + 120 a^{7} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) - 120 a^{6} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} + 40 a^{5} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-27*a**(32/3)*(-1 + b*(a/b + x)/a)**(2/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 27*a**(32/3)*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 63*a**(29/3)*b*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 81*a**(29/3)*b*(a/b + x)*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 42*a**(26/3)*b**2*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**2/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 81*a**(26/3)*b**2*(a/b + x)**2*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 18*a**(23/3)*b**3*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**3/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 27*a**(23/3)*b**3*(a/b + x)**3*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 27*a**(20/3)*b**4*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**4/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 15*a**(17/3)*b**5*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**5/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3), Abs(b*(a/b + x)/a) > 1), (-27*a**(32/3)*(1 - b*(a/b + x)/a)**(2/3)*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 27*a**(32/3)*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 63*a**(29/3)*b*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 81*a**(29/3)*b*(a/b + x)*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 42*a**(26/3)*b**2*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**2*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 81*a**(26/3)*b**2*(a/b + x)**2*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 18*a**(23/3)*b**3*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**3*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 27*a**(23/3)*b**3*(a/b + x)**3*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) - 27*a**(20/3)*b**4*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**4*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3) + 15*a**(17/3)*b**5*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**5*exp(2*I*pi/3)/(-40*a**8*b**(2/3) + 120*a**7*b**(5/3)*(a/b + x) - 120*a**6*b**(8/3)*(a/b + x)**2 + 40*a**5*b**(11/3)*(a/b + x)**3), True))","C",0
663,1,1741,0,2.075494," ","integrate((b*x+a)**2/x**(2/3),x)","\begin{cases} - \frac{27 a^{\frac{31}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{27 a^{\frac{31}{3}} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{72 a^{\frac{28}{3}} b \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{81 a^{\frac{28}{3}} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{60 a^{\frac{25}{3}} b^{2} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{81 a^{\frac{25}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{18 a^{\frac{22}{3}} b^{3} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{27 a^{\frac{22}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{9 a^{\frac{19}{3}} b^{4} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{6 a^{\frac{16}{3}} b^{5} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\- \frac{27 a^{\frac{31}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{27 a^{\frac{31}{3}} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{72 a^{\frac{28}{3}} b \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{81 a^{\frac{28}{3}} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{60 a^{\frac{25}{3}} b^{2} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{81 a^{\frac{25}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{18 a^{\frac{22}{3}} b^{3} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{27 a^{\frac{22}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} - \frac{9 a^{\frac{19}{3}} b^{4} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} + \frac{6 a^{\frac{16}{3}} b^{5} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{- 14 a^{8} \sqrt[3]{b} + 42 a^{7} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) - 42 a^{6} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} + 14 a^{5} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-27*a**(31/3)*(-1 + b*(a/b + x)/a)**(1/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 27*a**(31/3)*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 72*a**(28/3)*b*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 81*a**(28/3)*b*(a/b + x)*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 60*a**(25/3)*b**2*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**2/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 81*a**(25/3)*b**2*(a/b + x)**2*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 18*a**(22/3)*b**3*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**3/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 27*a**(22/3)*b**3*(a/b + x)**3*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 9*a**(19/3)*b**4*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**4/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 6*a**(16/3)*b**5*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**5/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3), Abs(b*(a/b + x)/a) > 1), (-27*a**(31/3)*(1 - b*(a/b + x)/a)**(1/3)*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 27*a**(31/3)*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 72*a**(28/3)*b*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 81*a**(28/3)*b*(a/b + x)*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 60*a**(25/3)*b**2*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**2*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 81*a**(25/3)*b**2*(a/b + x)**2*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 18*a**(22/3)*b**3*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**3*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 27*a**(22/3)*b**3*(a/b + x)**3*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) - 9*a**(19/3)*b**4*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**4*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3) + 6*a**(16/3)*b**5*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**5*exp(I*pi/3)/(-14*a**8*b**(1/3) + 42*a**7*b**(4/3)*(a/b + x) - 42*a**6*b**(7/3)*(a/b + x)**2 + 14*a**5*b**(10/3)*(a/b + x)**3), True))","C",0
664,1,1826,0,2.089671," ","integrate((b*x+a)**2/x**(4/3),x)","\begin{cases} - \frac{27 a^{\frac{29}{3}} \sqrt[3]{b} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{27 a^{\frac{29}{3}} \sqrt[3]{b}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{63 a^{\frac{26}{3}} b^{\frac{4}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{81 a^{\frac{26}{3}} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{42 a^{\frac{23}{3}} b^{\frac{7}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{81 a^{\frac{23}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{3 a^{\frac{20}{3}} b^{\frac{10}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{27 a^{\frac{20}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{3 a^{\frac{17}{3}} b^{\frac{13}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\\frac{27 a^{\frac{29}{3}} \sqrt[3]{b} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{27 a^{\frac{29}{3}} \sqrt[3]{b}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{63 a^{\frac{26}{3}} b^{\frac{4}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{81 a^{\frac{26}{3}} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right)}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{42 a^{\frac{23}{3}} b^{\frac{7}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{81 a^{\frac{23}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{3 a^{\frac{20}{3}} b^{\frac{10}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} + \frac{27 a^{\frac{20}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} - \frac{3 a^{\frac{17}{3}} b^{\frac{13}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4}}{- 5 a^{8} e^{\frac{i \pi}{3}} + 15 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} - 15 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} + 5 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-27*a**(29/3)*b**(1/3)*(-1 + b*(a/b + x)/a)**(2/3)*exp(I*pi/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 27*a**(29/3)*b**(1/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 63*a**(26/3)*b**(4/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)*exp(I*pi/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 81*a**(26/3)*b**(4/3)*(a/b + x)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 42*a**(23/3)*b**(7/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**2*exp(I*pi/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 81*a**(23/3)*b**(7/3)*(a/b + x)**2/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 3*a**(20/3)*b**(10/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**3*exp(I*pi/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 27*a**(20/3)*b**(10/3)*(a/b + x)**3/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 3*a**(17/3)*b**(13/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**4*exp(I*pi/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)), Abs(b*(a/b + x)/a) > 1), (27*a**(29/3)*b**(1/3)*(1 - b*(a/b + x)/a)**(2/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 27*a**(29/3)*b**(1/3)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 63*a**(26/3)*b**(4/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 81*a**(26/3)*b**(4/3)*(a/b + x)/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 42*a**(23/3)*b**(7/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**2/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 81*a**(23/3)*b**(7/3)*(a/b + x)**2/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 3*a**(20/3)*b**(10/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**3/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) + 27*a**(20/3)*b**(10/3)*(a/b + x)**3/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)) - 3*a**(17/3)*b**(13/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**4/(-5*a**8*exp(I*pi/3) + 15*a**7*b*(a/b + x)*exp(I*pi/3) - 15*a**6*b**2*(a/b + x)**2*exp(I*pi/3) + 5*a**5*b**3*(a/b + x)**3*exp(I*pi/3)), True))","C",0
665,1,1957,0,2.063434," ","integrate((b*x+a)**2/x**(5/3),x)","\begin{cases} - \frac{27 a^{\frac{28}{3}} b^{\frac{2}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} e^{\frac{2 i \pi}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{27 a^{\frac{28}{3}} b^{\frac{2}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{72 a^{\frac{25}{3}} b^{\frac{5}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{81 a^{\frac{25}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{60 a^{\frac{22}{3}} b^{\frac{8}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{81 a^{\frac{22}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{12 a^{\frac{19}{3}} b^{\frac{11}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{27 a^{\frac{19}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{3 a^{\frac{16}{3}} b^{\frac{14}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\\frac{27 a^{\frac{28}{3}} b^{\frac{2}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{27 a^{\frac{28}{3}} b^{\frac{2}{3}}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{72 a^{\frac{25}{3}} b^{\frac{5}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{81 a^{\frac{25}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right)}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{60 a^{\frac{22}{3}} b^{\frac{8}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{81 a^{\frac{22}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{12 a^{\frac{19}{3}} b^{\frac{11}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} + \frac{27 a^{\frac{19}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} - \frac{3 a^{\frac{16}{3}} b^{\frac{14}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4}}{- 4 a^{8} e^{\frac{2 i \pi}{3}} + 12 a^{7} b \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} - 12 a^{6} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} + 4 a^{5} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-27*a**(28/3)*b**(2/3)*(-1 + b*(a/b + x)/a)**(1/3)*exp(2*I*pi/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 27*a**(28/3)*b**(2/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 72*a**(25/3)*b**(5/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)*exp(2*I*pi/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 81*a**(25/3)*b**(5/3)*(a/b + x)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 60*a**(22/3)*b**(8/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**2*exp(2*I*pi/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 81*a**(22/3)*b**(8/3)*(a/b + x)**2/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 12*a**(19/3)*b**(11/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**3*exp(2*I*pi/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 27*a**(19/3)*b**(11/3)*(a/b + x)**3/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 3*a**(16/3)*b**(14/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**4*exp(2*I*pi/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)), Abs(b*(a/b + x)/a) > 1), (27*a**(28/3)*b**(2/3)*(1 - b*(a/b + x)/a)**(1/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 27*a**(28/3)*b**(2/3)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 72*a**(25/3)*b**(5/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 81*a**(25/3)*b**(5/3)*(a/b + x)/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 60*a**(22/3)*b**(8/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**2/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 81*a**(22/3)*b**(8/3)*(a/b + x)**2/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 12*a**(19/3)*b**(11/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**3/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) + 27*a**(19/3)*b**(11/3)*(a/b + x)**3/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)) - 3*a**(16/3)*b**(14/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**4/(-4*a**8*exp(2*I*pi/3) + 12*a**7*b*(a/b + x)*exp(2*I*pi/3) - 12*a**6*b**2*(a/b + x)**2*exp(2*I*pi/3) + 4*a**5*b**3*(a/b + x)**3*exp(2*I*pi/3)), True))","C",0
666,1,49,0,6.393478," ","integrate(x**(5/3)*(b*x+a)**3,x)","\frac{3 a^{3} x^{\frac{8}{3}}}{8} + \frac{9 a^{2} b x^{\frac{11}{3}}}{11} + \frac{9 a b^{2} x^{\frac{14}{3}}}{14} + \frac{3 b^{3} x^{\frac{17}{3}}}{17}"," ",0,"3*a**3*x**(8/3)/8 + 9*a**2*b*x**(11/3)/11 + 9*a*b**2*x**(14/3)/14 + 3*b**3*x**(17/3)/17","A",0
667,1,49,0,4.551093," ","integrate(x**(4/3)*(b*x+a)**3,x)","\frac{3 a^{3} x^{\frac{7}{3}}}{7} + \frac{9 a^{2} b x^{\frac{10}{3}}}{10} + \frac{9 a b^{2} x^{\frac{13}{3}}}{13} + \frac{3 b^{3} x^{\frac{16}{3}}}{16}"," ",0,"3*a**3*x**(7/3)/7 + 9*a**2*b*x**(10/3)/10 + 9*a*b**2*x**(13/3)/13 + 3*b**3*x**(16/3)/16","A",0
668,1,49,0,2.186630," ","integrate(x**(2/3)*(b*x+a)**3,x)","\frac{3 a^{3} x^{\frac{5}{3}}}{5} + \frac{9 a^{2} b x^{\frac{8}{3}}}{8} + \frac{9 a b^{2} x^{\frac{11}{3}}}{11} + \frac{3 b^{3} x^{\frac{14}{3}}}{14}"," ",0,"3*a**3*x**(5/3)/5 + 9*a**2*b*x**(8/3)/8 + 9*a*b**2*x**(11/3)/11 + 3*b**3*x**(14/3)/14","A",0
669,1,5012,0,3.223455," ","integrate(x**(1/3)*(b*x+a)**3,x)","\begin{cases} - \frac{243 a^{\frac{73}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{243 a^{\frac{73}{3}} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{1377 a^{\frac{70}{3}} b \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{1458 a^{\frac{70}{3}} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{3213 a^{\frac{67}{3}} b^{2} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{3645 a^{\frac{67}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{3927 a^{\frac{64}{3}} b^{3} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{4860 a^{\frac{64}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{2163 a^{\frac{61}{3}} b^{4} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{3645 a^{\frac{61}{3}} b^{4} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{1827 a^{\frac{58}{3}} b^{5} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{1458 a^{\frac{58}{3}} b^{5} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{6573 a^{\frac{55}{3}} b^{6} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{243 a^{\frac{55}{3}} b^{6} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{8787 a^{\frac{52}{3}} b^{7} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{7}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{6498 a^{\frac{49}{3}} b^{8} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{8}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{2562 a^{\frac{46}{3}} b^{9} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{9}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{420 a^{\frac{43}{3}} b^{10} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{10}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\- \frac{243 a^{\frac{73}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{243 a^{\frac{73}{3}} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{1377 a^{\frac{70}{3}} b \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{1458 a^{\frac{70}{3}} b \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{3213 a^{\frac{67}{3}} b^{2} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{3645 a^{\frac{67}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{3927 a^{\frac{64}{3}} b^{3} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{4860 a^{\frac{64}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{2163 a^{\frac{61}{3}} b^{4} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{3645 a^{\frac{61}{3}} b^{4} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{1827 a^{\frac{58}{3}} b^{5} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{1458 a^{\frac{58}{3}} b^{5} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{6573 a^{\frac{55}{3}} b^{6} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{243 a^{\frac{55}{3}} b^{6} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{8787 a^{\frac{52}{3}} b^{7} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{7} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{6498 a^{\frac{49}{3}} b^{8} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{8} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} - \frac{2562 a^{\frac{46}{3}} b^{9} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{9} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} + \frac{420 a^{\frac{43}{3}} b^{10} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{10} e^{\frac{i \pi}{3}}}{1820 a^{20} b^{\frac{4}{3}} - 10920 a^{19} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right) + 27300 a^{18} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{2} - 36400 a^{17} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{3} + 27300 a^{16} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{4} - 10920 a^{15} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{5} + 1820 a^{14} b^{\frac{22}{3}} \left(\frac{a}{b} + x\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-243*a**(73/3)*(-1 + b*(a/b + x)/a)**(1/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 243*a**(73/3)*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 1377*a**(70/3)*b*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 1458*a**(70/3)*b*(a/b + x)*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 3213*a**(67/3)*b**2*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**2/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 3645*a**(67/3)*b**2*(a/b + x)**2*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 3927*a**(64/3)*b**3*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**3/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 4860*a**(64/3)*b**3*(a/b + x)**3*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 2163*a**(61/3)*b**4*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**4/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 3645*a**(61/3)*b**4*(a/b + x)**4*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 1827*a**(58/3)*b**5*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**5/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 1458*a**(58/3)*b**5*(a/b + x)**5*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 6573*a**(55/3)*b**6*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**6/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 243*a**(55/3)*b**6*(a/b + x)**6*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 8787*a**(52/3)*b**7*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**7/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 6498*a**(49/3)*b**8*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**8/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 2562*a**(46/3)*b**9*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**9/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 420*a**(43/3)*b**10*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**10/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6), Abs(b*(a/b + x)/a) > 1), (-243*a**(73/3)*(1 - b*(a/b + x)/a)**(1/3)*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 243*a**(73/3)*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 1377*a**(70/3)*b*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 1458*a**(70/3)*b*(a/b + x)*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 3213*a**(67/3)*b**2*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**2*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 3645*a**(67/3)*b**2*(a/b + x)**2*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 3927*a**(64/3)*b**3*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**3*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 4860*a**(64/3)*b**3*(a/b + x)**3*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 2163*a**(61/3)*b**4*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**4*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 3645*a**(61/3)*b**4*(a/b + x)**4*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 1827*a**(58/3)*b**5*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**5*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 1458*a**(58/3)*b**5*(a/b + x)**5*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 6573*a**(55/3)*b**6*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**6*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 243*a**(55/3)*b**6*(a/b + x)**6*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 8787*a**(52/3)*b**7*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**7*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 6498*a**(49/3)*b**8*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**8*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) - 2562*a**(46/3)*b**9*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**9*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6) + 420*a**(43/3)*b**10*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**10*exp(I*pi/3)/(1820*a**20*b**(4/3) - 10920*a**19*b**(7/3)*(a/b + x) + 27300*a**18*b**(10/3)*(a/b + x)**2 - 36400*a**17*b**(13/3)*(a/b + x)**3 + 27300*a**16*b**(16/3)*(a/b + x)**4 - 10920*a**15*b**(19/3)*(a/b + x)**5 + 1820*a**14*b**(22/3)*(a/b + x)**6), True))","C",0
670,1,6246,0,3.191221," ","integrate((b*x+a)**3/x**(1/3),x)","\begin{cases} \frac{243 a^{\frac{71}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{71}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1296 a^{\frac{68}{3}} b \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{68}{3}} b \left(\frac{a}{b} + x\right)}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{2808 a^{\frac{65}{3}} b^{2} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{65}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{3120 a^{\frac{62}{3}} b^{3} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{4860 a^{\frac{62}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{1710 a^{\frac{59}{3}} b^{4} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{59}{3}} b^{4} \left(\frac{a}{b} + x\right)^{4}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{72 a^{\frac{56}{3}} b^{5} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{56}{3}} b^{5} \left(\frac{a}{b} + x\right)^{5}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1104 a^{\frac{53}{3}} b^{6} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{53}{3}} b^{6} \left(\frac{a}{b} + x\right)^{6}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{1152 a^{\frac{50}{3}} b^{7} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{7} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{585 a^{\frac{47}{3}} b^{8} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{8} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{120 a^{\frac{44}{3}} b^{9} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{9} e^{\frac{i \pi}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\- \frac{243 a^{\frac{71}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{71}{3}}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{1296 a^{\frac{68}{3}} b \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{68}{3}} b \left(\frac{a}{b} + x\right)}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{2808 a^{\frac{65}{3}} b^{2} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{65}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{3120 a^{\frac{62}{3}} b^{3} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{4860 a^{\frac{62}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1710 a^{\frac{59}{3}} b^{4} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{3645 a^{\frac{59}{3}} b^{4} \left(\frac{a}{b} + x\right)^{4}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{72 a^{\frac{56}{3}} b^{5} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{5}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1458 a^{\frac{56}{3}} b^{5} \left(\frac{a}{b} + x\right)^{5}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{1104 a^{\frac{53}{3}} b^{6} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{6}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{243 a^{\frac{53}{3}} b^{6} \left(\frac{a}{b} + x\right)^{6}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{1152 a^{\frac{50}{3}} b^{7} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{7}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} + \frac{585 a^{\frac{47}{3}} b^{8} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{8}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} - \frac{120 a^{\frac{44}{3}} b^{9} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{9}}{440 a^{20} b^{\frac{2}{3}} e^{\frac{i \pi}{3}} - 2640 a^{19} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}} + 6600 a^{18} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}} - 8800 a^{17} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}} + 6600 a^{16} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}} - 2640 a^{15} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}} + 440 a^{14} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((243*a**(71/3)*(-1 + b*(a/b + x)/a)**(2/3)*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 243*a**(71/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1296*a**(68/3)*b*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1458*a**(68/3)*b*(a/b + x)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 2808*a**(65/3)*b**2*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**2*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 3645*a**(65/3)*b**2*(a/b + x)**2/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 3120*a**(62/3)*b**3*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**3*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 4860*a**(62/3)*b**3*(a/b + x)**3/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 1710*a**(59/3)*b**4*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**4*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 3645*a**(59/3)*b**4*(a/b + x)**4/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 72*a**(56/3)*b**5*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**5*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1458*a**(56/3)*b**5*(a/b + x)**5/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1104*a**(53/3)*b**6*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**6*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 243*a**(53/3)*b**6*(a/b + x)**6/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 1152*a**(50/3)*b**7*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**7*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 585*a**(47/3)*b**8*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**8*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 120*a**(44/3)*b**9*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**9*exp(I*pi/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)), Abs(b*(a/b + x)/a) > 1), (-243*a**(71/3)*(1 - b*(a/b + x)/a)**(2/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 243*a**(71/3)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 1296*a**(68/3)*b*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1458*a**(68/3)*b*(a/b + x)/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 2808*a**(65/3)*b**2*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**2/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 3645*a**(65/3)*b**2*(a/b + x)**2/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 3120*a**(62/3)*b**3*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**3/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 4860*a**(62/3)*b**3*(a/b + x)**3/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1710*a**(59/3)*b**4*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**4/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 3645*a**(59/3)*b**4*(a/b + x)**4/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 72*a**(56/3)*b**5*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**5/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1458*a**(56/3)*b**5*(a/b + x)**5/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 1104*a**(53/3)*b**6*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**6/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 243*a**(53/3)*b**6*(a/b + x)**6/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 1152*a**(50/3)*b**7*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**7/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) + 585*a**(47/3)*b**8*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**8/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)) - 120*a**(44/3)*b**9*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**9/(440*a**20*b**(2/3)*exp(I*pi/3) - 2640*a**19*b**(5/3)*(a/b + x)*exp(I*pi/3) + 6600*a**18*b**(8/3)*(a/b + x)**2*exp(I*pi/3) - 8800*a**17*b**(11/3)*(a/b + x)**3*exp(I*pi/3) + 6600*a**16*b**(14/3)*(a/b + x)**4*exp(I*pi/3) - 2640*a**15*b**(17/3)*(a/b + x)**5*exp(I*pi/3) + 440*a**14*b**(20/3)*(a/b + x)**6*exp(I*pi/3)), True))","C",0
671,1,6667,0,3.171302," ","integrate((b*x+a)**3/x**(2/3),x)","\begin{cases} \frac{243 a^{\frac{70}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{243 a^{\frac{70}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{1377 a^{\frac{67}{3}} b \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{1458 a^{\frac{67}{3}} b \left(\frac{a}{b} + x\right)}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{3213 a^{\frac{64}{3}} b^{2} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{3645 a^{\frac{64}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{3927 a^{\frac{61}{3}} b^{3} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{4860 a^{\frac{61}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{2583 a^{\frac{58}{3}} b^{4} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{3645 a^{\frac{58}{3}} b^{4} \left(\frac{a}{b} + x\right)^{4}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{693 a^{\frac{55}{3}} b^{5} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{1458 a^{\frac{55}{3}} b^{5} \left(\frac{a}{b} + x\right)^{5}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{273 a^{\frac{52}{3}} b^{6} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{243 a^{\frac{52}{3}} b^{6} \left(\frac{a}{b} + x\right)^{6}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{387 a^{\frac{49}{3}} b^{7} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{7} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{198 a^{\frac{46}{3}} b^{8} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{8} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{42 a^{\frac{43}{3}} b^{9} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{9} e^{\frac{2 i \pi}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\- \frac{243 a^{\frac{70}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{243 a^{\frac{70}{3}}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{1377 a^{\frac{67}{3}} b \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{1458 a^{\frac{67}{3}} b \left(\frac{a}{b} + x\right)}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{3213 a^{\frac{64}{3}} b^{2} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{3645 a^{\frac{64}{3}} b^{2} \left(\frac{a}{b} + x\right)^{2}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{3927 a^{\frac{61}{3}} b^{3} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{4860 a^{\frac{61}{3}} b^{3} \left(\frac{a}{b} + x\right)^{3}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{2583 a^{\frac{58}{3}} b^{4} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{3645 a^{\frac{58}{3}} b^{4} \left(\frac{a}{b} + x\right)^{4}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{693 a^{\frac{55}{3}} b^{5} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{1458 a^{\frac{55}{3}} b^{5} \left(\frac{a}{b} + x\right)^{5}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{273 a^{\frac{52}{3}} b^{6} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{243 a^{\frac{52}{3}} b^{6} \left(\frac{a}{b} + x\right)^{6}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{387 a^{\frac{49}{3}} b^{7} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{7}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} + \frac{198 a^{\frac{46}{3}} b^{8} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{8}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} - \frac{42 a^{\frac{43}{3}} b^{9} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{9}}{140 a^{20} \sqrt[3]{b} e^{\frac{2 i \pi}{3}} - 840 a^{19} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}} + 2100 a^{18} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}} - 2800 a^{17} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}} + 2100 a^{16} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}} - 840 a^{15} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}} + 140 a^{14} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((243*a**(70/3)*(-1 + b*(a/b + x)/a)**(1/3)*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 243*a**(70/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 1377*a**(67/3)*b*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 1458*a**(67/3)*b*(a/b + x)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 3213*a**(64/3)*b**2*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**2*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 3645*a**(64/3)*b**2*(a/b + x)**2/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 3927*a**(61/3)*b**3*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**3*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 4860*a**(61/3)*b**3*(a/b + x)**3/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 2583*a**(58/3)*b**4*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**4*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 3645*a**(58/3)*b**4*(a/b + x)**4/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 693*a**(55/3)*b**5*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**5*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 1458*a**(55/3)*b**5*(a/b + x)**5/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 273*a**(52/3)*b**6*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**6*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 243*a**(52/3)*b**6*(a/b + x)**6/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 387*a**(49/3)*b**7*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**7*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 198*a**(46/3)*b**8*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**8*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 42*a**(43/3)*b**9*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**9*exp(2*I*pi/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)), Abs(b*(a/b + x)/a) > 1), (-243*a**(70/3)*(1 - b*(a/b + x)/a)**(1/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 243*a**(70/3)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 1377*a**(67/3)*b*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 1458*a**(67/3)*b*(a/b + x)/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 3213*a**(64/3)*b**2*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**2/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 3645*a**(64/3)*b**2*(a/b + x)**2/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 3927*a**(61/3)*b**3*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**3/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 4860*a**(61/3)*b**3*(a/b + x)**3/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 2583*a**(58/3)*b**4*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**4/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 3645*a**(58/3)*b**4*(a/b + x)**4/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 693*a**(55/3)*b**5*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**5/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 1458*a**(55/3)*b**5*(a/b + x)**5/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 273*a**(52/3)*b**6*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**6/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 243*a**(52/3)*b**6*(a/b + x)**6/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 387*a**(49/3)*b**7*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**7/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) + 198*a**(46/3)*b**8*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**8/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)) - 42*a**(43/3)*b**9*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**9/(140*a**20*b**(1/3)*exp(2*I*pi/3) - 840*a**19*b**(4/3)*(a/b + x)*exp(2*I*pi/3) + 2100*a**18*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3) - 2800*a**17*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3) + 2100*a**16*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3) - 840*a**15*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3) + 140*a**14*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)), True))","C",0
672,1,4004,0,3.260939," ","integrate((b*x+a)**3/x**(4/3),x)","\begin{cases} \frac{243 a^{\frac{68}{3}} \sqrt[3]{b} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{68}{3}} \sqrt[3]{b} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{1296 a^{\frac{65}{3}} b^{\frac{4}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{65}{3}} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{2808 a^{\frac{62}{3}} b^{\frac{7}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{62}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3120 a^{\frac{59}{3}} b^{\frac{10}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{4860 a^{\frac{59}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1830 a^{\frac{56}{3}} b^{\frac{13}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{56}{3}} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{528 a^{\frac{53}{3}} b^{\frac{16}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{5}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{53}{3}} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{96 a^{\frac{50}{3}} b^{\frac{19}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{6}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{50}{3}} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{48 a^{\frac{47}{3}} b^{\frac{22}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{7}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{15 a^{\frac{44}{3}} b^{\frac{25}{3}} \left(-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{8}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\\frac{243 a^{\frac{68}{3}} \sqrt[3]{b} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{68}{3}} \sqrt[3]{b} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{1296 a^{\frac{65}{3}} b^{\frac{4}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{65}{3}} b^{\frac{4}{3}} \left(\frac{a}{b} + x\right) e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{2808 a^{\frac{62}{3}} b^{\frac{7}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{62}{3}} b^{\frac{7}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3120 a^{\frac{59}{3}} b^{\frac{10}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{4860 a^{\frac{59}{3}} b^{\frac{10}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1830 a^{\frac{56}{3}} b^{\frac{13}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{56}{3}} b^{\frac{13}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{528 a^{\frac{53}{3}} b^{\frac{16}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{53}{3}} b^{\frac{16}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{96 a^{\frac{50}{3}} b^{\frac{19}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{50}{3}} b^{\frac{19}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{48 a^{\frac{47}{3}} b^{\frac{22}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{7} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{15 a^{\frac{44}{3}} b^{\frac{25}{3}} \left(1 - \frac{b \left(\frac{a}{b} + x\right)}{a}\right)^{\frac{2}{3}} \left(\frac{a}{b} + x\right)^{8} e^{\frac{2 i \pi}{3}}}{40 a^{20} - 240 a^{19} b \left(\frac{a}{b} + x\right) + 600 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 800 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 600 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 240 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 40 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((243*a**(68/3)*b**(1/3)*(-1 + b*(a/b + x)/a)**(2/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 243*a**(68/3)*b**(1/3)*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 1296*a**(65/3)*b**(4/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 1458*a**(65/3)*b**(4/3)*(a/b + x)*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 2808*a**(62/3)*b**(7/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**2/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 3645*a**(62/3)*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 3120*a**(59/3)*b**(10/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**3/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 4860*a**(59/3)*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 1830*a**(56/3)*b**(13/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**4/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 3645*a**(56/3)*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 528*a**(53/3)*b**(16/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**5/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 1458*a**(53/3)*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 96*a**(50/3)*b**(19/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**6/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 243*a**(50/3)*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 48*a**(47/3)*b**(22/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**7/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 15*a**(44/3)*b**(25/3)*(-1 + b*(a/b + x)/a)**(2/3)*(a/b + x)**8/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6), Abs(b*(a/b + x)/a) > 1), (243*a**(68/3)*b**(1/3)*(1 - b*(a/b + x)/a)**(2/3)*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 243*a**(68/3)*b**(1/3)*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 1296*a**(65/3)*b**(4/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 1458*a**(65/3)*b**(4/3)*(a/b + x)*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 2808*a**(62/3)*b**(7/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**2*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 3645*a**(62/3)*b**(7/3)*(a/b + x)**2*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 3120*a**(59/3)*b**(10/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**3*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 4860*a**(59/3)*b**(10/3)*(a/b + x)**3*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 1830*a**(56/3)*b**(13/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**4*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 3645*a**(56/3)*b**(13/3)*(a/b + x)**4*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 528*a**(53/3)*b**(16/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**5*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 1458*a**(53/3)*b**(16/3)*(a/b + x)**5*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 96*a**(50/3)*b**(19/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**6*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 243*a**(50/3)*b**(19/3)*(a/b + x)**6*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) - 48*a**(47/3)*b**(22/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**7*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6) + 15*a**(44/3)*b**(25/3)*(1 - b*(a/b + x)/a)**(2/3)*(a/b + x)**8*exp(2*I*pi/3)/(40*a**20 - 240*a**19*b*(a/b + x) + 600*a**18*b**2*(a/b + x)**2 - 800*a**17*b**3*(a/b + x)**3 + 600*a**16*b**4*(a/b + x)**4 - 240*a**15*b**5*(a/b + x)**5 + 40*a**14*b**6*(a/b + x)**6), True))","C",0
673,1,3964,0,3.237817," ","integrate((b*x+a)**3/x**(5/3),x)","\begin{cases} \frac{243 a^{\frac{67}{3}} b^{\frac{2}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{67}{3}} b^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{1377 a^{\frac{64}{3}} b^{\frac{5}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{64}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{3213 a^{\frac{61}{3}} b^{\frac{8}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{61}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3927 a^{\frac{58}{3}} b^{\frac{11}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{4860 a^{\frac{58}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{2625 a^{\frac{55}{3}} b^{\frac{14}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{55}{3}} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{903 a^{\frac{52}{3}} b^{\frac{17}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{52}{3}} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{147 a^{\frac{49}{3}} b^{\frac{20}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{49}{3}} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{33 a^{\frac{46}{3}} b^{\frac{23}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{7}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{12 a^{\frac{43}{3}} b^{\frac{26}{3}} \sqrt[3]{-1 + \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{8}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} & \text{for}\: \left|{\frac{b \left(\frac{a}{b} + x\right)}{a}}\right| > 1 \\\frac{243 a^{\frac{67}{3}} b^{\frac{2}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{67}{3}} b^{\frac{2}{3}} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{1377 a^{\frac{64}{3}} b^{\frac{5}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{64}{3}} b^{\frac{5}{3}} \left(\frac{a}{b} + x\right) e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{3213 a^{\frac{61}{3}} b^{\frac{8}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{61}{3}} b^{\frac{8}{3}} \left(\frac{a}{b} + x\right)^{2} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3927 a^{\frac{58}{3}} b^{\frac{11}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{4860 a^{\frac{58}{3}} b^{\frac{11}{3}} \left(\frac{a}{b} + x\right)^{3} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{2625 a^{\frac{55}{3}} b^{\frac{14}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{3645 a^{\frac{55}{3}} b^{\frac{14}{3}} \left(\frac{a}{b} + x\right)^{4} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{903 a^{\frac{52}{3}} b^{\frac{17}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{1458 a^{\frac{52}{3}} b^{\frac{17}{3}} \left(\frac{a}{b} + x\right)^{5} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{147 a^{\frac{49}{3}} b^{\frac{20}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{243 a^{\frac{49}{3}} b^{\frac{20}{3}} \left(\frac{a}{b} + x\right)^{6} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} - \frac{33 a^{\frac{46}{3}} b^{\frac{23}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{7} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} + \frac{12 a^{\frac{43}{3}} b^{\frac{26}{3}} \sqrt[3]{1 - \frac{b \left(\frac{a}{b} + x\right)}{a}} \left(\frac{a}{b} + x\right)^{8} e^{\frac{i \pi}{3}}}{28 a^{20} - 168 a^{19} b \left(\frac{a}{b} + x\right) + 420 a^{18} b^{2} \left(\frac{a}{b} + x\right)^{2} - 560 a^{17} b^{3} \left(\frac{a}{b} + x\right)^{3} + 420 a^{16} b^{4} \left(\frac{a}{b} + x\right)^{4} - 168 a^{15} b^{5} \left(\frac{a}{b} + x\right)^{5} + 28 a^{14} b^{6} \left(\frac{a}{b} + x\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((243*a**(67/3)*b**(2/3)*(-1 + b*(a/b + x)/a)**(1/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 243*a**(67/3)*b**(2/3)*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 1377*a**(64/3)*b**(5/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 1458*a**(64/3)*b**(5/3)*(a/b + x)*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 3213*a**(61/3)*b**(8/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**2/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 3645*a**(61/3)*b**(8/3)*(a/b + x)**2*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 3927*a**(58/3)*b**(11/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**3/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 4860*a**(58/3)*b**(11/3)*(a/b + x)**3*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 2625*a**(55/3)*b**(14/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**4/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 3645*a**(55/3)*b**(14/3)*(a/b + x)**4*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 903*a**(52/3)*b**(17/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**5/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 1458*a**(52/3)*b**(17/3)*(a/b + x)**5*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 147*a**(49/3)*b**(20/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**6/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 243*a**(49/3)*b**(20/3)*(a/b + x)**6*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 33*a**(46/3)*b**(23/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**7/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 12*a**(43/3)*b**(26/3)*(-1 + b*(a/b + x)/a)**(1/3)*(a/b + x)**8/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6), Abs(b*(a/b + x)/a) > 1), (243*a**(67/3)*b**(2/3)*(1 - b*(a/b + x)/a)**(1/3)*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 243*a**(67/3)*b**(2/3)*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 1377*a**(64/3)*b**(5/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 1458*a**(64/3)*b**(5/3)*(a/b + x)*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 3213*a**(61/3)*b**(8/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**2*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 3645*a**(61/3)*b**(8/3)*(a/b + x)**2*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 3927*a**(58/3)*b**(11/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**3*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 4860*a**(58/3)*b**(11/3)*(a/b + x)**3*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 2625*a**(55/3)*b**(14/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**4*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 3645*a**(55/3)*b**(14/3)*(a/b + x)**4*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 903*a**(52/3)*b**(17/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**5*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 1458*a**(52/3)*b**(17/3)*(a/b + x)**5*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 147*a**(49/3)*b**(20/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**6*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 243*a**(49/3)*b**(20/3)*(a/b + x)**6*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) - 33*a**(46/3)*b**(23/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**7*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6) + 12*a**(43/3)*b**(26/3)*(1 - b*(a/b + x)/a)**(1/3)*(a/b + x)**8*exp(I*pi/3)/(28*a**20 - 168*a**19*b*(a/b + x) + 420*a**18*b**2*(a/b + x)**2 - 560*a**17*b**3*(a/b + x)**3 + 420*a**16*b**4*(a/b + x)**4 - 168*a**15*b**5*(a/b + x)**5 + 28*a**14*b**6*(a/b + x)**6), True))","C",0
674,1,241,0,47.121343," ","integrate(x**(5/3)/(b*x+a),x)","\begin{cases} \tilde{\infty} x^{\frac{5}{3}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{8}{3}}}{8 a} & \text{for}\: b = 0 \\\frac{3 x^{\frac{5}{3}}}{5 b} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{2}{3}} a^{\frac{5}{3}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{b^{4} \left(\frac{1}{b}\right)^{\frac{4}{3}}} + \frac{\left(-1\right)^{\frac{2}{3}} a^{\frac{5}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 b^{4} \left(\frac{1}{b}\right)^{\frac{4}{3}}} - \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} a^{\frac{5}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{b^{4} \left(\frac{1}{b}\right)^{\frac{4}{3}}} - \frac{3 a x^{\frac{2}{3}}}{2 b^{2}} + \frac{3 x^{\frac{5}{3}}}{5 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(5/3), Eq(a, 0) & Eq(b, 0)), (3*x**(8/3)/(8*a), Eq(b, 0)), (3*x**(5/3)/(5*b), Eq(a, 0)), (-(-1)**(2/3)*a**(5/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(b**4*(1/b)**(4/3)) + (-1)**(2/3)*a**(5/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*b**4*(1/b)**(4/3)) - (-1)**(2/3)*sqrt(3)*a**(5/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(b**4*(1/b)**(4/3)) - 3*a*x**(2/3)/(2*b**2) + 3*x**(5/3)/(5*b), True))","A",0
675,1,240,0,25.855316," ","integrate(x**(4/3)/(b*x+a),x)","\begin{cases} \tilde{\infty} x^{\frac{4}{3}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{7}{3}}}{7 a} & \text{for}\: b = 0 \\\frac{3 x^{\frac{4}{3}}}{4 b} & \text{for}\: a = 0 \\- \frac{\sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{b^{2}} + \frac{\sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 b^{2}} + \frac{\sqrt[3]{-1} \sqrt{3} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{b^{2}} - \frac{3 a \sqrt[3]{x}}{b^{2}} + \frac{3 x^{\frac{4}{3}}}{4 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(4/3), Eq(a, 0) & Eq(b, 0)), (3*x**(7/3)/(7*a), Eq(b, 0)), (3*x**(4/3)/(4*b), Eq(a, 0)), (-(-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/b**2 + (-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*b**2) + (-1)**(1/3)*sqrt(3)*a**(4/3)*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/b**2 - 3*a*x**(1/3)/b**2 + 3*x**(4/3)/(4*b), True))","A",0
676,1,228,0,9.084132," ","integrate(x**(2/3)/(b*x+a),x)","\begin{cases} \tilde{\infty} x^{\frac{2}{3}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{5}{3}}}{5 a} & \text{for}\: b = 0 \\\frac{3 x^{\frac{2}{3}}}{2 b} & \text{for}\: a = 0 \\\frac{\left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{b^{2} \sqrt[3]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 b^{2} \sqrt[3]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} a^{\frac{2}{3}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{b^{2} \sqrt[3]{\frac{1}{b}}} + \frac{3 x^{\frac{2}{3}}}{2 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(2/3), Eq(a, 0) & Eq(b, 0)), (3*x**(5/3)/(5*a), Eq(b, 0)), (3*x**(2/3)/(2*b), Eq(a, 0)), ((-1)**(2/3)*a**(2/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(b**2*(1/b)**(1/3)) - (-1)**(2/3)*a**(2/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*b**2*(1/b)**(1/3)) + (-1)**(2/3)*sqrt(3)*a**(2/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(b**2*(1/b)**(1/3)) + 3*x**(2/3)/(2*b), True))","A",0
677,1,219,0,6.097706," ","integrate(x**(1/3)/(b*x+a),x)","\begin{cases} \tilde{\infty} \sqrt[3]{x} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{4}{3}}}{4 a} & \text{for}\: b = 0 \\\frac{3 \sqrt[3]{x}}{b} & \text{for}\: a = 0 \\\frac{\sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{b} - \frac{\sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 b} - \frac{\sqrt[3]{-1} \sqrt{3} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{b} + \frac{3 \sqrt[3]{x}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**(1/3), Eq(a, 0) & Eq(b, 0)), (3*x**(4/3)/(4*a), Eq(b, 0)), (3*x**(1/3)/b, Eq(a, 0)), ((-1)**(1/3)*a**(1/3)*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/b - (-1)**(1/3)*a**(1/3)*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*b) - (-1)**(1/3)*sqrt(3)*a**(1/3)*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/b + 3*x**(1/3)/b, True))","A",0
678,1,212,0,7.412031," ","integrate(1/x**(1/3)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt[3]{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{2}{3}}}{2 a} & \text{for}\: b = 0 \\- \frac{3}{b \sqrt[3]{x}} & \text{for}\: a = 0 \\- \frac{\left(-1\right)^{\frac{2}{3}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{\sqrt[3]{a} b \sqrt[3]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{2}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 \sqrt[3]{a} b \sqrt[3]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{\sqrt[3]{a} b \sqrt[3]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(1/3), Eq(a, 0) & Eq(b, 0)), (3*x**(2/3)/(2*a), Eq(b, 0)), (-3/(b*x**(1/3)), Eq(a, 0)), (-(-1)**(2/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(a**(1/3)*b*(1/b)**(1/3)) + (-1)**(2/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*a**(1/3)*b*(1/b)**(1/3)) - (-1)**(2/3)*sqrt(3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(a**(1/3)*b*(1/b)**(1/3)), True))","A",0
679,1,212,0,11.347631," ","integrate(1/x**(2/3)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{2}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 \sqrt[3]{x}}{a} & \text{for}\: b = 0 \\- \frac{3}{2 b x^{\frac{2}{3}}} & \text{for}\: a = 0 \\- \frac{\sqrt[3]{-1} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{a^{\frac{2}{3}} b \left(\frac{1}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt[3]{-1} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 a^{\frac{2}{3}} b \left(\frac{1}{b}\right)^{\frac{2}{3}}} + \frac{\sqrt[3]{-1} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{a^{\frac{2}{3}} b \left(\frac{1}{b}\right)^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(2/3), Eq(a, 0) & Eq(b, 0)), (3*x**(1/3)/a, Eq(b, 0)), (-3/(2*b*x**(2/3)), Eq(a, 0)), (-(-1)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(a**(2/3)*b*(1/b)**(2/3)) + (-1)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*a**(2/3)*b*(1/b)**(2/3)) + (-1)**(1/3)*sqrt(3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(a**(2/3)*b*(1/b)**(2/3)), True))","A",0
680,1,218,0,25.291901," ","integrate(1/x**(4/3)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{4}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{4 b x^{\frac{4}{3}}} & \text{for}\: a = 0 \\- \frac{3}{a \sqrt[3]{x}} & \text{for}\: b = 0 \\- \frac{3}{a \sqrt[3]{x}} + \frac{\left(-1\right)^{\frac{2}{3}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}}} - \frac{\left(-1\right)^{\frac{2}{3}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}}} + \frac{\left(-1\right)^{\frac{2}{3}} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(4/3), Eq(a, 0) & Eq(b, 0)), (-3/(4*b*x**(4/3)), Eq(a, 0)), (-3/(a*x**(1/3)), Eq(b, 0)), (-3/(a*x**(1/3)) + (-1)**(2/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(a**(4/3)*(1/b)**(1/3)) - (-1)**(2/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*a**(4/3)*(1/b)**(1/3)) + (-1)**(2/3)*sqrt(3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(a**(4/3)*(1/b)**(1/3)), True))","A",0
681,1,221,0,34.964006," ","integrate(1/x**(5/3)/(b*x+a),x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{3}{2 a x^{\frac{2}{3}}} & \text{for}\: b = 0 \\- \frac{3}{5 b x^{\frac{5}{3}}} & \text{for}\: a = 0 \\- \frac{3}{2 a x^{\frac{2}{3}}} + \frac{\sqrt[3]{-1} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{a^{\frac{5}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt[3]{-1} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{2 a^{\frac{5}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}}} - \frac{\sqrt[3]{-1} \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{a^{\frac{5}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/3), Eq(a, 0) & Eq(b, 0)), (-3/(2*a*x**(2/3)), Eq(b, 0)), (-3/(5*b*x**(5/3)), Eq(a, 0)), (-3/(2*a*x**(2/3)) + (-1)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(a**(5/3)*(1/b)**(2/3)) - (-1)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(2*a**(5/3)*(1/b)**(2/3)) - (-1)**(1/3)*sqrt(3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(a**(5/3)*(1/b)**(2/3)), True))","A",0
682,-1,0,0,0.000000," ","integrate(x**(5/3)/(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
683,-1,0,0,0.000000," ","integrate(x**(4/3)/(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
684,1,787,0,106.983347," ","integrate(x**(2/3)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt[3]{x}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{5}{3}}}{5 a^{2}} & \text{for}\: b = 0 \\- \frac{3}{b^{2} \sqrt[3]{x}} & \text{for}\: a = 0 \\- \frac{3 \sqrt[3]{-1} \sqrt[3]{a} b x^{\frac{2}{3}} \sqrt[3]{\frac{1}{b}}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} + \frac{2 a \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} - \frac{a \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} + \frac{2 \sqrt{3} a \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} + \frac{2 a \log{\left(2 \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} + \frac{2 b x \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} - \frac{b x \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} + \frac{2 \sqrt{3} b x \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} + \frac{2 b x \log{\left(2 \right)}}{3 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} \sqrt[3]{\frac{1}{b}} + 3 \sqrt[3]{-1} \sqrt[3]{a} b^{3} x \sqrt[3]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(1/3), Eq(a, 0) & Eq(b, 0)), (3*x**(5/3)/(5*a**2), Eq(b, 0)), (-3/(b**2*x**(1/3)), Eq(a, 0)), (-3*(-1)**(1/3)*a**(1/3)*b*x**(2/3)*(1/b)**(1/3)/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) + 2*a*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) - a*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) + 2*sqrt(3)*a*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) + 2*a*log(2)/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) + 2*b*x*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) - b*x*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) + 2*sqrt(3)*b*x*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)) + 2*b*x*log(2)/(3*(-1)**(1/3)*a**(4/3)*b**2*(1/b)**(1/3) + 3*(-1)**(1/3)*a**(1/3)*b**3*x*(1/b)**(1/3)), True))","A",0
685,1,607,0,71.720160," ","integrate(x**(1/3)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{2}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{4}{3}}}{4 a^{2}} & \text{for}\: b = 0 \\- \frac{3}{2 b^{2} x^{\frac{2}{3}}} & \text{for}\: a = 0 \\- \frac{2 \sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{6 a^{2} b + 6 a b^{2} x} + \frac{\sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{6 a^{2} b + 6 a b^{2} x} + \frac{2 \sqrt[3]{-1} \sqrt{3} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{6 a^{2} b + 6 a b^{2} x} - \frac{2 \sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(2 \right)}}{6 a^{2} b + 6 a b^{2} x} - \frac{2 \sqrt[3]{-1} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{6 a^{2} b + 6 a b^{2} x} + \frac{\sqrt[3]{-1} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{6 a^{2} b + 6 a b^{2} x} + \frac{2 \sqrt[3]{-1} \sqrt{3} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{6 a^{2} b + 6 a b^{2} x} - \frac{2 \sqrt[3]{-1} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \log{\left(2 \right)}}{6 a^{2} b + 6 a b^{2} x} - \frac{6 a \sqrt[3]{x}}{6 a^{2} b + 6 a b^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(2/3), Eq(a, 0) & Eq(b, 0)), (3*x**(4/3)/(4*a**2), Eq(b, 0)), (-3/(2*b**2*x**(2/3)), Eq(a, 0)), (-2*(-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(6*a**2*b + 6*a*b**2*x) + (-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(6*a**2*b + 6*a*b**2*x) + 2*(-1)**(1/3)*sqrt(3)*a**(4/3)*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(6*a**2*b + 6*a*b**2*x) - 2*(-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(2)/(6*a**2*b + 6*a*b**2*x) - 2*(-1)**(1/3)*a**(1/3)*b*x*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(6*a**2*b + 6*a*b**2*x) + (-1)**(1/3)*a**(1/3)*b*x*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(6*a**2*b + 6*a*b**2*x) + 2*(-1)**(1/3)*sqrt(3)*a**(1/3)*b*x*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(6*a**2*b + 6*a*b**2*x) - 2*(-1)**(1/3)*a**(1/3)*b*x*(1/b)**(1/3)*log(2)/(6*a**2*b + 6*a*b**2*x) - 6*a*x**(1/3)/(6*a**2*b + 6*a*b**2*x), True))","A",0
686,1,774,0,79.660218," ","integrate(1/x**(1/3)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{4}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 x^{\frac{2}{3}}}{2 a^{2}} & \text{for}\: b = 0 \\- \frac{3}{4 b^{2} x^{\frac{4}{3}}} & \text{for}\: a = 0 \\\frac{6 \sqrt[3]{-1} \sqrt[3]{a} b x^{\frac{2}{3}} \sqrt[3]{\frac{1}{b}}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} + \frac{2 a \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} - \frac{a \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} + \frac{2 \sqrt{3} a \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} + \frac{2 a \log{\left(2 \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} + \frac{2 b x \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} - \frac{b x \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} + \frac{2 \sqrt{3} b x \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} + \frac{2 b x \log{\left(2 \right)}}{6 \sqrt[3]{-1} a^{\frac{7}{3}} b \sqrt[3]{\frac{1}{b}} + 6 \sqrt[3]{-1} a^{\frac{4}{3}} b^{2} x \sqrt[3]{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(4/3), Eq(a, 0) & Eq(b, 0)), (3*x**(2/3)/(2*a**2), Eq(b, 0)), (-3/(4*b**2*x**(4/3)), Eq(a, 0)), (6*(-1)**(1/3)*a**(1/3)*b*x**(2/3)*(1/b)**(1/3)/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) + 2*a*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) - a*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) + 2*sqrt(3)*a*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) + 2*a*log(2)/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) + 2*b*x*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) - b*x*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) + 2*sqrt(3)*b*x*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)) + 2*b*x*log(2)/(6*(-1)**(1/3)*a**(7/3)*b*(1/b)**(1/3) + 6*(-1)**(1/3)*a**(4/3)*b**2*x*(1/b)**(1/3)), True))","A",0
687,1,590,0,115.984895," ","integrate(1/x**(2/3)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty}}{x^{\frac{5}{3}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{3 \sqrt[3]{x}}{a^{2}} & \text{for}\: b = 0 \\- \frac{3}{5 b^{2} x^{\frac{5}{3}}} & \text{for}\: a = 0 \\- \frac{2 \sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{3 a^{3} + 3 a^{2} b x} + \frac{\sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{3 a^{3} + 3 a^{2} b x} + \frac{2 \sqrt[3]{-1} \sqrt{3} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{3 a^{3} + 3 a^{2} b x} - \frac{2 \sqrt[3]{-1} a^{\frac{4}{3}} \sqrt[3]{\frac{1}{b}} \log{\left(2 \right)}}{3 a^{3} + 3 a^{2} b x} - \frac{2 \sqrt[3]{-1} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sqrt[3]{x} \right)}}{3 a^{3} + 3 a^{2} b x} + \frac{\sqrt[3]{-1} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{x} \sqrt[3]{\frac{1}{b}} + 4 x^{\frac{2}{3}} \right)}}{3 a^{3} + 3 a^{2} b x} + \frac{2 \sqrt[3]{-1} \sqrt{3} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sqrt[3]{x}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{3 a^{3} + 3 a^{2} b x} - \frac{2 \sqrt[3]{-1} \sqrt[3]{a} b x \sqrt[3]{\frac{1}{b}} \log{\left(2 \right)}}{3 a^{3} + 3 a^{2} b x} + \frac{3 a \sqrt[3]{x}}{3 a^{3} + 3 a^{2} b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/x**(5/3), Eq(a, 0) & Eq(b, 0)), (3*x**(1/3)/a**2, Eq(b, 0)), (-3/(5*b**2*x**(5/3)), Eq(a, 0)), (-2*(-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(3*a**3 + 3*a**2*b*x) + (-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(3*a**3 + 3*a**2*b*x) + 2*(-1)**(1/3)*sqrt(3)*a**(4/3)*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(3*a**3 + 3*a**2*b*x) - 2*(-1)**(1/3)*a**(4/3)*(1/b)**(1/3)*log(2)/(3*a**3 + 3*a**2*b*x) - 2*(-1)**(1/3)*a**(1/3)*b*x*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + x**(1/3))/(3*a**3 + 3*a**2*b*x) + (-1)**(1/3)*a**(1/3)*b*x*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*x**(1/3)*(1/b)**(1/3) + 4*x**(2/3))/(3*a**3 + 3*a**2*b*x) + 2*(-1)**(1/3)*sqrt(3)*a**(1/3)*b*x*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*x**(1/3)/(3*a**(1/3)*(1/b)**(1/3)))/(3*a**3 + 3*a**2*b*x) - 2*(-1)**(1/3)*a**(1/3)*b*x*(1/b)**(1/3)*log(2)/(3*a**3 + 3*a**2*b*x) + 3*a*x**(1/3)/(3*a**3 + 3*a**2*b*x), True))","A",0
688,-1,0,0,0.000000," ","integrate(1/x**(4/3)/(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate(1/x**(5/3)/(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate(x**(5/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate(x**(4/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate(x**(2/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate(x**(1/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate(1/x**(1/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate(1/x**(2/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,-1,0,0,0.000000," ","integrate(1/x**(4/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate(1/x**(5/3)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,1,243,0,2.352470," ","integrate((1-x)**(1/4)/(1+x),x)","\frac{5 \sqrt[4]{-1} \sqrt[4]{x - 1} \Gamma\left(\frac{5}{4}\right)}{\Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt[4]{-2} e^{- \frac{i \pi}{4}} \log{\left(- \frac{2^{\frac{3}{4}} \sqrt[4]{x - 1} e^{\frac{i \pi}{4}}}{2} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{5 \left(-1\right)^{\frac{3}{4}} \sqrt[4]{2} e^{- \frac{i \pi}{4}} \log{\left(- \frac{2^{\frac{3}{4}} \sqrt[4]{x - 1} e^{\frac{3 i \pi}{4}}}{2} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} - \frac{5 \sqrt[4]{-2} e^{- \frac{i \pi}{4}} \log{\left(- \frac{2^{\frac{3}{4}} \sqrt[4]{x - 1} e^{\frac{5 i \pi}{4}}}{2} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \left(-1\right)^{\frac{3}{4}} \sqrt[4]{2} e^{- \frac{i \pi}{4}} \log{\left(- \frac{2^{\frac{3}{4}} \sqrt[4]{x - 1} e^{\frac{7 i \pi}{4}}}{2} + 1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)}"," ",0,"5*(-1)**(1/4)*(x - 1)**(1/4)*gamma(5/4)/gamma(9/4) + 5*(-2)**(1/4)*exp(-I*pi/4)*log(-2**(3/4)*(x - 1)**(1/4)*exp_polar(I*pi/4)/2 + 1)*gamma(5/4)/(4*gamma(9/4)) - 5*(-1)**(3/4)*2**(1/4)*exp(-I*pi/4)*log(-2**(3/4)*(x - 1)**(1/4)*exp_polar(3*I*pi/4)/2 + 1)*gamma(5/4)/(4*gamma(9/4)) - 5*(-2)**(1/4)*exp(-I*pi/4)*log(-2**(3/4)*(x - 1)**(1/4)*exp_polar(5*I*pi/4)/2 + 1)*gamma(5/4)/(4*gamma(9/4)) + 5*(-1)**(3/4)*2**(1/4)*exp(-I*pi/4)*log(-2**(3/4)*(x - 1)**(1/4)*exp_polar(7*I*pi/4)/2 + 1)*gamma(5/4)/(4*gamma(9/4))","C",0
699,1,9996,0,6.929245," ","integrate(x**m*(b*x+a)**10,x)","\begin{cases} - \frac{a^{10}}{10 x^{10}} - \frac{10 a^{9} b}{9 x^{9}} - \frac{45 a^{8} b^{2}}{8 x^{8}} - \frac{120 a^{7} b^{3}}{7 x^{7}} - \frac{35 a^{6} b^{4}}{x^{6}} - \frac{252 a^{5} b^{5}}{5 x^{5}} - \frac{105 a^{4} b^{6}}{2 x^{4}} - \frac{40 a^{3} b^{7}}{x^{3}} - \frac{45 a^{2} b^{8}}{2 x^{2}} - \frac{10 a b^{9}}{x} + b^{10} \log{\left(x \right)} & \text{for}\: m = -11 \\- \frac{a^{10}}{9 x^{9}} - \frac{5 a^{9} b}{4 x^{8}} - \frac{45 a^{8} b^{2}}{7 x^{7}} - \frac{20 a^{7} b^{3}}{x^{6}} - \frac{42 a^{6} b^{4}}{x^{5}} - \frac{63 a^{5} b^{5}}{x^{4}} - \frac{70 a^{4} b^{6}}{x^{3}} - \frac{60 a^{3} b^{7}}{x^{2}} - \frac{45 a^{2} b^{8}}{x} + 10 a b^{9} \log{\left(x \right)} + b^{10} x & \text{for}\: m = -10 \\- \frac{a^{10}}{8 x^{8}} - \frac{10 a^{9} b}{7 x^{7}} - \frac{15 a^{8} b^{2}}{2 x^{6}} - \frac{24 a^{7} b^{3}}{x^{5}} - \frac{105 a^{6} b^{4}}{2 x^{4}} - \frac{84 a^{5} b^{5}}{x^{3}} - \frac{105 a^{4} b^{6}}{x^{2}} - \frac{120 a^{3} b^{7}}{x} + 45 a^{2} b^{8} \log{\left(x \right)} + 10 a b^{9} x + \frac{b^{10} x^{2}}{2} & \text{for}\: m = -9 \\- \frac{a^{10}}{7 x^{7}} - \frac{5 a^{9} b}{3 x^{6}} - \frac{9 a^{8} b^{2}}{x^{5}} - \frac{30 a^{7} b^{3}}{x^{4}} - \frac{70 a^{6} b^{4}}{x^{3}} - \frac{126 a^{5} b^{5}}{x^{2}} - \frac{210 a^{4} b^{6}}{x} + 120 a^{3} b^{7} \log{\left(x \right)} + 45 a^{2} b^{8} x + 5 a b^{9} x^{2} + \frac{b^{10} x^{3}}{3} & \text{for}\: m = -8 \\- \frac{a^{10}}{6 x^{6}} - \frac{2 a^{9} b}{x^{5}} - \frac{45 a^{8} b^{2}}{4 x^{4}} - \frac{40 a^{7} b^{3}}{x^{3}} - \frac{105 a^{6} b^{4}}{x^{2}} - \frac{252 a^{5} b^{5}}{x} + 210 a^{4} b^{6} \log{\left(x \right)} + 120 a^{3} b^{7} x + \frac{45 a^{2} b^{8} x^{2}}{2} + \frac{10 a b^{9} x^{3}}{3} + \frac{b^{10} x^{4}}{4} & \text{for}\: m = -7 \\- \frac{a^{10}}{5 x^{5}} - \frac{5 a^{9} b}{2 x^{4}} - \frac{15 a^{8} b^{2}}{x^{3}} - \frac{60 a^{7} b^{3}}{x^{2}} - \frac{210 a^{6} b^{4}}{x} + 252 a^{5} b^{5} \log{\left(x \right)} + 210 a^{4} b^{6} x + 60 a^{3} b^{7} x^{2} + 15 a^{2} b^{8} x^{3} + \frac{5 a b^{9} x^{4}}{2} + \frac{b^{10} x^{5}}{5} & \text{for}\: m = -6 \\- \frac{a^{10}}{4 x^{4}} - \frac{10 a^{9} b}{3 x^{3}} - \frac{45 a^{8} b^{2}}{2 x^{2}} - \frac{120 a^{7} b^{3}}{x} + 210 a^{6} b^{4} \log{\left(x \right)} + 252 a^{5} b^{5} x + 105 a^{4} b^{6} x^{2} + 40 a^{3} b^{7} x^{3} + \frac{45 a^{2} b^{8} x^{4}}{4} + 2 a b^{9} x^{5} + \frac{b^{10} x^{6}}{6} & \text{for}\: m = -5 \\- \frac{a^{10}}{3 x^{3}} - \frac{5 a^{9} b}{x^{2}} - \frac{45 a^{8} b^{2}}{x} + 120 a^{7} b^{3} \log{\left(x \right)} + 210 a^{6} b^{4} x + 126 a^{5} b^{5} x^{2} + 70 a^{4} b^{6} x^{3} + 30 a^{3} b^{7} x^{4} + 9 a^{2} b^{8} x^{5} + \frac{5 a b^{9} x^{6}}{3} + \frac{b^{10} x^{7}}{7} & \text{for}\: m = -4 \\- \frac{a^{10}}{2 x^{2}} - \frac{10 a^{9} b}{x} + 45 a^{8} b^{2} \log{\left(x \right)} + 120 a^{7} b^{3} x + 105 a^{6} b^{4} x^{2} + 84 a^{5} b^{5} x^{3} + \frac{105 a^{4} b^{6} x^{4}}{2} + 24 a^{3} b^{7} x^{5} + \frac{15 a^{2} b^{8} x^{6}}{2} + \frac{10 a b^{9} x^{7}}{7} + \frac{b^{10} x^{8}}{8} & \text{for}\: m = -3 \\- \frac{a^{10}}{x} + 10 a^{9} b \log{\left(x \right)} + 45 a^{8} b^{2} x + 60 a^{7} b^{3} x^{2} + 70 a^{6} b^{4} x^{3} + 63 a^{5} b^{5} x^{4} + 42 a^{4} b^{6} x^{5} + 20 a^{3} b^{7} x^{6} + \frac{45 a^{2} b^{8} x^{7}}{7} + \frac{5 a b^{9} x^{8}}{4} + \frac{b^{10} x^{9}}{9} & \text{for}\: m = -2 \\a^{10} \log{\left(x \right)} + 10 a^{9} b x + \frac{45 a^{8} b^{2} x^{2}}{2} + 40 a^{7} b^{3} x^{3} + \frac{105 a^{6} b^{4} x^{4}}{2} + \frac{252 a^{5} b^{5} x^{5}}{5} + 35 a^{4} b^{6} x^{6} + \frac{120 a^{3} b^{7} x^{7}}{7} + \frac{45 a^{2} b^{8} x^{8}}{8} + \frac{10 a b^{9} x^{9}}{9} + \frac{b^{10} x^{10}}{10} & \text{for}\: m = -1 \\\frac{a^{10} m^{10} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{65 a^{10} m^{9} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1860 a^{10} m^{8} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{30810 a^{10} m^{7} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{326613 a^{10} m^{6} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{2310945 a^{10} m^{5} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{11028590 a^{10} m^{4} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{34967140 a^{10} m^{3} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{70290936 a^{10} m^{2} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{80627040 a^{10} m x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{39916800 a^{10} x x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{10 a^{9} b m^{10} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{640 a^{9} b m^{9} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{17970 a^{9} b m^{8} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{290760 a^{9} b m^{7} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{2992710 a^{9} b m^{6} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{20390160 a^{9} b m^{5} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{92615030 a^{9} b m^{4} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{274727240 a^{9} b m^{3} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{503126280 a^{9} b m^{2} x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{502927200 a^{9} b m x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{199584000 a^{9} b x^{2} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{45 a^{8} b^{2} m^{10} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{2835 a^{8} b^{2} m^{9} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{78120 a^{8} b^{2} m^{8} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1235790 a^{8} b^{2} m^{7} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{12376665 a^{8} b^{2} m^{6} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{81560115 a^{8} b^{2} m^{5} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{355598730 a^{8} b^{2} m^{4} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1003011660 a^{8} b^{2} m^{3} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1727578440 a^{8} b^{2} m^{2} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1608573600 a^{8} b^{2} m x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{598752000 a^{8} b^{2} x^{3} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{120 a^{7} b^{3} m^{10} x^{4} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} 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\frac{190200 a b^{9} m^{7} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1672230 a b^{9} m^{6} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{9653280 a b^{9} m^{5} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{36862550 a b^{9} m^{4} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{91331800 a b^{9} m^{3} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{139262760 a b^{9} m^{2} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{116552160 a b^{9} m x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{39916800 a b^{9} x^{10} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{b^{10} m^{10} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{55 b^{10} m^{9} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{1320 b^{10} m^{8} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{18150 b^{10} m^{7} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{157773 b^{10} m^{6} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{902055 b^{10} m^{5} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{3416930 b^{10} m^{4} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{8409500 b^{10} m^{3} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{12753576 b^{10} m^{2} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{10628640 b^{10} m x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} + \frac{3628800 b^{10} x^{11} x^{m}}{m^{11} + 66 m^{10} + 1925 m^{9} + 32670 m^{8} + 357423 m^{7} + 2637558 m^{6} + 13339535 m^{5} + 45995730 m^{4} + 105258076 m^{3} + 150917976 m^{2} + 120543840 m + 39916800} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**10/(10*x**10) - 10*a**9*b/(9*x**9) - 45*a**8*b**2/(8*x**8) - 120*a**7*b**3/(7*x**7) - 35*a**6*b**4/x**6 - 252*a**5*b**5/(5*x**5) - 105*a**4*b**6/(2*x**4) - 40*a**3*b**7/x**3 - 45*a**2*b**8/(2*x**2) - 10*a*b**9/x + b**10*log(x), Eq(m, -11)), (-a**10/(9*x**9) - 5*a**9*b/(4*x**8) - 45*a**8*b**2/(7*x**7) - 20*a**7*b**3/x**6 - 42*a**6*b**4/x**5 - 63*a**5*b**5/x**4 - 70*a**4*b**6/x**3 - 60*a**3*b**7/x**2 - 45*a**2*b**8/x + 10*a*b**9*log(x) + b**10*x, Eq(m, -10)), (-a**10/(8*x**8) - 10*a**9*b/(7*x**7) - 15*a**8*b**2/(2*x**6) - 24*a**7*b**3/x**5 - 105*a**6*b**4/(2*x**4) - 84*a**5*b**5/x**3 - 105*a**4*b**6/x**2 - 120*a**3*b**7/x + 45*a**2*b**8*log(x) + 10*a*b**9*x + b**10*x**2/2, Eq(m, -9)), (-a**10/(7*x**7) - 5*a**9*b/(3*x**6) - 9*a**8*b**2/x**5 - 30*a**7*b**3/x**4 - 70*a**6*b**4/x**3 - 126*a**5*b**5/x**2 - 210*a**4*b**6/x + 120*a**3*b**7*log(x) + 45*a**2*b**8*x + 5*a*b**9*x**2 + b**10*x**3/3, Eq(m, -8)), (-a**10/(6*x**6) - 2*a**9*b/x**5 - 45*a**8*b**2/(4*x**4) - 40*a**7*b**3/x**3 - 105*a**6*b**4/x**2 - 252*a**5*b**5/x + 210*a**4*b**6*log(x) + 120*a**3*b**7*x + 45*a**2*b**8*x**2/2 + 10*a*b**9*x**3/3 + b**10*x**4/4, Eq(m, -7)), (-a**10/(5*x**5) - 5*a**9*b/(2*x**4) - 15*a**8*b**2/x**3 - 60*a**7*b**3/x**2 - 210*a**6*b**4/x + 252*a**5*b**5*log(x) + 210*a**4*b**6*x + 60*a**3*b**7*x**2 + 15*a**2*b**8*x**3 + 5*a*b**9*x**4/2 + b**10*x**5/5, Eq(m, -6)), (-a**10/(4*x**4) - 10*a**9*b/(3*x**3) - 45*a**8*b**2/(2*x**2) - 120*a**7*b**3/x + 210*a**6*b**4*log(x) + 252*a**5*b**5*x + 105*a**4*b**6*x**2 + 40*a**3*b**7*x**3 + 45*a**2*b**8*x**4/4 + 2*a*b**9*x**5 + b**10*x**6/6, Eq(m, -5)), (-a**10/(3*x**3) - 5*a**9*b/x**2 - 45*a**8*b**2/x + 120*a**7*b**3*log(x) + 210*a**6*b**4*x + 126*a**5*b**5*x**2 + 70*a**4*b**6*x**3 + 30*a**3*b**7*x**4 + 9*a**2*b**8*x**5 + 5*a*b**9*x**6/3 + b**10*x**7/7, Eq(m, -4)), (-a**10/(2*x**2) - 10*a**9*b/x + 45*a**8*b**2*log(x) + 120*a**7*b**3*x + 105*a**6*b**4*x**2 + 84*a**5*b**5*x**3 + 105*a**4*b**6*x**4/2 + 24*a**3*b**7*x**5 + 15*a**2*b**8*x**6/2 + 10*a*b**9*x**7/7 + b**10*x**8/8, Eq(m, -3)), (-a**10/x + 10*a**9*b*log(x) + 45*a**8*b**2*x + 60*a**7*b**3*x**2 + 70*a**6*b**4*x**3 + 63*a**5*b**5*x**4 + 42*a**4*b**6*x**5 + 20*a**3*b**7*x**6 + 45*a**2*b**8*x**7/7 + 5*a*b**9*x**8/4 + b**10*x**9/9, Eq(m, -2)), (a**10*log(x) + 10*a**9*b*x + 45*a**8*b**2*x**2/2 + 40*a**7*b**3*x**3 + 105*a**6*b**4*x**4/2 + 252*a**5*b**5*x**5/5 + 35*a**4*b**6*x**6 + 120*a**3*b**7*x**7/7 + 45*a**2*b**8*x**8/8 + 10*a*b**9*x**9/9 + b**10*x**10/10, Eq(m, -1)), (a**10*m**10*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 65*a**10*m**9*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 1860*a**10*m**8*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 30810*a**10*m**7*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 326613*a**10*m**6*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 2310945*a**10*m**5*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 11028590*a**10*m**4*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 34967140*a**10*m**3*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 70290936*a**10*m**2*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 80627040*a**10*m*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 39916800*a**10*x*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 10*a**9*b*m**10*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 640*a**9*b*m**9*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 17970*a**9*b*m**8*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 290760*a**9*b*m**7*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 2992710*a**9*b*m**6*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 20390160*a**9*b*m**5*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 92615030*a**9*b*m**4*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 274727240*a**9*b*m**3*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 503126280*a**9*b*m**2*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 502927200*a**9*b*m*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 199584000*a**9*b*x**2*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 45*a**8*b**2*m**10*x**3*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 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150917976*m**2 + 120543840*m + 39916800) + 18150*b**10*m**7*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 157773*b**10*m**6*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 902055*b**10*m**5*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 3416930*b**10*m**4*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 8409500*b**10*m**3*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 12753576*b**10*m**2*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 10628640*b**10*m*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800) + 3628800*b**10*x**11*x**m/(m**11 + 66*m**10 + 1925*m**9 + 32670*m**8 + 357423*m**7 + 2637558*m**6 + 13339535*m**5 + 45995730*m**4 + 105258076*m**3 + 150917976*m**2 + 120543840*m + 39916800), True))","A",0
700,1,4257,0,3.336898," ","integrate(x**m*(b*x+a)**7,x)","\begin{cases} - \frac{a^{7}}{7 x^{7}} - \frac{7 a^{6} b}{6 x^{6}} - \frac{21 a^{5} b^{2}}{5 x^{5}} - \frac{35 a^{4} b^{3}}{4 x^{4}} - \frac{35 a^{3} b^{4}}{3 x^{3}} - \frac{21 a^{2} b^{5}}{2 x^{2}} - \frac{7 a b^{6}}{x} + b^{7} \log{\left(x \right)} & \text{for}\: m = -8 \\- \frac{a^{7}}{6 x^{6}} - \frac{7 a^{6} b}{5 x^{5}} - \frac{21 a^{5} b^{2}}{4 x^{4}} - \frac{35 a^{4} b^{3}}{3 x^{3}} - \frac{35 a^{3} b^{4}}{2 x^{2}} - \frac{21 a^{2} b^{5}}{x} + 7 a b^{6} \log{\left(x \right)} + b^{7} x & \text{for}\: m = -7 \\- \frac{a^{7}}{5 x^{5}} - \frac{7 a^{6} b}{4 x^{4}} - \frac{7 a^{5} b^{2}}{x^{3}} - \frac{35 a^{4} b^{3}}{2 x^{2}} - \frac{35 a^{3} b^{4}}{x} + 21 a^{2} b^{5} \log{\left(x \right)} + 7 a b^{6} x + \frac{b^{7} x^{2}}{2} & \text{for}\: m = -6 \\- \frac{a^{7}}{4 x^{4}} - \frac{7 a^{6} b}{3 x^{3}} - \frac{21 a^{5} b^{2}}{2 x^{2}} - \frac{35 a^{4} b^{3}}{x} + 35 a^{3} b^{4} \log{\left(x \right)} + 21 a^{2} b^{5} x + \frac{7 a b^{6} x^{2}}{2} + \frac{b^{7} x^{3}}{3} & \text{for}\: m = -5 \\- \frac{a^{7}}{3 x^{3}} - \frac{7 a^{6} b}{2 x^{2}} - \frac{21 a^{5} b^{2}}{x} + 35 a^{4} b^{3} \log{\left(x \right)} + 35 a^{3} b^{4} x + \frac{21 a^{2} b^{5} x^{2}}{2} + \frac{7 a b^{6} x^{3}}{3} + \frac{b^{7} x^{4}}{4} & \text{for}\: m = -4 \\- \frac{a^{7}}{2 x^{2}} - \frac{7 a^{6} b}{x} + 21 a^{5} b^{2} \log{\left(x \right)} + 35 a^{4} b^{3} x + \frac{35 a^{3} b^{4} x^{2}}{2} + 7 a^{2} b^{5} x^{3} + \frac{7 a b^{6} x^{4}}{4} + \frac{b^{7} x^{5}}{5} & \text{for}\: m = -3 \\- \frac{a^{7}}{x} + 7 a^{6} b \log{\left(x \right)} + 21 a^{5} b^{2} x + \frac{35 a^{4} b^{3} x^{2}}{2} + \frac{35 a^{3} b^{4} x^{3}}{3} + \frac{21 a^{2} b^{5} x^{4}}{4} + \frac{7 a b^{6} x^{5}}{5} + \frac{b^{7} x^{6}}{6} & \text{for}\: m = -2 \\a^{7} \log{\left(x \right)} + 7 a^{6} b x + \frac{21 a^{5} b^{2} x^{2}}{2} + \frac{35 a^{4} b^{3} x^{3}}{3} + \frac{35 a^{3} b^{4} x^{4}}{4} + \frac{21 a^{2} b^{5} x^{5}}{5} + \frac{7 a b^{6} x^{6}}{6} + \frac{b^{7} x^{7}}{7} & \text{for}\: m = -1 \\\frac{a^{7} m^{7} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35 a^{7} m^{6} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{511 a^{7} m^{5} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{4025 a^{7} m^{4} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{18424 a^{7} m^{3} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{48860 a^{7} m^{2} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{69264 a^{7} m x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 a^{7} x x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7 a^{6} b m^{7} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{238 a^{6} b m^{6} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{3346 a^{6} b m^{5} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{25060 a^{6} b m^{4} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{107023 a^{6} b m^{3} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{256942 a^{6} b m^{2} x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{312984 a^{6} b m x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{141120 a^{6} b x^{2} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{21 a^{5} b^{2} m^{7} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{693 a^{5} b^{2} m^{6} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{9387 a^{5} b^{2} m^{5} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{67095 a^{5} b^{2} m^{4} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{270144 a^{5} b^{2} m^{3} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{602532 a^{5} b^{2} m^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{673008 a^{5} b^{2} m x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{282240 a^{5} b^{2} x^{3} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35 a^{4} b^{3} m^{7} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1120 a^{4} b^{3} m^{6} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14630 a^{4} b^{3} m^{5} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{100240 a^{4} b^{3} m^{4} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{384755 a^{4} b^{3} m^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{815920 a^{4} b^{3} m^{2} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{870660 a^{4} b^{3} m x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{352800 a^{4} b^{3} x^{4} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{35 a^{3} b^{4} m^{7} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1085 a^{3} b^{4} m^{6} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13685 a^{3} b^{4} m^{5} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{90335 a^{3} b^{4} m^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{334040 a^{3} b^{4} m^{3} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{684740 a^{3} b^{4} m^{2} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{710640 a^{3} b^{4} m x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{282240 a^{3} b^{4} x^{5} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{21 a^{2} b^{5} m^{7} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{630 a^{2} b^{5} m^{6} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7686 a^{2} b^{5} m^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{49140 a^{2} b^{5} m^{4} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{176589 a^{2} b^{5} m^{3} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{353430 a^{2} b^{5} m^{2} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{360024 a^{2} b^{5} m x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{141120 a^{2} b^{5} x^{6} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{7 a b^{6} m^{7} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{203 a b^{6} m^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{2401 a b^{6} m^{5} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{14945 a b^{6} m^{4} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{52528 a b^{6} m^{3} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{103292 a b^{6} m^{2} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{103824 a b^{6} m x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{40320 a b^{6} x^{7} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{b^{7} m^{7} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{28 b^{7} m^{6} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{322 b^{7} m^{5} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{1960 b^{7} m^{4} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{6769 b^{7} m^{3} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13132 b^{7} m^{2} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{13068 b^{7} m x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} + \frac{5040 b^{7} x^{8} x^{m}}{m^{8} + 36 m^{7} + 546 m^{6} + 4536 m^{5} + 22449 m^{4} + 67284 m^{3} + 118124 m^{2} + 109584 m + 40320} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**7/(7*x**7) - 7*a**6*b/(6*x**6) - 21*a**5*b**2/(5*x**5) - 35*a**4*b**3/(4*x**4) - 35*a**3*b**4/(3*x**3) - 21*a**2*b**5/(2*x**2) - 7*a*b**6/x + b**7*log(x), Eq(m, -8)), (-a**7/(6*x**6) - 7*a**6*b/(5*x**5) - 21*a**5*b**2/(4*x**4) - 35*a**4*b**3/(3*x**3) - 35*a**3*b**4/(2*x**2) - 21*a**2*b**5/x + 7*a*b**6*log(x) + b**7*x, Eq(m, -7)), (-a**7/(5*x**5) - 7*a**6*b/(4*x**4) - 7*a**5*b**2/x**3 - 35*a**4*b**3/(2*x**2) - 35*a**3*b**4/x + 21*a**2*b**5*log(x) + 7*a*b**6*x + b**7*x**2/2, Eq(m, -6)), (-a**7/(4*x**4) - 7*a**6*b/(3*x**3) - 21*a**5*b**2/(2*x**2) - 35*a**4*b**3/x + 35*a**3*b**4*log(x) + 21*a**2*b**5*x + 7*a*b**6*x**2/2 + b**7*x**3/3, Eq(m, -5)), (-a**7/(3*x**3) - 7*a**6*b/(2*x**2) - 21*a**5*b**2/x + 35*a**4*b**3*log(x) + 35*a**3*b**4*x + 21*a**2*b**5*x**2/2 + 7*a*b**6*x**3/3 + b**7*x**4/4, Eq(m, -4)), (-a**7/(2*x**2) - 7*a**6*b/x + 21*a**5*b**2*log(x) + 35*a**4*b**3*x + 35*a**3*b**4*x**2/2 + 7*a**2*b**5*x**3 + 7*a*b**6*x**4/4 + b**7*x**5/5, Eq(m, -3)), (-a**7/x + 7*a**6*b*log(x) + 21*a**5*b**2*x + 35*a**4*b**3*x**2/2 + 35*a**3*b**4*x**3/3 + 21*a**2*b**5*x**4/4 + 7*a*b**6*x**5/5 + b**7*x**6/6, Eq(m, -2)), (a**7*log(x) + 7*a**6*b*x + 21*a**5*b**2*x**2/2 + 35*a**4*b**3*x**3/3 + 35*a**3*b**4*x**4/4 + 21*a**2*b**5*x**5/5 + 7*a*b**6*x**6/6 + b**7*x**7/7, Eq(m, -1)), (a**7*m**7*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35*a**7*m**6*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 511*a**7*m**5*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 4025*a**7*m**4*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 18424*a**7*m**3*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 48860*a**7*m**2*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 69264*a**7*m*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*a**7*x*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7*a**6*b*m**7*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 238*a**6*b*m**6*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 3346*a**6*b*m**5*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 25060*a**6*b*m**4*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 107023*a**6*b*m**3*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 256942*a**6*b*m**2*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 312984*a**6*b*m*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 141120*a**6*b*x**2*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 21*a**5*b**2*m**7*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 693*a**5*b**2*m**6*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 9387*a**5*b**2*m**5*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 67095*a**5*b**2*m**4*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 270144*a**5*b**2*m**3*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 602532*a**5*b**2*m**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 673008*a**5*b**2*m*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 282240*a**5*b**2*x**3*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35*a**4*b**3*m**7*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1120*a**4*b**3*m**6*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14630*a**4*b**3*m**5*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 100240*a**4*b**3*m**4*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 384755*a**4*b**3*m**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 815920*a**4*b**3*m**2*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 870660*a**4*b**3*m*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 352800*a**4*b**3*x**4*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 35*a**3*b**4*m**7*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1085*a**3*b**4*m**6*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13685*a**3*b**4*m**5*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 90335*a**3*b**4*m**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 334040*a**3*b**4*m**3*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 684740*a**3*b**4*m**2*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 710640*a**3*b**4*m*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 282240*a**3*b**4*x**5*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 21*a**2*b**5*m**7*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 630*a**2*b**5*m**6*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7686*a**2*b**5*m**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 49140*a**2*b**5*m**4*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 176589*a**2*b**5*m**3*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 353430*a**2*b**5*m**2*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 360024*a**2*b**5*m*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 141120*a**2*b**5*x**6*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 7*a*b**6*m**7*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 203*a*b**6*m**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 2401*a*b**6*m**5*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 14945*a*b**6*m**4*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 52528*a*b**6*m**3*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 103292*a*b**6*m**2*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 103824*a*b**6*m*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 40320*a*b**6*x**7*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + b**7*m**7*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 28*b**7*m**6*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 322*b**7*m**5*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 1960*b**7*m**4*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 6769*b**7*m**3*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13132*b**7*m**2*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 13068*b**7*m*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320) + 5040*b**7*x**8*x**m/(m**8 + 36*m**7 + 546*m**6 + 4536*m**5 + 22449*m**4 + 67284*m**3 + 118124*m**2 + 109584*m + 40320), True))","A",0
701,1,663,0,0.916702," ","integrate(x**m*(b*x+a)**3,x)","\begin{cases} - \frac{a^{3}}{3 x^{3}} - \frac{3 a^{2} b}{2 x^{2}} - \frac{3 a b^{2}}{x} + b^{3} \log{\left(x \right)} & \text{for}\: m = -4 \\- \frac{a^{3}}{2 x^{2}} - \frac{3 a^{2} b}{x} + 3 a b^{2} \log{\left(x \right)} + b^{3} x & \text{for}\: m = -3 \\- \frac{a^{3}}{x} + 3 a^{2} b \log{\left(x \right)} + 3 a b^{2} x + \frac{b^{3} x^{2}}{2} & \text{for}\: m = -2 \\a^{3} \log{\left(x \right)} + 3 a^{2} b x + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{3}}{3} & \text{for}\: m = -1 \\\frac{a^{3} m^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{9 a^{3} m^{2} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{26 a^{3} m x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 a^{3} x x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{3 a^{2} b m^{3} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 a^{2} b m^{2} x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{57 a^{2} b m x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{36 a^{2} b x^{2} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{3 a b^{2} m^{3} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{21 a b^{2} m^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{42 a b^{2} m x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{24 a b^{2} x^{3} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{b^{3} m^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 b^{3} m^{2} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{11 b^{3} m x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} + \frac{6 b^{3} x^{4} x^{m}}{m^{4} + 10 m^{3} + 35 m^{2} + 50 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3/(3*x**3) - 3*a**2*b/(2*x**2) - 3*a*b**2/x + b**3*log(x), Eq(m, -4)), (-a**3/(2*x**2) - 3*a**2*b/x + 3*a*b**2*log(x) + b**3*x, Eq(m, -3)), (-a**3/x + 3*a**2*b*log(x) + 3*a*b**2*x + b**3*x**2/2, Eq(m, -2)), (a**3*log(x) + 3*a**2*b*x + 3*a*b**2*x**2/2 + b**3*x**3/3, Eq(m, -1)), (a**3*m**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 9*a**3*m**2*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 26*a**3*m*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*a**3*x*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 3*a**2*b*m**3*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*a**2*b*m**2*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 57*a**2*b*m*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 36*a**2*b*x**2*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 3*a*b**2*m**3*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 21*a*b**2*m**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 42*a*b**2*m*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 24*a*b**2*x**3*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + b**3*m**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*b**3*m**2*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 11*b**3*m*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24) + 6*b**3*x**4*x**m/(m**4 + 10*m**3 + 35*m**2 + 50*m + 24), True))","A",0
702,1,299,0,0.545553," ","integrate(x**m*(b*x+a)**2,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} - \frac{2 a b}{x} + b^{2} \log{\left(x \right)} & \text{for}\: m = -3 \\- \frac{a^{2}}{x} + 2 a b \log{\left(x \right)} + b^{2} x & \text{for}\: m = -2 \\a^{2} \log{\left(x \right)} + 2 a b x + \frac{b^{2} x^{2}}{2} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{5 a^{2} m x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{6 a^{2} x x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{2 a b m^{2} x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{8 a b m x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{6 a b x^{2} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{b^{2} m^{2} x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{3 b^{2} m x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} + \frac{2 b^{2} x^{3} x^{m}}{m^{3} + 6 m^{2} + 11 m + 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) - 2*a*b/x + b**2*log(x), Eq(m, -3)), (-a**2/x + 2*a*b*log(x) + b**2*x, Eq(m, -2)), (a**2*log(x) + 2*a*b*x + b**2*x**2/2, Eq(m, -1)), (a**2*m**2*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 5*a**2*m*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 6*a**2*x*x**m/(m**3 + 6*m**2 + 11*m + 6) + 2*a*b*m**2*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + 8*a*b*m*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + 6*a*b*x**2*x**m/(m**3 + 6*m**2 + 11*m + 6) + b**2*m**2*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6) + 3*b**2*m*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6) + 2*b**2*x**3*x**m/(m**3 + 6*m**2 + 11*m + 6), True))","A",0
703,1,87,0,0.307857," ","integrate(x**m*(b*x+a),x)","\begin{cases} - \frac{a}{x} + b \log{\left(x \right)} & \text{for}\: m = -2 \\a \log{\left(x \right)} + b x & \text{for}\: m = -1 \\\frac{a m x x^{m}}{m^{2} + 3 m + 2} + \frac{2 a x x^{m}}{m^{2} + 3 m + 2} + \frac{b m x^{2} x^{m}}{m^{2} + 3 m + 2} + \frac{b x^{2} x^{m}}{m^{2} + 3 m + 2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + b*log(x), Eq(m, -2)), (a*log(x) + b*x, Eq(m, -1)), (a*m*x*x**m/(m**2 + 3*m + 2) + 2*a*x*x**m/(m**2 + 3*m + 2) + b*m*x**2*x**m/(m**2 + 3*m + 2) + b*x**2*x**m/(m**2 + 3*m + 2), True))","A",0
704,1,61,0,0.784805," ","integrate(x**m/(b*x+a),x)","\frac{m x x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{a \Gamma\left(m + 2\right)} + \frac{x x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{a \Gamma\left(m + 2\right)}"," ",0,"m*x*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(a*gamma(m + 2)) + x*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(a*gamma(m + 2))","C",0
705,1,262,0,1.038651," ","integrate(x**m/(b*x+a)**2,x)","- \frac{a m^{2} x x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{a^{3} \Gamma\left(m + 2\right) + a^{2} b x \Gamma\left(m + 2\right)} - \frac{a m x x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{a^{3} \Gamma\left(m + 2\right) + a^{2} b x \Gamma\left(m + 2\right)} + \frac{a m x x^{m} \Gamma\left(m + 1\right)}{a^{3} \Gamma\left(m + 2\right) + a^{2} b x \Gamma\left(m + 2\right)} + \frac{a x x^{m} \Gamma\left(m + 1\right)}{a^{3} \Gamma\left(m + 2\right) + a^{2} b x \Gamma\left(m + 2\right)} - \frac{b m^{2} x^{2} x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{a^{3} \Gamma\left(m + 2\right) + a^{2} b x \Gamma\left(m + 2\right)} - \frac{b m x^{2} x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{a^{3} \Gamma\left(m + 2\right) + a^{2} b x \Gamma\left(m + 2\right)}"," ",0,"-a*m**2*x*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(a**3*gamma(m + 2) + a**2*b*x*gamma(m + 2)) - a*m*x*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(a**3*gamma(m + 2) + a**2*b*x*gamma(m + 2)) + a*m*x*x**m*gamma(m + 1)/(a**3*gamma(m + 2) + a**2*b*x*gamma(m + 2)) + a*x*x**m*gamma(m + 1)/(a**3*gamma(m + 2) + a**2*b*x*gamma(m + 2)) - b*m**2*x**2*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(a**3*gamma(m + 2) + a**2*b*x*gamma(m + 2)) - b*m*x**2*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(a**3*gamma(m + 2) + a**2*b*x*gamma(m + 2))","C",0
706,1,717,0,1.449182," ","integrate(x**m/(b*x+a)**3,x)","\frac{a^{2} m^{3} x x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} - \frac{a^{2} m^{2} x x^{m} \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} - \frac{a^{2} m x x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} + \frac{a^{2} m x x^{m} \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} + \frac{2 a^{2} x x^{m} \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} + \frac{2 a b m^{3} x^{2} x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} - \frac{a b m^{2} x^{2} x^{m} \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} - \frac{2 a b m x^{2} x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} + \frac{a b x^{2} x^{m} \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} + \frac{b^{2} m^{3} x^{3} x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)} - \frac{b^{2} m x^{3} x^{m} \Phi\left(\frac{b x e^{i \pi}}{a}, 1, m + 1\right) \Gamma\left(m + 1\right)}{2 a^{5} \Gamma\left(m + 2\right) + 4 a^{4} b x \Gamma\left(m + 2\right) + 2 a^{3} b^{2} x^{2} \Gamma\left(m + 2\right)}"," ",0,"a**2*m**3*x*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) - a**2*m**2*x*x**m*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) - a**2*m*x*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) + a**2*m*x*x**m*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) + 2*a**2*x*x**m*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) + 2*a*b*m**3*x**2*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) - a*b*m**2*x**2*x**m*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) - 2*a*b*m*x**2*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) + a*b*x**2*x**m*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) + b**2*m**3*x**3*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2)) - b**2*m*x**3*x**m*lerchphi(b*x*exp_polar(I*pi)/a, 1, m + 1)*gamma(m + 1)/(2*a**5*gamma(m + 2) + 4*a**4*b*x*gamma(m + 2) + 2*a**3*b**2*x**2*gamma(m + 2))","C",0
707,1,37,0,10.167503," ","integrate(x**m*(b*x+a)**(5/2),x)","\frac{a^{\frac{5}{2}} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"a**(5/2)*x*x**m*gamma(m + 1)*hyper((-5/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/gamma(m + 2)","C",0
708,1,37,0,3.455346," ","integrate(x**m*(b*x+a)**(3/2),x)","\frac{a^{\frac{3}{2}} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"a**(3/2)*x*x**m*gamma(m + 1)*hyper((-3/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/gamma(m + 2)","C",0
709,1,37,0,1.684021," ","integrate(x**m*(b*x+a)**(1/2),x)","\frac{\sqrt{a} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"sqrt(a)*x*x**m*gamma(m + 1)*hyper((-1/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/gamma(m + 2)","C",0
710,1,36,0,1.561748," ","integrate(x**m/(b*x+a)**(1/2),x)","\frac{x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 2\right)}"," ",0,"x*x**m*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 2))","C",0
711,1,36,0,1.902525," ","integrate(x**m/(b*x+a)**(3/2),x)","\frac{x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{a^{\frac{3}{2}} \Gamma\left(m + 2\right)}"," ",0,"x*x**m*gamma(m + 1)*hyper((3/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(a**(3/2)*gamma(m + 2))","C",0
712,1,36,0,3.539823," ","integrate(x**m/(b*x+a)**(5/2),x)","\frac{x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{a^{\frac{5}{2}} \Gamma\left(m + 2\right)}"," ",0,"x*x**m*gamma(m + 1)*hyper((5/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(a**(5/2)*gamma(m + 2))","C",0
713,1,37,0,3.378093," ","integrate(x**(2+m)/(b*x+a)**(1/2),x)","\frac{x^{3} x^{m} \Gamma\left(m + 3\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 3 \\ m + 4 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 4\right)}"," ",0,"x**3*x**m*gamma(m + 3)*hyper((1/2, m + 3), (m + 4,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 4))","C",0
714,1,37,0,2.465126," ","integrate(x**(1+m)/(b*x+a)**(1/2),x)","\frac{x^{2} x^{m} \Gamma\left(m + 2\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 2 \\ m + 3 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 3\right)}"," ",0,"x**2*x**m*gamma(m + 2)*hyper((1/2, m + 2), (m + 3,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 3))","C",0
715,1,36,0,1.507505," ","integrate(x**m/(b*x+a)**(1/2),x)","\frac{x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 2\right)}"," ",0,"x*x**m*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 2))","C",0
716,1,31,0,3.748466," ","integrate(x**(-1+m)/(b*x+a)**(1/2),x)","\frac{x^{m} \Gamma\left(m\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m \\ m + 1 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 1\right)}"," ",0,"x**m*gamma(m)*hyper((1/2, m), (m + 1,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 1))","C",0
717,1,32,0,9.261191," ","integrate(x**(-2+m)/(b*x+a)**(1/2),x)","\frac{x^{m} \Gamma\left(m - 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m - 1 \\ m \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} x \Gamma\left(m\right)}"," ",0,"x**m*gamma(m - 1)*hyper((1/2, m - 1), (m,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*x*gamma(m))","C",0
718,1,37,0,24.005610," ","integrate(x**(-3+m)/(b*x+a)**(1/2),x)","\frac{x^{m} \Gamma\left(m - 2\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m - 2 \\ m - 1 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} x^{2} \Gamma\left(m - 1\right)}"," ",0,"x**m*gamma(m - 2)*hyper((1/2, m - 2), (m - 1,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*x**2*gamma(m - 1))","C",0
719,1,37,0,1.198813," ","integrate(x**m/(2+3*x)**(1/2),x)","\frac{\sqrt{2} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{3 x e^{i \pi}}{2}} \right)}}{2 \Gamma\left(m + 2\right)}"," ",0,"sqrt(2)*x*x**m*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), 3*x*exp_polar(I*pi)/2)/(2*gamma(m + 2))","C",0
720,1,46,0,1.216104," ","integrate(x**m/(2-3*x)**(1/2),x)","- \frac{2 \cdot 2^{m} \sqrt{3} \cdot 3^{- m} i \sqrt{x - \frac{2}{3}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - m \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 \left(x - \frac{2}{3}\right) e^{i \pi}}{2}} \right)}}{3}"," ",0,"-2*2**m*sqrt(3)*3**(-m)*I*sqrt(x - 2/3)*hyper((1/2, -m), (3/2,), 3*(x - 2/3)*exp_polar(I*pi)/2)/3","C",0
721,1,36,0,1.216070," ","integrate(x**m/(-2+3*x)**(1/2),x)","- \frac{\sqrt{2} i x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{3 x}{2}} \right)}}{2 \Gamma\left(m + 2\right)}"," ",0,"-sqrt(2)*I*x*x**m*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), 3*x/2)/(2*gamma(m + 2))","C",0
722,1,41,0,1.191138," ","integrate(x**m/(-2-3*x)**(1/2),x)","- \frac{\sqrt{2} i x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{3 x e^{i \pi}}{2}} \right)}}{2 \Gamma\left(m + 2\right)}"," ",0,"-sqrt(2)*I*x*x**m*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), 3*x*exp_polar(I*pi)/2)/(2*gamma(m + 2))","C",0
723,1,42,0,1.537060," ","integrate((-x)**m/(b*x+a)**(1/2),x)","\frac{x x^{m} e^{i \pi m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{a} \Gamma\left(m + 2\right)}"," ",0,"x*x**m*exp(I*pi*m)*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/(sqrt(a)*gamma(m + 2))","C",0
724,1,44,0,1.201127," ","integrate((-x)**m/(2+3*x)**(1/2),x)","\frac{2 \cdot 2^{m} \sqrt{3} \cdot 3^{- m} \sqrt{x + \frac{2}{3}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - m \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 \left(x + \frac{2}{3}\right) e^{2 i \pi}}{2}} \right)}}{3}"," ",0,"2*2**m*sqrt(3)*3**(-m)*sqrt(x + 2/3)*hyper((1/2, -m), (3/2,), 3*(x + 2/3)*exp_polar(2*I*pi)/2)/3","C",0
725,1,53,0,1.257900," ","integrate((-x)**m/(2-3*x)**(1/2),x)","- \frac{2 \cdot 2^{m} \sqrt{3} \cdot 3^{- m} i \sqrt{x - \frac{2}{3}} e^{i \pi m} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - m \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 \left(x - \frac{2}{3}\right) e^{i \pi}}{2}} \right)}}{3}"," ",0,"-2*2**m*sqrt(3)*3**(-m)*I*sqrt(x - 2/3)*exp(I*pi*m)*hyper((1/2, -m), (3/2,), 3*(x - 2/3)*exp_polar(I*pi)/2)/3","C",0
726,1,42,0,1.278373," ","integrate((-x)**m/(-2+3*x)**(1/2),x)","- \frac{\sqrt{2} i x x^{m} e^{i \pi m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{3 x}{2}} \right)}}{2 \Gamma\left(m + 2\right)}"," ",0,"-sqrt(2)*I*x*x**m*exp(I*pi*m)*gamma(m + 1)*hyper((1/2, m + 1), (m + 2,), 3*x/2)/(2*gamma(m + 2))","C",0
727,1,48,0,1.192742," ","integrate((-x)**m/(-2-3*x)**(1/2),x)","- \frac{2 \cdot 2^{m} \sqrt{3} \cdot 3^{- m} i \sqrt{x + \frac{2}{3}} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - m \\ \frac{3}{2} \end{matrix}\middle| {\frac{3 \left(x + \frac{2}{3}\right) e^{2 i \pi}}{2}} \right)}}{3}"," ",0,"-2*2**m*sqrt(3)*3**(-m)*I*sqrt(x + 2/3)*hyper((1/2, -m), (3/2,), 3*(x + 2/3)*exp_polar(2*I*pi)/2)/3","C",0
728,1,26,0,1.112098," ","integrate(x**n/(1-x)**(1/2),x)","- 2 i \sqrt{x - 1} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - n \\ \frac{3}{2} \end{matrix}\middle| {\left(x - 1\right) e^{i \pi}} \right)}"," ",0,"-2*I*sqrt(x - 1)*hyper((1/2, -n), (3/2,), (x - 1)*exp_polar(I*pi))","C",0
729,1,31,0,1.159705," ","integrate(x**n/(-a*x+a)**(1/2),x)","- \frac{2 i \sqrt{x - 1} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - n \\ \frac{3}{2} \end{matrix}\middle| {\left(x - 1\right) e^{i \pi}} \right)}}{\sqrt{a}}"," ",0,"-2*I*sqrt(x - 1)*hyper((1/2, -n), (3/2,), (x - 1)*exp_polar(I*pi))/sqrt(a)","C",0
730,1,34,0,3.569725," ","integrate(x**m*(b*x+a)**n,x)","\frac{a^{n} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"a**n*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/gamma(m + 2)","C",0
731,1,37,0,3.138770," ","integrate((c*x)**m*(b*x+a)**n,x)","\frac{a^{n} c^{m} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"a**n*c**m*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), b*x*exp_polar(I*pi)/a)/gamma(m + 2)","C",0
732,1,1318,0,2.326108," ","integrate(x**3*(b*x+a)**n,x)","\begin{cases} \frac{a^{n} x^{4}}{4} & \text{for}\: b = 0 \\\frac{6 a^{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}}{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 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 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} 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} 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} 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}\: n = -4 \\- \frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{9 a^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: n = -3 \\\frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} x^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: n = -2 \\- \frac{a^{3} \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{3}}{3 b} & \text{for}\: n = -1 \\- \frac{6 a^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 a^{3} b n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{3 a b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{2 a b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{11 b^{4} n x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**4/4, Eq(b, 0)), (6*a**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/(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*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*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*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*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*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(n, -4)), (-6*a**3*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 9*a**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(n, -3)), (6*a**3*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*x**2/(2*a*b**4 + 2*b**5*x) + b**3*x**3/(2*a*b**4 + 2*b**5*x), Eq(n, -2)), (-a**3*log(a/b + x)/b**4 + a**2*x/b**3 - a*x**2/(2*b**2) + x**3/(3*b), Eq(n, -1)), (-6*a**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*a**3*b*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*n**2*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*n*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*n**3*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 3*a*b**3*n**2*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 2*a*b**3*n*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*n**3*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*n**2*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 11*b**4*n*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4), True))","A",0
733,1,597,0,1.315084," ","integrate(x**2*(b*x+a)**n,x)","\begin{cases} \frac{a^{n} x^{3}}{3} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: n = -3 \\- \frac{2 a^{2} \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2}}{a b^{3} + b^{4} x} - \frac{2 a b x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{b^{2} x^{2}}{a b^{3} + b^{4} x} & \text{for}\: n = -2 \\\frac{a^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{a x}{b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: n = -1 \\\frac{2 a^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} - \frac{2 a^{2} b n x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{3 b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{2 b^{3} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**3/3, Eq(b, 0)), (2*a**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(n, -3)), (-2*a**2*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2/(a*b**3 + b**4*x) - 2*a*b*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*x**2/(a*b**3 + b**4*x), Eq(n, -2)), (a**2*log(a/b + x)/b**3 - a*x/b**2 + x**2/(2*b), Eq(n, -1)), (2*a**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) - 2*a**2*b*n*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n**2*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + b**3*n**2*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 3*b**3*n*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 2*b**3*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3), True))","A",0
734,1,201,0,0.701812," ","integrate(x*(b*x+a)**n,x)","\begin{cases} \frac{a^{n} x^{2}}{2} & \text{for}\: b = 0 \\\frac{a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a}{a b^{2} + b^{3} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: n = -2 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{x}{b} & \text{for}\: n = -1 \\- \frac{a^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{a b n x \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**2/2, Eq(b, 0)), (a*log(a/b + x)/(a*b**2 + b**3*x) + a/(a*b**2 + b**3*x) + b*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(n, -2)), (-a*log(a/b + x)/b**2 + x/b, Eq(n, -1)), (-a**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + a*b*n*x*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*n*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2), True))","A",0
735,1,20,0,0.065760," ","integrate((b*x+a)**n,x)","\frac{\begin{cases} \frac{\left(a + b x\right)^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(a + b x \right)} & \text{otherwise} \end{cases}}{b}"," ",0,"Piecewise(((a + b*x)**(n + 1)/(n + 1), Ne(n, -1)), (log(a + b*x), True))/b","A",0
736,1,83,0,1.599760," ","integrate((b*x+a)**n/x,x)","- \frac{b b^{n} n \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)} - \frac{b b^{n} \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)}"," ",0,"-b*b**n*n*(a/b + x)*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2)) - b*b**n*(a/b + x)*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2))","B",0
737,1,354,0,2.091778," ","integrate((b*x+a)**n/x**2,x)","\frac{a b^{2} b^{n} n^{2} \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{- a^{3} \Gamma\left(n + 2\right) + a^{2} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right)} + \frac{a b^{2} b^{n} n \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{- a^{3} \Gamma\left(n + 2\right) + a^{2} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right)} - \frac{a b^{2} b^{n} n \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{- a^{3} \Gamma\left(n + 2\right) + a^{2} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right)} - \frac{a b^{2} b^{n} \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{- a^{3} \Gamma\left(n + 2\right) + a^{2} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right)} - \frac{b^{3} b^{n} n^{2} \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{- a^{3} \Gamma\left(n + 2\right) + a^{2} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right)} - \frac{b^{3} b^{n} n \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{- a^{3} \Gamma\left(n + 2\right) + a^{2} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right)}"," ",0,"a*b**2*b**n*n**2*(a/b + x)*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(-a**3*gamma(n + 2) + a**2*b*(a/b + x)*gamma(n + 2)) + a*b**2*b**n*n*(a/b + x)*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(-a**3*gamma(n + 2) + a**2*b*(a/b + x)*gamma(n + 2)) - a*b**2*b**n*n*(a/b + x)*(a/b + x)**n*gamma(n + 1)/(-a**3*gamma(n + 2) + a**2*b*(a/b + x)*gamma(n + 2)) - a*b**2*b**n*(a/b + x)*(a/b + x)**n*gamma(n + 1)/(-a**3*gamma(n + 2) + a**2*b*(a/b + x)*gamma(n + 2)) - b**3*b**n*n**2*(a/b + x)**2*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(-a**3*gamma(n + 2) + a**2*b*(a/b + x)*gamma(n + 2)) - b**3*b**n*n*(a/b + x)**2*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(-a**3*gamma(n + 2) + a**2*b*(a/b + x)*gamma(n + 2))","B",0
738,1,918,0,2.839002," ","integrate((b*x+a)**n/x**3,x)","- \frac{a^{2} b^{3} b^{n} n^{3} \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} + \frac{a^{2} b^{3} b^{n} n^{2} \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} + \frac{a^{2} b^{3} b^{n} n \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} - \frac{a^{2} b^{3} b^{n} n \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} - \frac{2 a^{2} b^{3} b^{n} \left(\frac{a}{b} + x\right) \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} + \frac{2 a b^{4} b^{n} n^{3} \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} - \frac{a b^{4} b^{n} n^{2} \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} - \frac{2 a b^{4} b^{n} n \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} + \frac{a b^{4} b^{n} \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{n} \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} - \frac{b^{5} b^{n} n^{3} \left(\frac{a}{b} + x\right)^{3} \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)} + \frac{b^{5} b^{n} n \left(\frac{a}{b} + x\right)^{3} \left(\frac{a}{b} + x\right)^{n} \Phi\left(\frac{b \left(\frac{a}{b} + x\right)}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{2 a^{5} \Gamma\left(n + 2\right) - 4 a^{4} b \left(\frac{a}{b} + x\right) \Gamma\left(n + 2\right) + 2 a^{3} b^{2} \left(\frac{a}{b} + x\right)^{2} \Gamma\left(n + 2\right)}"," ",0,"-a**2*b**3*b**n*n**3*(a/b + x)*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) + a**2*b**3*b**n*n**2*(a/b + x)*(a/b + x)**n*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) + a**2*b**3*b**n*n*(a/b + x)*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) - a**2*b**3*b**n*n*(a/b + x)*(a/b + x)**n*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) - 2*a**2*b**3*b**n*(a/b + x)*(a/b + x)**n*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) + 2*a*b**4*b**n*n**3*(a/b + x)**2*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) - a*b**4*b**n*n**2*(a/b + x)**2*(a/b + x)**n*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) - 2*a*b**4*b**n*n*(a/b + x)**2*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) + a*b**4*b**n*(a/b + x)**2*(a/b + x)**n*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) - b**5*b**n*n**3*(a/b + x)**3*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2)) + b**5*b**n*n*(a/b + x)**3*(a/b + x)**n*lerchphi(b*(a/b + x)/a, 1, n + 1)*gamma(n + 1)/(2*a**5*gamma(n + 2) - 4*a**4*b*(a/b + x)*gamma(n + 2) + 2*a**3*b**2*(a/b + x)**2*gamma(n + 2))","B",0
739,-1,0,0,0.000000," ","integrate(x**(-4+n)/((b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-1,0,0,0.000000," ","integrate(x**(-3+n)/((b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,-1,0,0,0.000000," ","integrate(x**(-2+n)/((b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate(x**(-1+n)/((b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,1,32,0,28.690588," ","integrate(x**n/((b*x+a)**n),x)","\frac{a^{- n} x x^{n} \Gamma\left(n + 1\right) {{}_{2}F_{1}\left(\begin{matrix} n, n + 1 \\ n + 2 \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\Gamma\left(n + 2\right)}"," ",0,"a**(-n)*x*x**n*gamma(n + 1)*hyper((n, n + 1), (n + 2,), b*x*exp_polar(I*pi)/a)/gamma(n + 2)","C",0
744,-1,0,0,0.000000," ","integrate(x**(1+n)/((b*x+a)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,1,27,0,87.985017," ","integrate(x**(3/2)*(b*x+a)**n,x)","\frac{2 a^{n} x^{\frac{5}{2}} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - n \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{5}"," ",0,"2*a**n*x**(5/2)*hyper((5/2, -n), (7/2,), b*x*exp_polar(I*pi)/a)/5","C",0
746,1,27,0,8.377848," ","integrate(x**(1/2)*(b*x+a)**n,x)","\frac{2 a^{n} x^{\frac{3}{2}} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - n \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{3}"," ",0,"2*a**n*x**(3/2)*hyper((3/2, -n), (5/2,), b*x*exp_polar(I*pi)/a)/3","C",0
747,1,26,0,5.692145," ","integrate((b*x+a)**n/x**(1/2),x)","2 a^{n} \sqrt{x} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - n \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}"," ",0,"2*a**n*sqrt(x)*hyper((1/2, -n), (3/2,), b*x*exp_polar(I*pi)/a)","C",0
748,1,29,0,31.961232," ","integrate((b*x+a)**n/x**(3/2),x)","- \frac{2 a^{n} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - n \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x e^{i \pi}}{a}} \right)}}{\sqrt{x}}"," ",0,"-2*a**n*hyper((-1/2, -n), (1/2,), b*x*exp_polar(I*pi)/a)/sqrt(x)","C",0
749,-1,0,0,0.000000," ","integrate((b*x+a)**n/x**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,1,37,0,2.529884," ","integrate((b*x)**m*(d*x+2)**n,x)","\frac{2^{n} b^{m} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{d x e^{i \pi}}{2}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"2**n*b**m*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), d*x*exp_polar(I*pi)/2)/gamma(m + 2)","C",0
751,1,37,0,2.501677," ","integrate((b*x)**m*(-b*c*x+c)**n,x)","\frac{b^{m} c^{n} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {b x e^{2 i \pi}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"b**m*c**n*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), b*x*exp_polar(2*I*pi))/gamma(m + 2)","C",0
752,1,37,0,3.171207," ","integrate((b*x)**m*(d*x+c)**n,x)","\frac{b^{m} c^{n} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{d x e^{i \pi}}{c}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"b**m*c**n*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), d*x*exp_polar(I*pi)/c)/gamma(m + 2)","C",0
753,-1,0,0,0.000000," ","integrate(x**(-1+n)*(b*x+a)**(-1-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
754,1,323,0,94.815280," ","integrate(x**(-3-n)*(b*x+a)**n,x)","\begin{cases} - \frac{b^{n}}{2 x^{2}} & \text{for}\: a = 0 \\\frac{a \log{\left(x \right)}}{a^{3} + a^{2} b x} - \frac{a \log{\left(\frac{a}{b} + x \right)}}{a^{3} + a^{2} b x} + \frac{a}{a^{3} + a^{2} b x} + \frac{b x \log{\left(x \right)}}{a^{3} + a^{2} b x} - \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a^{3} + a^{2} b x} & \text{for}\: n = -2 \\- \frac{1}{a x} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x \right)}}{a^{2}} & \text{for}\: n = -1 \\- \frac{a^{2} n \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} - \frac{a^{2} \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} - \frac{a b n x \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} + \frac{b^{2} x^{2} \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**n/(2*x**2), Eq(a, 0)), (a*log(x)/(a**3 + a**2*b*x) - a*log(a/b + x)/(a**3 + a**2*b*x) + a/(a**3 + a**2*b*x) + b*x*log(x)/(a**3 + a**2*b*x) - b*x*log(a/b + x)/(a**3 + a**2*b*x), Eq(n, -2)), (-1/(a*x) - b*log(x)/a**2 + b*log(a/b + x)/a**2, Eq(n, -1)), (-a**2*n*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n) - a**2*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n) - a*b*n*x*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n) + b**2*x**2*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n), True))","A",0
755,1,323,0,94.487898," ","integrate(x**(-3-n)*(b*x+a)**n,x)","\begin{cases} - \frac{b^{n}}{2 x^{2}} & \text{for}\: a = 0 \\\frac{a \log{\left(x \right)}}{a^{3} + a^{2} b x} - \frac{a \log{\left(\frac{a}{b} + x \right)}}{a^{3} + a^{2} b x} + \frac{a}{a^{3} + a^{2} b x} + \frac{b x \log{\left(x \right)}}{a^{3} + a^{2} b x} - \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a^{3} + a^{2} b x} & \text{for}\: n = -2 \\- \frac{1}{a x} - \frac{b \log{\left(x \right)}}{a^{2}} + \frac{b \log{\left(\frac{a}{b} + x \right)}}{a^{2}} & \text{for}\: n = -1 \\- \frac{a^{2} n \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} - \frac{a^{2} \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} - \frac{a b n x \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} + \frac{b^{2} x^{2} \left(a + b x\right)^{n}}{a^{2} n^{2} x^{2} x^{n} + 3 a^{2} n x^{2} x^{n} + 2 a^{2} x^{2} x^{n}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**n/(2*x**2), Eq(a, 0)), (a*log(x)/(a**3 + a**2*b*x) - a*log(a/b + x)/(a**3 + a**2*b*x) + a/(a**3 + a**2*b*x) + b*x*log(x)/(a**3 + a**2*b*x) - b*x*log(a/b + x)/(a**3 + a**2*b*x), Eq(n, -2)), (-1/(a*x) - b*log(x)/a**2 + b*log(a/b + x)/a**2, Eq(n, -1)), (-a**2*n*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n) - a**2*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n) - a*b*n*x*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n) + b**2*x**2*(a + b*x)**n/(a**2*n**2*x**2*x**n + 3*a**2*n*x**2*x**n + 2*a**2*x**2*x**n), True))","A",0
756,1,36,0,0.434550," ","integrate(x**3*(b*x+a)*(c*x**2)**(1/2),x)","\frac{a \sqrt{c} x^{4} \sqrt{x^{2}}}{5} + \frac{b \sqrt{c} x^{5} \sqrt{x^{2}}}{6}"," ",0,"a*sqrt(c)*x**4*sqrt(x**2)/5 + b*sqrt(c)*x**5*sqrt(x**2)/6","A",0
757,1,36,0,0.338684," ","integrate(x**2*(b*x+a)*(c*x**2)**(1/2),x)","\frac{a \sqrt{c} x^{3} \sqrt{x^{2}}}{4} + \frac{b \sqrt{c} x^{4} \sqrt{x^{2}}}{5}"," ",0,"a*sqrt(c)*x**3*sqrt(x**2)/4 + b*sqrt(c)*x**4*sqrt(x**2)/5","A",0
758,1,36,0,0.268498," ","integrate(x*(b*x+a)*(c*x**2)**(1/2),x)","\frac{a \sqrt{c} x^{2} \sqrt{x^{2}}}{3} + \frac{b \sqrt{c} x^{3} \sqrt{x^{2}}}{4}"," ",0,"a*sqrt(c)*x**2*sqrt(x**2)/3 + b*sqrt(c)*x**3*sqrt(x**2)/4","A",0
759,1,34,0,0.223893," ","integrate((b*x+a)*(c*x**2)**(1/2),x)","\frac{a \sqrt{c} x \sqrt{x^{2}}}{2} + \frac{b \sqrt{c} x^{2} \sqrt{x^{2}}}{3}"," ",0,"a*sqrt(c)*x*sqrt(x**2)/2 + b*sqrt(c)*x**2*sqrt(x**2)/3","A",0
760,1,29,0,0.228456," ","integrate((b*x+a)*(c*x**2)**(1/2)/x,x)","a \sqrt{c} \sqrt{x^{2}} + \frac{b \sqrt{c} x \sqrt{x^{2}}}{2}"," ",0,"a*sqrt(c)*sqrt(x**2) + b*sqrt(c)*x*sqrt(x**2)/2","A",0
761,0,0,0,0.000000," ","integrate((b*x+a)*(c*x**2)**(1/2)/x**2,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)/x**2, x)","F",0
762,0,0,0,0.000000," ","integrate((b*x+a)*(c*x**2)**(1/2)/x**3,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)/x**3, x)","F",0
763,1,36,0,0.507417," ","integrate((b*x+a)*(c*x**2)**(1/2)/x**4,x)","- \frac{a \sqrt{c} \sqrt{x^{2}}}{2 x^{3}} - \frac{b \sqrt{c} \sqrt{x^{2}}}{x^{2}}"," ",0,"-a*sqrt(c)*sqrt(x**2)/(2*x**3) - b*sqrt(c)*sqrt(x**2)/x**2","A",0
764,1,36,0,1.161407," ","integrate(x**3*(c*x**2)**(3/2)*(b*x+a),x)","\frac{a c^{\frac{3}{2}} x^{4} \left(x^{2}\right)^{\frac{3}{2}}}{7} + \frac{b c^{\frac{3}{2}} x^{5} \left(x^{2}\right)^{\frac{3}{2}}}{8}"," ",0,"a*c**(3/2)*x**4*(x**2)**(3/2)/7 + b*c**(3/2)*x**5*(x**2)**(3/2)/8","A",0
765,1,36,0,0.909194," ","integrate(x**2*(c*x**2)**(3/2)*(b*x+a),x)","\frac{a c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}}{6} + \frac{b c^{\frac{3}{2}} x^{4} \left(x^{2}\right)^{\frac{3}{2}}}{7}"," ",0,"a*c**(3/2)*x**3*(x**2)**(3/2)/6 + b*c**(3/2)*x**4*(x**2)**(3/2)/7","A",0
766,1,36,0,0.728089," ","integrate(x*(c*x**2)**(3/2)*(b*x+a),x)","\frac{a c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}{5} + \frac{b c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}}{6}"," ",0,"a*c**(3/2)*x**2*(x**2)**(3/2)/5 + b*c**(3/2)*x**3*(x**2)**(3/2)/6","A",0
767,1,34,0,0.557988," ","integrate((c*x**2)**(3/2)*(b*x+a),x)","\frac{a c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{4} + \frac{b c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}{5}"," ",0,"a*c**(3/2)*x*(x**2)**(3/2)/4 + b*c**(3/2)*x**2*(x**2)**(3/2)/5","A",0
768,1,31,0,0.577343," ","integrate((c*x**2)**(3/2)*(b*x+a)/x,x)","\frac{a c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3} + \frac{b c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{4}"," ",0,"a*c**(3/2)*(x**2)**(3/2)/3 + b*c**(3/2)*x*(x**2)**(3/2)/4","A",0
769,1,31,0,0.572321," ","integrate((c*x**2)**(3/2)*(b*x+a)/x**2,x)","\frac{a c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{2 x} + \frac{b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3}"," ",0,"a*c**(3/2)*(x**2)**(3/2)/(2*x) + b*c**(3/2)*(x**2)**(3/2)/3","A",0
770,1,32,0,0.740847," ","integrate((c*x**2)**(3/2)*(b*x+a)/x**3,x)","\frac{a c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{x^{2}} + \frac{b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{2 x}"," ",0,"a*c**(3/2)*(x**2)**(3/2)/x**2 + b*c**(3/2)*(x**2)**(3/2)/(2*x)","A",0
771,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)/x**4,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}{x^{4}}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)/x**4, x)","F",0
772,1,36,0,2.542781," ","integrate(x**3*(c*x**2)**(5/2)*(b*x+a),x)","\frac{a c^{\frac{5}{2}} x^{4} \left(x^{2}\right)^{\frac{5}{2}}}{9} + \frac{b c^{\frac{5}{2}} x^{5} \left(x^{2}\right)^{\frac{5}{2}}}{10}"," ",0,"a*c**(5/2)*x**4*(x**2)**(5/2)/9 + b*c**(5/2)*x**5*(x**2)**(5/2)/10","A",0
773,1,36,0,2.097088," ","integrate(x**2*(c*x**2)**(5/2)*(b*x+a),x)","\frac{a c^{\frac{5}{2}} x^{3} \left(x^{2}\right)^{\frac{5}{2}}}{8} + \frac{b c^{\frac{5}{2}} x^{4} \left(x^{2}\right)^{\frac{5}{2}}}{9}"," ",0,"a*c**(5/2)*x**3*(x**2)**(5/2)/8 + b*c**(5/2)*x**4*(x**2)**(5/2)/9","A",0
774,1,36,0,1.741722," ","integrate(x*(c*x**2)**(5/2)*(b*x+a),x)","\frac{a c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}{7} + \frac{b c^{\frac{5}{2}} x^{3} \left(x^{2}\right)^{\frac{5}{2}}}{8}"," ",0,"a*c**(5/2)*x**2*(x**2)**(5/2)/7 + b*c**(5/2)*x**3*(x**2)**(5/2)/8","A",0
775,1,34,0,1.410298," ","integrate((c*x**2)**(5/2)*(b*x+a),x)","\frac{a c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}{6} + \frac{b c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}{7}"," ",0,"a*c**(5/2)*x*(x**2)**(5/2)/6 + b*c**(5/2)*x**2*(x**2)**(5/2)/7","A",0
776,1,31,0,1.428715," ","integrate((c*x**2)**(5/2)*(b*x+a)/x,x)","\frac{a c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{5} + \frac{b c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}{6}"," ",0,"a*c**(5/2)*(x**2)**(5/2)/5 + b*c**(5/2)*x*(x**2)**(5/2)/6","A",0
777,1,31,0,1.529393," ","integrate((c*x**2)**(5/2)*(b*x+a)/x**2,x)","\frac{a c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{4 x} + \frac{b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{5}"," ",0,"a*c**(5/2)*(x**2)**(5/2)/(4*x) + b*c**(5/2)*(x**2)**(5/2)/5","A",0
778,1,34,0,1.577743," ","integrate((c*x**2)**(5/2)*(b*x+a)/x**3,x)","\frac{a c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{2}} + \frac{b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{4 x}"," ",0,"a*c**(5/2)*(x**2)**(5/2)/(3*x**2) + b*c**(5/2)*(x**2)**(5/2)/(4*x)","A",0
779,1,36,0,1.623252," ","integrate((c*x**2)**(5/2)*(b*x+a)/x**4,x)","\frac{a c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{2 x^{3}} + \frac{b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{2}}"," ",0,"a*c**(5/2)*(x**2)**(5/2)/(2*x**3) + b*c**(5/2)*(x**2)**(5/2)/(3*x**2)","A",0
780,1,36,0,0.606281," ","integrate(x**3*(b*x+a)/(c*x**2)**(1/2),x)","\frac{a x^{4}}{3 \sqrt{c} \sqrt{x^{2}}} + \frac{b x^{5}}{4 \sqrt{c} \sqrt{x^{2}}}"," ",0,"a*x**4/(3*sqrt(c)*sqrt(x**2)) + b*x**5/(4*sqrt(c)*sqrt(x**2))","A",0
781,1,36,0,0.521629," ","integrate(x**2*(b*x+a)/(c*x**2)**(1/2),x)","\frac{a x^{3}}{2 \sqrt{c} \sqrt{x^{2}}} + \frac{b x^{4}}{3 \sqrt{c} \sqrt{x^{2}}}"," ",0,"a*x**3/(2*sqrt(c)*sqrt(x**2)) + b*x**4/(3*sqrt(c)*sqrt(x**2))","A",0
782,1,34,0,0.461715," ","integrate(x*(b*x+a)/(c*x**2)**(1/2),x)","\frac{a x^{2}}{\sqrt{c} \sqrt{x^{2}}} + \frac{b x^{3}}{2 \sqrt{c} \sqrt{x^{2}}}"," ",0,"a*x**2/(sqrt(c)*sqrt(x**2)) + b*x**3/(2*sqrt(c)*sqrt(x**2))","A",0
783,0,0,0,0.000000," ","integrate((b*x+a)/(c*x**2)**(1/2),x)","\int \frac{a + b x}{\sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)/sqrt(c*x**2), x)","F",0
784,0,0,0,0.000000," ","integrate((b*x+a)/x/(c*x**2)**(1/2),x)","\int \frac{a + b x}{x \sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)/(x*sqrt(c*x**2)), x)","F",0
785,1,31,0,0.544368," ","integrate((b*x+a)/x**2/(c*x**2)**(1/2),x)","- \frac{a}{2 \sqrt{c} x \sqrt{x^{2}}} - \frac{b}{\sqrt{c} \sqrt{x^{2}}}"," ",0,"-a/(2*sqrt(c)*x*sqrt(x**2)) - b/(sqrt(c)*sqrt(x**2))","A",0
786,1,36,0,0.635648," ","integrate((b*x+a)/x**3/(c*x**2)**(1/2),x)","- \frac{a}{3 \sqrt{c} x^{2} \sqrt{x^{2}}} - \frac{b}{2 \sqrt{c} x \sqrt{x^{2}}}"," ",0,"-a/(3*sqrt(c)*x**2*sqrt(x**2)) - b/(2*sqrt(c)*x*sqrt(x**2))","A",0
787,1,37,0,0.809833," ","integrate((b*x+a)/x**4/(c*x**2)**(1/2),x)","- \frac{a}{4 \sqrt{c} x^{3} \sqrt{x^{2}}} - \frac{b}{3 \sqrt{c} x^{2} \sqrt{x^{2}}}"," ",0,"-a/(4*sqrt(c)*x**3*sqrt(x**2)) - b/(3*sqrt(c)*x**2*sqrt(x**2))","A",0
788,1,34,0,0.635198," ","integrate(x**3*(b*x+a)/(c*x**2)**(3/2),x)","\frac{a x^{4}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b x^{5}}{2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"a*x**4/(c**(3/2)*(x**2)**(3/2)) + b*x**5/(2*c**(3/2)*(x**2)**(3/2))","A",0
789,0,0,0,0.000000," ","integrate(x**2*(b*x+a)/(c*x**2)**(3/2),x)","\int \frac{x^{2} \left(a + b x\right)}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x)/(c*x**2)**(3/2), x)","F",0
790,0,0,0,0.000000," ","integrate(x*(b*x+a)/(c*x**2)**(3/2),x)","\int \frac{x \left(a + b x\right)}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*x)/(c*x**2)**(3/2), x)","F",0
791,1,34,0,0.538157," ","integrate((b*x+a)/(c*x**2)**(3/2),x)","- \frac{a x}{2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b x^{2}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a*x/(2*c**(3/2)*(x**2)**(3/2)) - b*x**2/(c**(3/2)*(x**2)**(3/2))","A",0
792,1,32,0,0.631622," ","integrate((b*x+a)/x/(c*x**2)**(3/2),x)","- \frac{a}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b x}{2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a/(3*c**(3/2)*(x**2)**(3/2)) - b*x/(2*c**(3/2)*(x**2)**(3/2))","A",0
793,1,32,0,0.768830," ","integrate((b*x+a)/x**2/(c*x**2)**(3/2),x)","- \frac{a}{4 c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a/(4*c**(3/2)*x*(x**2)**(3/2)) - b/(3*c**(3/2)*(x**2)**(3/2))","A",0
794,1,36,0,0.934237," ","integrate((b*x+a)/x**3/(c*x**2)**(3/2),x)","- \frac{a}{5 c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b}{4 c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a/(5*c**(3/2)*x**2*(x**2)**(3/2)) - b/(4*c**(3/2)*x*(x**2)**(3/2))","A",0
795,1,37,0,1.164204," ","integrate((b*x+a)/x**4/(c*x**2)**(3/2),x)","- \frac{a}{6 c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b}{5 c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a/(6*c**(3/2)*x**3*(x**2)**(3/2)) - b/(5*c**(3/2)*x**2*(x**2)**(3/2))","A",0
796,0,0,0,0.000000," ","integrate(x**3*(b*x+a)/(c*x**2)**(5/2),x)","\int \frac{x^{3} \left(a + b x\right)}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*x)/(c*x**2)**(5/2), x)","F",0
797,1,36,0,0.931156," ","integrate(x**2*(b*x+a)/(c*x**2)**(5/2),x)","- \frac{a x^{3}}{2 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b x^{4}}{c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a*x**3/(2*c**(5/2)*(x**2)**(5/2)) - b*x**4/(c**(5/2)*(x**2)**(5/2))","A",0
798,1,37,0,0.918146," ","integrate(x*(b*x+a)/(c*x**2)**(5/2),x)","- \frac{a x^{2}}{3 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b x^{3}}{2 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a*x**2/(3*c**(5/2)*(x**2)**(5/2)) - b*x**3/(2*c**(5/2)*(x**2)**(5/2))","A",0
799,1,36,0,0.916420," ","integrate((b*x+a)/(c*x**2)**(5/2),x)","- \frac{a x}{4 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b x^{2}}{3 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a*x/(4*c**(5/2)*(x**2)**(5/2)) - b*x**2/(3*c**(5/2)*(x**2)**(5/2))","A",0
800,1,32,0,1.121214," ","integrate((b*x+a)/x/(c*x**2)**(5/2),x)","- \frac{a}{5 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b x}{4 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a/(5*c**(5/2)*(x**2)**(5/2)) - b*x/(4*c**(5/2)*(x**2)**(5/2))","A",0
801,1,32,0,1.340947," ","integrate((b*x+a)/x**2/(c*x**2)**(5/2),x)","- \frac{a}{6 c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b}{5 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a/(6*c**(5/2)*x*(x**2)**(5/2)) - b/(5*c**(5/2)*(x**2)**(5/2))","A",0
802,1,36,0,1.643942," ","integrate((b*x+a)/x**3/(c*x**2)**(5/2),x)","- \frac{a}{7 c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b}{6 c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a/(7*c**(5/2)*x**2*(x**2)**(5/2)) - b/(6*c**(5/2)*x*(x**2)**(5/2))","A",0
803,1,37,0,1.968115," ","integrate((b*x+a)/x**4/(c*x**2)**(5/2),x)","- \frac{a}{8 c^{\frac{5}{2}} x^{3} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b}{7 c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a/(8*c**(5/2)*x**3*(x**2)**(5/2)) - b/(7*c**(5/2)*x**2*(x**2)**(5/2))","A",0
804,1,60,0,0.586879," ","integrate(x**3*(b*x+a)**2*(c*x**2)**(1/2),x)","\frac{a^{2} \sqrt{c} x^{4} \sqrt{x^{2}}}{5} + \frac{a b \sqrt{c} x^{5} \sqrt{x^{2}}}{3} + \frac{b^{2} \sqrt{c} x^{6} \sqrt{x^{2}}}{7}"," ",0,"a**2*sqrt(c)*x**4*sqrt(x**2)/5 + a*b*sqrt(c)*x**5*sqrt(x**2)/3 + b**2*sqrt(c)*x**6*sqrt(x**2)/7","A",0
805,1,61,0,0.462699," ","integrate(x**2*(b*x+a)**2*(c*x**2)**(1/2),x)","\frac{a^{2} \sqrt{c} x^{3} \sqrt{x^{2}}}{4} + \frac{2 a b \sqrt{c} x^{4} \sqrt{x^{2}}}{5} + \frac{b^{2} \sqrt{c} x^{5} \sqrt{x^{2}}}{6}"," ",0,"a**2*sqrt(c)*x**3*sqrt(x**2)/4 + 2*a*b*sqrt(c)*x**4*sqrt(x**2)/5 + b**2*sqrt(c)*x**5*sqrt(x**2)/6","A",0
806,1,60,0,0.367795," ","integrate(x*(b*x+a)**2*(c*x**2)**(1/2),x)","\frac{a^{2} \sqrt{c} x^{2} \sqrt{x^{2}}}{3} + \frac{a b \sqrt{c} x^{3} \sqrt{x^{2}}}{2} + \frac{b^{2} \sqrt{c} x^{4} \sqrt{x^{2}}}{5}"," ",0,"a**2*sqrt(c)*x**2*sqrt(x**2)/3 + a*b*sqrt(c)*x**3*sqrt(x**2)/2 + b**2*sqrt(c)*x**4*sqrt(x**2)/5","A",0
807,1,60,0,0.297472," ","integrate((b*x+a)**2*(c*x**2)**(1/2),x)","\frac{a^{2} \sqrt{c} x \sqrt{x^{2}}}{2} + \frac{2 a b \sqrt{c} x^{2} \sqrt{x^{2}}}{3} + \frac{b^{2} \sqrt{c} x^{3} \sqrt{x^{2}}}{4}"," ",0,"a**2*sqrt(c)*x*sqrt(x**2)/2 + 2*a*b*sqrt(c)*x**2*sqrt(x**2)/3 + b**2*sqrt(c)*x**3*sqrt(x**2)/4","A",0
808,1,51,0,0.297403," ","integrate((b*x+a)**2*(c*x**2)**(1/2)/x,x)","a^{2} \sqrt{c} \sqrt{x^{2}} + a b \sqrt{c} x \sqrt{x^{2}} + \frac{b^{2} \sqrt{c} x^{2} \sqrt{x^{2}}}{3}"," ",0,"a**2*sqrt(c)*sqrt(x**2) + a*b*sqrt(c)*x*sqrt(x**2) + b**2*sqrt(c)*x**2*sqrt(x**2)/3","B",0
809,0,0,0,0.000000," ","integrate((b*x+a)**2*(c*x**2)**(1/2)/x**2,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)^{2}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)**2/x**2, x)","F",0
810,0,0,0,0.000000," ","integrate((b*x+a)**2*(c*x**2)**(1/2)/x**3,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)^{2}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)**2/x**3, x)","F",0
811,0,0,0,0.000000," ","integrate((b*x+a)**2*(c*x**2)**(1/2)/x**4,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)^{2}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)**2/x**4, x)","F",0
812,1,60,0,1.497596," ","integrate(x**3*(c*x**2)**(3/2)*(b*x+a)**2,x)","\frac{a^{2} c^{\frac{3}{2}} x^{4} \left(x^{2}\right)^{\frac{3}{2}}}{7} + \frac{a b c^{\frac{3}{2}} x^{5} \left(x^{2}\right)^{\frac{3}{2}}}{4} + \frac{b^{2} c^{\frac{3}{2}} x^{6} \left(x^{2}\right)^{\frac{3}{2}}}{9}"," ",0,"a**2*c**(3/2)*x**4*(x**2)**(3/2)/7 + a*b*c**(3/2)*x**5*(x**2)**(3/2)/4 + b**2*c**(3/2)*x**6*(x**2)**(3/2)/9","A",0
813,1,61,0,1.224944," ","integrate(x**2*(c*x**2)**(3/2)*(b*x+a)**2,x)","\frac{a^{2} c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}}{6} + \frac{2 a b c^{\frac{3}{2}} x^{4} \left(x^{2}\right)^{\frac{3}{2}}}{7} + \frac{b^{2} c^{\frac{3}{2}} x^{5} \left(x^{2}\right)^{\frac{3}{2}}}{8}"," ",0,"a**2*c**(3/2)*x**3*(x**2)**(3/2)/6 + 2*a*b*c**(3/2)*x**4*(x**2)**(3/2)/7 + b**2*c**(3/2)*x**5*(x**2)**(3/2)/8","A",0
814,1,60,0,0.971471," ","integrate(x*(c*x**2)**(3/2)*(b*x+a)**2,x)","\frac{a^{2} c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}{5} + \frac{a b c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}}{3} + \frac{b^{2} c^{\frac{3}{2}} x^{4} \left(x^{2}\right)^{\frac{3}{2}}}{7}"," ",0,"a**2*c**(3/2)*x**2*(x**2)**(3/2)/5 + a*b*c**(3/2)*x**3*(x**2)**(3/2)/3 + b**2*c**(3/2)*x**4*(x**2)**(3/2)/7","A",0
815,1,60,0,0.769774," ","integrate((c*x**2)**(3/2)*(b*x+a)**2,x)","\frac{a^{2} c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{4} + \frac{2 a b c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}{5} + \frac{b^{2} c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}}{6}"," ",0,"a**2*c**(3/2)*x*(x**2)**(3/2)/4 + 2*a*b*c**(3/2)*x**2*(x**2)**(3/2)/5 + b**2*c**(3/2)*x**3*(x**2)**(3/2)/6","A",0
816,1,54,0,0.793433," ","integrate((c*x**2)**(3/2)*(b*x+a)**2/x,x)","\frac{a^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3} + \frac{a b c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{2} + \frac{b^{2} c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}}{5}"," ",0,"a**2*c**(3/2)*(x**2)**(3/2)/3 + a*b*c**(3/2)*x*(x**2)**(3/2)/2 + b**2*c**(3/2)*x**2*(x**2)**(3/2)/5","A",0
817,1,54,0,0.804952," ","integrate((c*x**2)**(3/2)*(b*x+a)**2/x**2,x)","\frac{a^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{2 x} + \frac{2 a b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3} + \frac{b^{2} c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}{4}"," ",0,"a**2*c**(3/2)*(x**2)**(3/2)/(2*x) + 2*a*b*c**(3/2)*(x**2)**(3/2)/3 + b**2*c**(3/2)*x*(x**2)**(3/2)/4","A",0
818,1,51,0,0.938611," ","integrate((c*x**2)**(3/2)*(b*x+a)**2/x**3,x)","\frac{a^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{x^{2}} + \frac{a b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{x} + \frac{b^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{3}"," ",0,"a**2*c**(3/2)*(x**2)**(3/2)/x**2 + a*b*c**(3/2)*(x**2)**(3/2)/x + b**2*c**(3/2)*(x**2)**(3/2)/3","B",0
819,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**2/x**4,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)**2/x**4, x)","F",0
820,1,60,0,2.186386," ","integrate(x*(c*x**2)**(5/2)*(b*x+a)**2,x)","\frac{a^{2} c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}{7} + \frac{a b c^{\frac{5}{2}} x^{3} \left(x^{2}\right)^{\frac{5}{2}}}{4} + \frac{b^{2} c^{\frac{5}{2}} x^{4} \left(x^{2}\right)^{\frac{5}{2}}}{9}"," ",0,"a**2*c**(5/2)*x**2*(x**2)**(5/2)/7 + a*b*c**(5/2)*x**3*(x**2)**(5/2)/4 + b**2*c**(5/2)*x**4*(x**2)**(5/2)/9","A",0
821,1,60,0,1.801865," ","integrate((c*x**2)**(5/2)*(b*x+a)**2,x)","\frac{a^{2} c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}{6} + \frac{2 a b c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}{7} + \frac{b^{2} c^{\frac{5}{2}} x^{3} \left(x^{2}\right)^{\frac{5}{2}}}{8}"," ",0,"a**2*c**(5/2)*x*(x**2)**(5/2)/6 + 2*a*b*c**(5/2)*x**2*(x**2)**(5/2)/7 + b**2*c**(5/2)*x**3*(x**2)**(5/2)/8","A",0
822,1,54,0,1.822816," ","integrate((c*x**2)**(5/2)*(b*x+a)**2/x,x)","\frac{a^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{5} + \frac{a b c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}{3} + \frac{b^{2} c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}}{7}"," ",0,"a**2*c**(5/2)*(x**2)**(5/2)/5 + a*b*c**(5/2)*x*(x**2)**(5/2)/3 + b**2*c**(5/2)*x**2*(x**2)**(5/2)/7","A",0
823,1,54,0,1.840540," ","integrate((c*x**2)**(5/2)*(b*x+a)**2/x**2,x)","\frac{a^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{4 x} + \frac{2 a b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{5} + \frac{b^{2} c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}{6}"," ",0,"a**2*c**(5/2)*(x**2)**(5/2)/(4*x) + 2*a*b*c**(5/2)*(x**2)**(5/2)/5 + b**2*c**(5/2)*x*(x**2)**(5/2)/6","A",0
824,1,54,0,1.948373," ","integrate((c*x**2)**(5/2)*(b*x+a)**2/x**3,x)","\frac{a^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{2}} + \frac{a b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{2 x} + \frac{b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{5}"," ",0,"a**2*c**(5/2)*(x**2)**(5/2)/(3*x**2) + a*b*c**(5/2)*(x**2)**(5/2)/(2*x) + b**2*c**(5/2)*(x**2)**(5/2)/5","A",0
825,1,60,0,2.006749," ","integrate((c*x**2)**(5/2)*(b*x+a)**2/x**4,x)","\frac{a^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{2 x^{3}} + \frac{2 a b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{2}} + \frac{b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{4 x}"," ",0,"a**2*c**(5/2)*(x**2)**(5/2)/(2*x**3) + 2*a*b*c**(5/2)*(x**2)**(5/2)/(3*x**2) + b**2*c**(5/2)*(x**2)**(5/2)/(4*x)","A",0
826,1,56,0,2.033810," ","integrate((c*x**2)**(5/2)*(b*x+a)**2/x**5,x)","\frac{a^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{x^{4}} + \frac{a b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{x^{3}} + \frac{b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{3 x^{2}}"," ",0,"a**2*c**(5/2)*(x**2)**(5/2)/x**4 + a*b*c**(5/2)*(x**2)**(5/2)/x**3 + b**2*c**(5/2)*(x**2)**(5/2)/(3*x**2)","B",0
827,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**2/x**6,x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{2}}{x^{6}}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**2/x**6, x)","F",0
828,1,60,0,0.788210," ","integrate(x**3*(b*x+a)**2/(c*x**2)**(1/2),x)","\frac{a^{2} x^{4}}{3 \sqrt{c} \sqrt{x^{2}}} + \frac{a b x^{5}}{2 \sqrt{c} \sqrt{x^{2}}} + \frac{b^{2} x^{6}}{5 \sqrt{c} \sqrt{x^{2}}}"," ",0,"a**2*x**4/(3*sqrt(c)*sqrt(x**2)) + a*b*x**5/(2*sqrt(c)*sqrt(x**2)) + b**2*x**6/(5*sqrt(c)*sqrt(x**2))","A",0
829,1,61,0,0.647193," ","integrate(x**2*(b*x+a)**2/(c*x**2)**(1/2),x)","\frac{a^{2} x^{3}}{2 \sqrt{c} \sqrt{x^{2}}} + \frac{2 a b x^{4}}{3 \sqrt{c} \sqrt{x^{2}}} + \frac{b^{2} x^{5}}{4 \sqrt{c} \sqrt{x^{2}}}"," ",0,"a**2*x**3/(2*sqrt(c)*sqrt(x**2)) + 2*a*b*x**4/(3*sqrt(c)*sqrt(x**2)) + b**2*x**5/(4*sqrt(c)*sqrt(x**2))","A",0
830,1,56,0,0.540322," ","integrate(x*(b*x+a)**2/(c*x**2)**(1/2),x)","\frac{a^{2} x^{2}}{\sqrt{c} \sqrt{x^{2}}} + \frac{a b x^{3}}{\sqrt{c} \sqrt{x^{2}}} + \frac{b^{2} x^{4}}{3 \sqrt{c} \sqrt{x^{2}}}"," ",0,"a**2*x**2/(sqrt(c)*sqrt(x**2)) + a*b*x**3/(sqrt(c)*sqrt(x**2)) + b**2*x**4/(3*sqrt(c)*sqrt(x**2))","B",0
831,0,0,0,0.000000," ","integrate((b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{2}}{\sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)**2/sqrt(c*x**2), x)","F",0
832,0,0,0,0.000000," ","integrate((b*x+a)**2/x/(c*x**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{2}}{x \sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)**2/(x*sqrt(c*x**2)), x)","F",0
833,0,0,0,0.000000," ","integrate((b*x+a)**2/x**2/(c*x**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{2}}{x^{2} \sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)**2/(x**2*sqrt(c*x**2)), x)","F",0
834,1,53,0,0.662273," ","integrate((b*x+a)**2/x**3/(c*x**2)**(1/2),x)","- \frac{a^{2}}{3 \sqrt{c} x^{2} \sqrt{x^{2}}} - \frac{a b}{\sqrt{c} x \sqrt{x^{2}}} - \frac{b^{2}}{\sqrt{c} \sqrt{x^{2}}}"," ",0,"-a**2/(3*sqrt(c)*x**2*sqrt(x**2)) - a*b/(sqrt(c)*x*sqrt(x**2)) - b**2/(sqrt(c)*sqrt(x**2))","B",0
835,1,61,0,0.819286," ","integrate((b*x+a)**2/x**4/(c*x**2)**(1/2),x)","- \frac{a^{2}}{4 \sqrt{c} x^{3} \sqrt{x^{2}}} - \frac{2 a b}{3 \sqrt{c} x^{2} \sqrt{x^{2}}} - \frac{b^{2}}{2 \sqrt{c} x \sqrt{x^{2}}}"," ",0,"-a**2/(4*sqrt(c)*x**3*sqrt(x**2)) - 2*a*b/(3*sqrt(c)*x**2*sqrt(x**2)) - b**2/(2*sqrt(c)*x*sqrt(x**2))","A",0
836,1,56,0,0.804487," ","integrate(x**3*(b*x+a)**2/(c*x**2)**(3/2),x)","\frac{a^{2} x^{4}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{a b x^{5}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b^{2} x^{6}}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"a**2*x**4/(c**(3/2)*(x**2)**(3/2)) + a*b*x**5/(c**(3/2)*(x**2)**(3/2)) + b**2*x**6/(3*c**(3/2)*(x**2)**(3/2))","B",0
837,0,0,0,0.000000," ","integrate(x**2*(b*x+a)**2/(c*x**2)**(3/2),x)","\int \frac{x^{2} \left(a + b x\right)^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x)**2/(c*x**2)**(3/2), x)","F",0
838,0,0,0,0.000000," ","integrate(x*(b*x+a)**2/(c*x**2)**(3/2),x)","\int \frac{x \left(a + b x\right)^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*x)**2/(c*x**2)**(3/2), x)","F",0
839,0,0,0,0.000000," ","integrate((b*x+a)**2/(c*x**2)**(3/2),x)","\int \frac{\left(a + b x\right)^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)**2/(c*x**2)**(3/2), x)","F",0
840,1,53,0,0.667235," ","integrate((b*x+a)**2/x/(c*x**2)**(3/2),x)","- \frac{a^{2}}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{a b x}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b^{2} x^{2}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a**2/(3*c**(3/2)*(x**2)**(3/2)) - a*b*x/(c**(3/2)*(x**2)**(3/2)) - b**2*x**2/(c**(3/2)*(x**2)**(3/2))","B",0
841,1,56,0,0.812262," ","integrate((b*x+a)**2/x**2/(c*x**2)**(3/2),x)","- \frac{a^{2}}{4 c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}} - \frac{2 a b}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b^{2} x}{2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a**2/(4*c**(3/2)*x*(x**2)**(3/2)) - 2*a*b/(3*c**(3/2)*(x**2)**(3/2)) - b**2*x/(2*c**(3/2)*(x**2)**(3/2))","A",0
842,1,56,0,0.982187," ","integrate((b*x+a)**2/x**3/(c*x**2)**(3/2),x)","- \frac{a^{2}}{5 c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{a b}{2 c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b^{2}}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a**2/(5*c**(3/2)*x**2*(x**2)**(3/2)) - a*b/(2*c**(3/2)*x*(x**2)**(3/2)) - b**2/(3*c**(3/2)*(x**2)**(3/2))","A",0
843,1,61,0,1.183204," ","integrate((b*x+a)**2/x**4/(c*x**2)**(3/2),x)","- \frac{a^{2}}{6 c^{\frac{3}{2}} x^{3} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{2 a b}{5 c^{\frac{3}{2}} x^{2} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{b^{2}}{4 c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a**2/(6*c**(3/2)*x**3*(x**2)**(3/2)) - 2*a*b/(5*c**(3/2)*x**2*(x**2)**(3/2)) - b**2/(4*c**(3/2)*x*(x**2)**(3/2))","A",0
844,0,0,0,0.000000," ","integrate(x**3*(b*x+a)**2/(c*x**2)**(5/2),x)","\int \frac{x^{3} \left(a + b x\right)^{2}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*x)**2/(c*x**2)**(5/2), x)","F",0
845,0,0,0,0.000000," ","integrate(x**2*(b*x+a)**2/(c*x**2)**(5/2),x)","\int \frac{x^{2} \left(a + b x\right)^{2}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x)**2/(c*x**2)**(5/2), x)","F",0
846,1,58,0,0.956934," ","integrate(x*(b*x+a)**2/(c*x**2)**(5/2),x)","- \frac{a^{2} x^{2}}{3 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{a b x^{3}}{c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b^{2} x^{4}}{c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a**2*x**2/(3*c**(5/2)*(x**2)**(5/2)) - a*b*x**3/(c**(5/2)*(x**2)**(5/2)) - b**2*x**4/(c**(5/2)*(x**2)**(5/2))","B",0
847,1,61,0,0.963417," ","integrate((b*x+a)**2/(c*x**2)**(5/2),x)","- \frac{a^{2} x}{4 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{2 a b x^{2}}{3 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b^{2} x^{3}}{2 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a**2*x/(4*c**(5/2)*(x**2)**(5/2)) - 2*a*b*x**2/(3*c**(5/2)*(x**2)**(5/2)) - b**2*x**3/(2*c**(5/2)*(x**2)**(5/2))","A",0
848,1,56,0,1.153968," ","integrate((b*x+a)**2/x/(c*x**2)**(5/2),x)","- \frac{a^{2}}{5 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{a b x}{2 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b^{2} x^{2}}{3 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a**2/(5*c**(5/2)*(x**2)**(5/2)) - a*b*x/(2*c**(5/2)*(x**2)**(5/2)) - b**2*x**2/(3*c**(5/2)*(x**2)**(5/2))","A",0
849,1,56,0,1.399187," ","integrate((b*x+a)**2/x**2/(c*x**2)**(5/2),x)","- \frac{a^{2}}{6 c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}} - \frac{2 a b}{5 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b^{2} x}{4 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a**2/(6*c**(5/2)*x*(x**2)**(5/2)) - 2*a*b/(5*c**(5/2)*(x**2)**(5/2)) - b**2*x/(4*c**(5/2)*(x**2)**(5/2))","A",0
850,1,56,0,1.704321," ","integrate((b*x+a)**2/x**3/(c*x**2)**(5/2),x)","- \frac{a^{2}}{7 c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{a b}{3 c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b^{2}}{5 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a**2/(7*c**(5/2)*x**2*(x**2)**(5/2)) - a*b/(3*c**(5/2)*x*(x**2)**(5/2)) - b**2/(5*c**(5/2)*(x**2)**(5/2))","A",0
851,1,61,0,2.028826," ","integrate((b*x+a)**2/x**4/(c*x**2)**(5/2),x)","- \frac{a^{2}}{8 c^{\frac{5}{2}} x^{3} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{2 a b}{7 c^{\frac{5}{2}} x^{2} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{b^{2}}{6 c^{\frac{5}{2}} x \left(x^{2}\right)^{\frac{5}{2}}}"," ",0,"-a**2/(8*c**(5/2)*x**3*(x**2)**(5/2)) - 2*a*b/(7*c**(5/2)*x**2*(x**2)**(5/2)) - b**2/(6*c**(5/2)*x*(x**2)**(5/2))","A",0
852,0,0,0,0.000000," ","integrate(x**3*(c*x**2)**(1/2)/(b*x+a),x)","\int \frac{x^{3} \sqrt{c x^{2}}}{a + b x}\, dx"," ",0,"Integral(x**3*sqrt(c*x**2)/(a + b*x), x)","F",0
853,0,0,0,0.000000," ","integrate(x**2*(c*x**2)**(1/2)/(b*x+a),x)","\int \frac{x^{2} \sqrt{c x^{2}}}{a + b x}\, dx"," ",0,"Integral(x**2*sqrt(c*x**2)/(a + b*x), x)","F",0
854,0,0,0,0.000000," ","integrate(x*(c*x**2)**(1/2)/(b*x+a),x)","\int \frac{x \sqrt{c x^{2}}}{a + b x}\, dx"," ",0,"Integral(x*sqrt(c*x**2)/(a + b*x), x)","F",0
855,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/(b*x+a),x)","\int \frac{\sqrt{c x^{2}}}{a + b x}\, dx"," ",0,"Integral(sqrt(c*x**2)/(a + b*x), x)","F",0
856,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x/(b*x+a),x)","\int \frac{\sqrt{c x^{2}}}{x \left(a + b x\right)}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x*(a + b*x)), x)","F",0
857,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x**2/(b*x+a),x)","\int \frac{\sqrt{c x^{2}}}{x^{2} \left(a + b x\right)}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x**2*(a + b*x)), x)","F",0
858,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x**3/(b*x+a),x)","\int \frac{\sqrt{c x^{2}}}{x^{3} \left(a + b x\right)}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x**3*(a + b*x)), x)","F",0
859,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x**4/(b*x+a),x)","\int \frac{\sqrt{c x^{2}}}{x^{4} \left(a + b x\right)}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x**4*(a + b*x)), x)","F",0
860,0,0,0,0.000000," ","integrate(x*(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x \left(c x^{2}\right)^{\frac{3}{2}}}{a + b x}\, dx"," ",0,"Integral(x*(c*x**2)**(3/2)/(a + b*x), x)","F",0
861,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{a + b x}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(a + b*x), x)","F",0
862,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x*(a + b*x)), x)","F",0
863,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**2/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{2} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**2*(a + b*x)), x)","F",0
864,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**3/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{3} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**3*(a + b*x)), x)","F",0
865,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**4/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{4} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**4*(a + b*x)), x)","F",0
866,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**5/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{5} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**5*(a + b*x)), x)","F",0
867,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**6/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{6} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**6*(a + b*x)), x)","F",0
868,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**7/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{7} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**7*(a + b*x)), x)","F",0
869,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{a + b x}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(a + b*x), x)","F",0
870,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x*(a + b*x)), x)","F",0
871,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x**2/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{2} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x**2*(a + b*x)), x)","F",0
872,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x**3/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{3} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x**3*(a + b*x)), x)","F",0
873,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x**4/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{4} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x**4*(a + b*x)), x)","F",0
874,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x**5/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{5} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x**5*(a + b*x)), x)","F",0
875,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x**6/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{6} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x**6*(a + b*x)), x)","F",0
876,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)/x**7/(b*x+a),x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{7} \left(a + b x\right)}\, dx"," ",0,"Integral((c*x**2)**(5/2)/(x**7*(a + b*x)), x)","F",0
877,0,0,0,0.000000," ","integrate(x**4/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{x^{4}}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**4/(sqrt(c*x**2)*(a + b*x)), x)","F",0
878,0,0,0,0.000000," ","integrate(x**3/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**3/(sqrt(c*x**2)*(a + b*x)), x)","F",0
879,0,0,0,0.000000," ","integrate(x**2/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**2/(sqrt(c*x**2)*(a + b*x)), x)","F",0
880,0,0,0,0.000000," ","integrate(x/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{x}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x/(sqrt(c*x**2)*(a + b*x)), x)","F",0
881,0,0,0,0.000000," ","integrate(1/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{1}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(1/(sqrt(c*x**2)*(a + b*x)), x)","F",0
882,0,0,0,0.000000," ","integrate(1/x/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{1}{x \sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(1/(x*sqrt(c*x**2)*(a + b*x)), x)","F",0
883,0,0,0,0.000000," ","integrate(1/x**2/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*x**2)*(a + b*x)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/x**3/(b*x+a)/(c*x**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{c x^{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(1/(x**3*sqrt(c*x**2)*(a + b*x)), x)","F",0
885,0,0,0,0.000000," ","integrate(x**6/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**6/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
886,0,0,0,0.000000," ","integrate(x**5/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x^{5}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**5/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
887,0,0,0,0.000000," ","integrate(x**4/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x^{4}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**4/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
888,0,0,0,0.000000," ","integrate(x**3/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x^{3}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**3/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
889,0,0,0,0.000000," ","integrate(x**2/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x^{2}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x**2/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
890,0,0,0,0.000000," ","integrate(x/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{x}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(x/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
891,0,0,0,0.000000," ","integrate(1/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{1}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(1/((c*x**2)**(3/2)*(a + b*x)), x)","F",0
892,0,0,0,0.000000," ","integrate(1/x/(c*x**2)**(3/2)/(b*x+a),x)","\int \frac{1}{x \left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx"," ",0,"Integral(1/(x*(c*x**2)**(3/2)*(a + b*x)), x)","F",0
893,0,0,0,0.000000," ","integrate(x**3*(c*x**2)**(1/2)/(b*x+a)**2,x)","\int \frac{x^{3} \sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**3*sqrt(c*x**2)/(a + b*x)**2, x)","F",0
894,0,0,0,0.000000," ","integrate(x**2*(c*x**2)**(1/2)/(b*x+a)**2,x)","\int \frac{x^{2} \sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**2*sqrt(c*x**2)/(a + b*x)**2, x)","F",0
895,0,0,0,0.000000," ","integrate(x*(c*x**2)**(1/2)/(b*x+a)**2,x)","\int \frac{x \sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x*sqrt(c*x**2)/(a + b*x)**2, x)","F",0
896,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/(b*x+a)**2,x)","\int \frac{\sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)/(a + b*x)**2, x)","F",0
897,1,39,0,0.816090," ","integrate((c*x**2)**(1/2)/x/(b*x+a)**2,x)","\begin{cases} - \frac{\sqrt{c} \sqrt{x^{2}}}{a b x + b^{2} x^{2}} & \text{for}\: b \neq 0 \\\frac{\sqrt{c} \sqrt{x^{2}}}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(c)*sqrt(x**2)/(a*b*x + b**2*x**2), Ne(b, 0)), (sqrt(c)*sqrt(x**2)/a**2, True))","A",0
898,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x**2/(b*x+a)**2,x)","\int \frac{\sqrt{c x^{2}}}{x^{2} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x**2*(a + b*x)**2), x)","F",0
899,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x**3/(b*x+a)**2,x)","\int \frac{\sqrt{c x^{2}}}{x^{3} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x**3*(a + b*x)**2), x)","F",0
900,0,0,0,0.000000," ","integrate((c*x**2)**(1/2)/x**4/(b*x+a)**2,x)","\int \frac{\sqrt{c x^{2}}}{x^{4} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)/(x**4*(a + b*x)**2), x)","F",0
901,0,0,0,0.000000," ","integrate(x*(c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{x \left(c x^{2}\right)^{\frac{3}{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x*(c*x**2)**(3/2)/(a + b*x)**2, x)","F",0
902,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(a + b*x)**2, x)","F",0
903,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x/(b*x+a)**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x \left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x*(a + b*x)**2), x)","F",0
904,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**2/(b*x+a)**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{2} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**2*(a + b*x)**2), x)","F",0
905,1,44,0,2.225589," ","integrate((c*x**2)**(3/2)/x**3/(b*x+a)**2,x)","\begin{cases} - \frac{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{a b x^{3} + b^{2} x^{4}} & \text{for}\: b \neq 0 \\\frac{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{a^{2} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c**(3/2)*(x**2)**(3/2)/(a*b*x**3 + b**2*x**4), Ne(b, 0)), (c**(3/2)*(x**2)**(3/2)/(a**2*x**2), True))","A",0
906,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**4/(b*x+a)**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{4} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**4*(a + b*x)**2), x)","F",0
907,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**5/(b*x+a)**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{5} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**5*(a + b*x)**2), x)","F",0
908,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)/x**6/(b*x+a)**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{6} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c*x**2)**(3/2)/(x**6*(a + b*x)**2), x)","F",0
909,0,0,0,0.000000," ","integrate(x**5/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{x^{5}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**5/(sqrt(c*x**2)*(a + b*x)**2), x)","F",0
910,0,0,0,0.000000," ","integrate(x**4/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{x^{4}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**4/(sqrt(c*x**2)*(a + b*x)**2), x)","F",0
911,0,0,0,0.000000," ","integrate(x**3/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**3/(sqrt(c*x**2)*(a + b*x)**2), x)","F",0
912,0,0,0,0.000000," ","integrate(x**2/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**2/(sqrt(c*x**2)*(a + b*x)**2), x)","F",0
913,1,85,0,1.169129," ","integrate(x/(b*x+a)**2/(c*x**2)**(1/2),x)","\begin{cases} \frac{\tilde{\infty}}{\sqrt{c} \sqrt{x^{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\tilde{\infty} x^{2}}{\sqrt{c} \sqrt{x^{2}}} & \text{for}\: a = - b x \\\frac{x^{2}}{a^{2} \sqrt{c} \sqrt{x^{2}}} & \text{for}\: b = 0 \\- \frac{x}{a b \sqrt{c} \sqrt{x^{2}} + b^{2} \sqrt{c} x \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/(sqrt(c)*sqrt(x**2)), Eq(a, 0) & Eq(b, 0)), (zoo*x**2/(sqrt(c)*sqrt(x**2)), Eq(a, -b*x)), (x**2/(a**2*sqrt(c)*sqrt(x**2)), Eq(b, 0)), (-x/(a*b*sqrt(c)*sqrt(x**2) + b**2*sqrt(c)*x*sqrt(x**2)), True))","A",0
914,0,0,0,0.000000," ","integrate(1/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{1}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(c*x**2)*(a + b*x)**2), x)","F",0
915,0,0,0,0.000000," ","integrate(1/x/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{1}{x \sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(1/(x*sqrt(c*x**2)*(a + b*x)**2), x)","F",0
916,0,0,0,0.000000," ","integrate(1/x**2/(b*x+a)**2/(c*x**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*sqrt(c*x**2)*(a + b*x)**2), x)","F",0
917,0,0,0,0.000000," ","integrate(x**5/(c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{x^{5}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**5/((c*x**2)**(3/2)*(a + b*x)**2), x)","F",0
918,0,0,0,0.000000," ","integrate(x**4/(c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{x^{4}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**4/((c*x**2)**(3/2)*(a + b*x)**2), x)","F",0
919,1,90,0,1.939990," ","integrate(x**3/(c*x**2)**(3/2)/(b*x+a)**2,x)","\begin{cases} \frac{\tilde{\infty} x^{2}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: a = 0 \wedge b = 0 \\\frac{\tilde{\infty} x^{4}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: a = - b x \\\frac{x^{4}}{a^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \\- \frac{x^{3}}{a b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}} + b^{2} c^{\frac{3}{2}} x \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x**2/(c**(3/2)*(x**2)**(3/2)), Eq(a, 0) & Eq(b, 0)), (zoo*x**4/(c**(3/2)*(x**2)**(3/2)), Eq(a, -b*x)), (x**4/(a**2*c**(3/2)*(x**2)**(3/2)), Eq(b, 0)), (-x**3/(a*b*c**(3/2)*(x**2)**(3/2) + b**2*c**(3/2)*x*(x**2)**(3/2)), True))","A",0
920,0,0,0,0.000000," ","integrate(x**2/(c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{x^{2}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x**2/((c*x**2)**(3/2)*(a + b*x)**2), x)","F",0
921,0,0,0,0.000000," ","integrate(x/(c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{x}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(x/((c*x**2)**(3/2)*(a + b*x)**2), x)","F",0
922,0,0,0,0.000000," ","integrate(1/(c*x**2)**(3/2)/(b*x+a)**2,x)","\int \frac{1}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx"," ",0,"Integral(1/((c*x**2)**(3/2)*(a + b*x)**2), x)","F",0
923,0,0,0,0.000000," ","integrate(x**2*(b*x+a)**n*(c*x**2)**(1/2),x)","\begin{cases} \frac{a^{n} \sqrt{c} x^{3} \sqrt{x^{2}}}{4} & \text{for}\: b = 0 \\\int \frac{x^{2} \sqrt{c x^{2}}}{\left(a + b x\right)^{4}}\, dx & \text{for}\: n = -4 \\\int \frac{x^{2} \sqrt{c x^{2}}}{\left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{2} \sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{2} \sqrt{c x^{2}}}{a + b x}\, dx & \text{for}\: n = -1 \\- \frac{6 a^{4} \sqrt{c} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{6 a^{3} b \sqrt{c} n x \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} - \frac{3 a^{2} b^{2} \sqrt{c} n^{2} x^{2} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} - \frac{3 a^{2} b^{2} \sqrt{c} n x^{2} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{a b^{3} \sqrt{c} n^{3} x^{3} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{3 a b^{3} \sqrt{c} n^{2} x^{3} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{2 a b^{3} \sqrt{c} n x^{3} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{b^{4} \sqrt{c} n^{3} x^{4} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{6 b^{4} \sqrt{c} n^{2} x^{4} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{11 b^{4} \sqrt{c} n x^{4} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} + \frac{6 b^{4} \sqrt{c} x^{4} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{4} n^{4} x + 10 b^{4} n^{3} x + 35 b^{4} n^{2} x + 50 b^{4} n x + 24 b^{4} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*sqrt(c)*x**3*sqrt(x**2)/4, Eq(b, 0)), (Integral(x**2*sqrt(c*x**2)/(a + b*x)**4, x), Eq(n, -4)), (Integral(x**2*sqrt(c*x**2)/(a + b*x)**3, x), Eq(n, -3)), (Integral(x**2*sqrt(c*x**2)/(a + b*x)**2, x), Eq(n, -2)), (Integral(x**2*sqrt(c*x**2)/(a + b*x), x), Eq(n, -1)), (-6*a**4*sqrt(c)*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + 6*a**3*b*sqrt(c)*n*x*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) - 3*a**2*b**2*sqrt(c)*n**2*x**2*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) - 3*a**2*b**2*sqrt(c)*n*x**2*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + a*b**3*sqrt(c)*n**3*x**3*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + 3*a*b**3*sqrt(c)*n**2*x**3*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + 2*a*b**3*sqrt(c)*n*x**3*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + b**4*sqrt(c)*n**3*x**4*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + 6*b**4*sqrt(c)*n**2*x**4*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + 11*b**4*sqrt(c)*n*x**4*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x) + 6*b**4*sqrt(c)*x**4*(a + b*x)**n*sqrt(x**2)/(b**4*n**4*x + 10*b**4*n**3*x + 35*b**4*n**2*x + 50*b**4*n*x + 24*b**4*x), True))","F",0
924,0,0,0,0.000000," ","integrate(x*(b*x+a)**n*(c*x**2)**(1/2),x)","\begin{cases} \frac{a^{n} \sqrt{c} x^{2} \sqrt{x^{2}}}{3} & \text{for}\: b = 0 \\\int \frac{x \sqrt{c x^{2}}}{\left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x \sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x \sqrt{c x^{2}}}{a + b x}\, dx & \text{for}\: n = -1 \\\frac{2 a^{3} \sqrt{c} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} - \frac{2 a^{2} b \sqrt{c} n x \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} + \frac{a b^{2} \sqrt{c} n^{2} x^{2} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} + \frac{a b^{2} \sqrt{c} n x^{2} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} + \frac{b^{3} \sqrt{c} n^{2} x^{3} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} + \frac{3 b^{3} \sqrt{c} n x^{3} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} + \frac{2 b^{3} \sqrt{c} x^{3} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{3} n^{3} x + 6 b^{3} n^{2} x + 11 b^{3} n x + 6 b^{3} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*sqrt(c)*x**2*sqrt(x**2)/3, Eq(b, 0)), (Integral(x*sqrt(c*x**2)/(a + b*x)**3, x), Eq(n, -3)), (Integral(x*sqrt(c*x**2)/(a + b*x)**2, x), Eq(n, -2)), (Integral(x*sqrt(c*x**2)/(a + b*x), x), Eq(n, -1)), (2*a**3*sqrt(c)*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x) - 2*a**2*b*sqrt(c)*n*x*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x) + a*b**2*sqrt(c)*n**2*x**2*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x) + a*b**2*sqrt(c)*n*x**2*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x) + b**3*sqrt(c)*n**2*x**3*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x) + 3*b**3*sqrt(c)*n*x**3*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x) + 2*b**3*sqrt(c)*x**3*(a + b*x)**n*sqrt(x**2)/(b**3*n**3*x + 6*b**3*n**2*x + 11*b**3*n*x + 6*b**3*x), True))","F",0
925,0,0,0,0.000000," ","integrate((b*x+a)**n*(c*x**2)**(1/2),x)","\begin{cases} \frac{a^{n} \sqrt{c} x \sqrt{x^{2}}}{2} & \text{for}\: b = 0 \\\int \frac{\sqrt{c x^{2}}}{\left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{\sqrt{c x^{2}}}{a + b x}\, dx & \text{for}\: n = -1 \\- \frac{a^{2} \sqrt{c} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{2} n^{2} x + 3 b^{2} n x + 2 b^{2} x} + \frac{a b \sqrt{c} n x \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{2} n^{2} x + 3 b^{2} n x + 2 b^{2} x} + \frac{b^{2} \sqrt{c} n x^{2} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{2} n^{2} x + 3 b^{2} n x + 2 b^{2} x} + \frac{b^{2} \sqrt{c} x^{2} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b^{2} n^{2} x + 3 b^{2} n x + 2 b^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*sqrt(c)*x*sqrt(x**2)/2, Eq(b, 0)), (Integral(sqrt(c*x**2)/(a + b*x)**2, x), Eq(n, -2)), (Integral(sqrt(c*x**2)/(a + b*x), x), Eq(n, -1)), (-a**2*sqrt(c)*(a + b*x)**n*sqrt(x**2)/(b**2*n**2*x + 3*b**2*n*x + 2*b**2*x) + a*b*sqrt(c)*n*x*(a + b*x)**n*sqrt(x**2)/(b**2*n**2*x + 3*b**2*n*x + 2*b**2*x) + b**2*sqrt(c)*n*x**2*(a + b*x)**n*sqrt(x**2)/(b**2*n**2*x + 3*b**2*n*x + 2*b**2*x) + b**2*sqrt(c)*x**2*(a + b*x)**n*sqrt(x**2)/(b**2*n**2*x + 3*b**2*n*x + 2*b**2*x), True))","F",0
926,0,0,0,0.000000," ","integrate((b*x+a)**n*(c*x**2)**(1/2)/x,x)","\begin{cases} \frac{\sqrt{c} \sqrt{x^{2}}}{a} & \text{for}\: b = 0 \wedge n = -1 \\a^{n} \sqrt{c} \sqrt{x^{2}} & \text{for}\: b = 0 \\\int \frac{\sqrt{c x^{2}}}{x \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{a \sqrt{c} \left(a + b x\right)^{n} \sqrt{x^{2}}}{b n x + b x} + \frac{b \sqrt{c} x \left(a + b x\right)^{n} \sqrt{x^{2}}}{b n x + b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(c)*sqrt(x**2)/a, Eq(b, 0) & Eq(n, -1)), (a**n*sqrt(c)*sqrt(x**2), Eq(b, 0)), (Integral(sqrt(c*x**2)/(x*(a + b*x)), x), Eq(n, -1)), (a*sqrt(c)*(a + b*x)**n*sqrt(x**2)/(b*n*x + b*x) + b*sqrt(c)*x*(a + b*x)**n*sqrt(x**2)/(b*n*x + b*x), True))","F",0
927,0,0,0,0.000000," ","integrate((b*x+a)**n*(c*x**2)**(1/2)/x**2,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)^{n}}{x^{2}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)**n/x**2, x)","F",0
928,0,0,0,0.000000," ","integrate((b*x+a)**n*(c*x**2)**(1/2)/x**3,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)^{n}}{x^{3}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)**n/x**3, x)","F",0
929,0,0,0,0.000000," ","integrate((b*x+a)**n*(c*x**2)**(1/2)/x**4,x)","\int \frac{\sqrt{c x^{2}} \left(a + b x\right)^{n}}{x^{4}}\, dx"," ",0,"Integral(sqrt(c*x**2)*(a + b*x)**n/x**4, x)","F",0
930,0,0,0,0.000000," ","integrate(x*(c*x**2)**(3/2)*(b*x+a)**n,x)","\int x \left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{n}\, dx"," ",0,"Integral(x*(c*x**2)**(3/2)*(a + b*x)**n, x)","F",0
931,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n,x)","\int \left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{n}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)**n, x)","F",0
932,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n/x,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{n}}{x}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)**n/x, x)","F",0
933,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n/x**2,x)","\begin{cases} \frac{a^{n} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{2 x} & \text{for}\: b = 0 \\\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{2} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{2} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{a^{2} c^{\frac{3}{2}} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{3}{2}}}{b^{2} n^{2} x^{3} + 3 b^{2} n x^{3} + 2 b^{2} x^{3}} + \frac{a b c^{\frac{3}{2}} n x \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{3}{2}}}{b^{2} n^{2} x^{3} + 3 b^{2} n x^{3} + 2 b^{2} x^{3}} + \frac{b^{2} c^{\frac{3}{2}} n x^{2} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{3}{2}}}{b^{2} n^{2} x^{3} + 3 b^{2} n x^{3} + 2 b^{2} x^{3}} + \frac{b^{2} c^{\frac{3}{2}} x^{2} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{3}{2}}}{b^{2} n^{2} x^{3} + 3 b^{2} n x^{3} + 2 b^{2} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*c**(3/2)*(x**2)**(3/2)/(2*x), Eq(b, 0)), (Integral((c*x**2)**(3/2)/(x**2*(a + b*x)**2), x), Eq(n, -2)), (Integral((c*x**2)**(3/2)/(x**2*(a + b*x)), x), Eq(n, -1)), (-a**2*c**(3/2)*(a + b*x)**n*(x**2)**(3/2)/(b**2*n**2*x**3 + 3*b**2*n*x**3 + 2*b**2*x**3) + a*b*c**(3/2)*n*x*(a + b*x)**n*(x**2)**(3/2)/(b**2*n**2*x**3 + 3*b**2*n*x**3 + 2*b**2*x**3) + b**2*c**(3/2)*n*x**2*(a + b*x)**n*(x**2)**(3/2)/(b**2*n**2*x**3 + 3*b**2*n*x**3 + 2*b**2*x**3) + b**2*c**(3/2)*x**2*(a + b*x)**n*(x**2)**(3/2)/(b**2*n**2*x**3 + 3*b**2*n*x**3 + 2*b**2*x**3), True))","F",0
934,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n/x**3,x)","\begin{cases} \frac{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{a x^{2}} & \text{for}\: b = 0 \wedge n = -1 \\\frac{a^{n} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}}{x^{2}} & \text{for}\: b = 0 \\\int \frac{\left(c x^{2}\right)^{\frac{3}{2}}}{x^{3} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{a c^{\frac{3}{2}} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{3}{2}}}{b n x^{3} + b x^{3}} + \frac{b c^{\frac{3}{2}} x \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{3}{2}}}{b n x^{3} + b x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**(3/2)*(x**2)**(3/2)/(a*x**2), Eq(b, 0) & Eq(n, -1)), (a**n*c**(3/2)*(x**2)**(3/2)/x**2, Eq(b, 0)), (Integral((c*x**2)**(3/2)/(x**3*(a + b*x)), x), Eq(n, -1)), (a*c**(3/2)*(a + b*x)**n*(x**2)**(3/2)/(b*n*x**3 + b*x**3) + b*c**(3/2)*x*(a + b*x)**n*(x**2)**(3/2)/(b*n*x**3 + b*x**3), True))","F",0
935,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n/x**4,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{n}}{x^{4}}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)**n/x**4, x)","F",0
936,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n/x**5,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{n}}{x^{5}}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)**n/x**5, x)","F",0
937,0,0,0,0.000000," ","integrate((c*x**2)**(3/2)*(b*x+a)**n/x**6,x)","\int \frac{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{n}}{x^{6}}\, dx"," ",0,"Integral((c*x**2)**(3/2)*(a + b*x)**n/x**6, x)","F",0
938,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n,x)","\int \left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{n}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**n, x)","F",0
939,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x,x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{n}}{x}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**n/x, x)","F",0
940,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x**2,x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{n}}{x^{2}}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**n/x**2, x)","F",0
941,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x**3,x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{n}}{x^{3}}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**n/x**3, x)","F",0
942,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x**4,x)","\begin{cases} \frac{a^{n} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{2 x^{3}} & \text{for}\: b = 0 \\\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{4} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{4} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{a^{2} c^{\frac{5}{2}} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{5}{2}}}{b^{2} n^{2} x^{5} + 3 b^{2} n x^{5} + 2 b^{2} x^{5}} + \frac{a b c^{\frac{5}{2}} n x \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{5}{2}}}{b^{2} n^{2} x^{5} + 3 b^{2} n x^{5} + 2 b^{2} x^{5}} + \frac{b^{2} c^{\frac{5}{2}} n x^{2} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{5}{2}}}{b^{2} n^{2} x^{5} + 3 b^{2} n x^{5} + 2 b^{2} x^{5}} + \frac{b^{2} c^{\frac{5}{2}} x^{2} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{5}{2}}}{b^{2} n^{2} x^{5} + 3 b^{2} n x^{5} + 2 b^{2} x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*c**(5/2)*(x**2)**(5/2)/(2*x**3), Eq(b, 0)), (Integral((c*x**2)**(5/2)/(x**4*(a + b*x)**2), x), Eq(n, -2)), (Integral((c*x**2)**(5/2)/(x**4*(a + b*x)), x), Eq(n, -1)), (-a**2*c**(5/2)*(a + b*x)**n*(x**2)**(5/2)/(b**2*n**2*x**5 + 3*b**2*n*x**5 + 2*b**2*x**5) + a*b*c**(5/2)*n*x*(a + b*x)**n*(x**2)**(5/2)/(b**2*n**2*x**5 + 3*b**2*n*x**5 + 2*b**2*x**5) + b**2*c**(5/2)*n*x**2*(a + b*x)**n*(x**2)**(5/2)/(b**2*n**2*x**5 + 3*b**2*n*x**5 + 2*b**2*x**5) + b**2*c**(5/2)*x**2*(a + b*x)**n*(x**2)**(5/2)/(b**2*n**2*x**5 + 3*b**2*n*x**5 + 2*b**2*x**5), True))","F",0
943,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x**5,x)","\begin{cases} \frac{c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{a x^{4}} & \text{for}\: b = 0 \wedge n = -1 \\\frac{a^{n} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}}{x^{4}} & \text{for}\: b = 0 \\\int \frac{\left(c x^{2}\right)^{\frac{5}{2}}}{x^{5} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{a c^{\frac{5}{2}} \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{5}{2}}}{b n x^{5} + b x^{5}} + \frac{b c^{\frac{5}{2}} x \left(a + b x\right)^{n} \left(x^{2}\right)^{\frac{5}{2}}}{b n x^{5} + b x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**(5/2)*(x**2)**(5/2)/(a*x**4), Eq(b, 0) & Eq(n, -1)), (a**n*c**(5/2)*(x**2)**(5/2)/x**4, Eq(b, 0)), (Integral((c*x**2)**(5/2)/(x**5*(a + b*x)), x), Eq(n, -1)), (a*c**(5/2)*(a + b*x)**n*(x**2)**(5/2)/(b*n*x**5 + b*x**5) + b*c**(5/2)*x*(a + b*x)**n*(x**2)**(5/2)/(b*n*x**5 + b*x**5), True))","F",0
944,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x**6,x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{n}}{x^{6}}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**n/x**6, x)","F",0
945,0,0,0,0.000000," ","integrate((c*x**2)**(5/2)*(b*x+a)**n/x**7,x)","\int \frac{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{n}}{x^{7}}\, dx"," ",0,"Integral((c*x**2)**(5/2)*(a + b*x)**n/x**7, x)","F",0
946,0,0,0,0.000000," ","integrate(x**4*(b*x+a)**n/(c*x**2)**(1/2),x)","\begin{cases} \frac{a^{n} x^{5}}{4 \sqrt{c} \sqrt{x^{2}}} & \text{for}\: b = 0 \\\int \frac{x^{4}}{\sqrt{c x^{2}} \left(a + b x\right)^{4}}\, dx & \text{for}\: n = -4 \\\int \frac{x^{4}}{\sqrt{c x^{2}} \left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{4}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{4}}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{6 a^{4} x \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{6 a^{3} b n x^{2} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} - \frac{3 a^{2} b^{2} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} - \frac{3 a^{2} b^{2} n x^{3} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{a b^{3} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{3 a b^{3} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{2 a b^{3} n x^{4} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{b^{4} n^{3} x^{5} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{6 b^{4} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{11 b^{4} n x^{5} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} + \frac{6 b^{4} x^{5} \left(a + b x\right)^{n}}{b^{4} \sqrt{c} n^{4} \sqrt{x^{2}} + 10 b^{4} \sqrt{c} n^{3} \sqrt{x^{2}} + 35 b^{4} \sqrt{c} n^{2} \sqrt{x^{2}} + 50 b^{4} \sqrt{c} n \sqrt{x^{2}} + 24 b^{4} \sqrt{c} \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**5/(4*sqrt(c)*sqrt(x**2)), Eq(b, 0)), (Integral(x**4/(sqrt(c*x**2)*(a + b*x)**4), x), Eq(n, -4)), (Integral(x**4/(sqrt(c*x**2)*(a + b*x)**3), x), Eq(n, -3)), (Integral(x**4/(sqrt(c*x**2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**4/(sqrt(c*x**2)*(a + b*x)), x), Eq(n, -1)), (-6*a**4*x*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + 6*a**3*b*n*x**2*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) - 3*a**2*b**2*n**2*x**3*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) - 3*a**2*b**2*n*x**3*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + a*b**3*n**3*x**4*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + 3*a*b**3*n**2*x**4*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + 2*a*b**3*n*x**4*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + b**4*n**3*x**5*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + 6*b**4*n**2*x**5*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + 11*b**4*n*x**5*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)) + 6*b**4*x**5*(a + b*x)**n/(b**4*sqrt(c)*n**4*sqrt(x**2) + 10*b**4*sqrt(c)*n**3*sqrt(x**2) + 35*b**4*sqrt(c)*n**2*sqrt(x**2) + 50*b**4*sqrt(c)*n*sqrt(x**2) + 24*b**4*sqrt(c)*sqrt(x**2)), True))","F",0
947,0,0,0,0.000000," ","integrate(x**3*(b*x+a)**n/(c*x**2)**(1/2),x)","\begin{cases} \frac{a^{n} x^{4}}{3 \sqrt{c} \sqrt{x^{2}}} & \text{for}\: b = 0 \\\int \frac{x^{3}}{\sqrt{c x^{2}} \left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{3}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{3}}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{2 a^{3} x \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} - \frac{2 a^{2} b n x^{2} \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} + \frac{a b^{2} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} + \frac{a b^{2} n x^{3} \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} + \frac{b^{3} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} + \frac{3 b^{3} n x^{4} \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} + \frac{2 b^{3} x^{4} \left(a + b x\right)^{n}}{b^{3} \sqrt{c} n^{3} \sqrt{x^{2}} + 6 b^{3} \sqrt{c} n^{2} \sqrt{x^{2}} + 11 b^{3} \sqrt{c} n \sqrt{x^{2}} + 6 b^{3} \sqrt{c} \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**4/(3*sqrt(c)*sqrt(x**2)), Eq(b, 0)), (Integral(x**3/(sqrt(c*x**2)*(a + b*x)**3), x), Eq(n, -3)), (Integral(x**3/(sqrt(c*x**2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**3/(sqrt(c*x**2)*(a + b*x)), x), Eq(n, -1)), (2*a**3*x*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)) - 2*a**2*b*n*x**2*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)) + a*b**2*n**2*x**3*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)) + a*b**2*n*x**3*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)) + b**3*n**2*x**4*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)) + 3*b**3*n*x**4*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)) + 2*b**3*x**4*(a + b*x)**n/(b**3*sqrt(c)*n**3*sqrt(x**2) + 6*b**3*sqrt(c)*n**2*sqrt(x**2) + 11*b**3*sqrt(c)*n*sqrt(x**2) + 6*b**3*sqrt(c)*sqrt(x**2)), True))","F",0
948,0,0,0,0.000000," ","integrate(x**2*(b*x+a)**n/(c*x**2)**(1/2),x)","\begin{cases} \frac{a^{n} x^{3}}{2 \sqrt{c} \sqrt{x^{2}}} & \text{for}\: b = 0 \\\int \frac{x^{2}}{\sqrt{c x^{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{2}}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{a^{2} x \left(a + b x\right)^{n}}{b^{2} \sqrt{c} n^{2} \sqrt{x^{2}} + 3 b^{2} \sqrt{c} n \sqrt{x^{2}} + 2 b^{2} \sqrt{c} \sqrt{x^{2}}} + \frac{a b n x^{2} \left(a + b x\right)^{n}}{b^{2} \sqrt{c} n^{2} \sqrt{x^{2}} + 3 b^{2} \sqrt{c} n \sqrt{x^{2}} + 2 b^{2} \sqrt{c} \sqrt{x^{2}}} + \frac{b^{2} n x^{3} \left(a + b x\right)^{n}}{b^{2} \sqrt{c} n^{2} \sqrt{x^{2}} + 3 b^{2} \sqrt{c} n \sqrt{x^{2}} + 2 b^{2} \sqrt{c} \sqrt{x^{2}}} + \frac{b^{2} x^{3} \left(a + b x\right)^{n}}{b^{2} \sqrt{c} n^{2} \sqrt{x^{2}} + 3 b^{2} \sqrt{c} n \sqrt{x^{2}} + 2 b^{2} \sqrt{c} \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**3/(2*sqrt(c)*sqrt(x**2)), Eq(b, 0)), (Integral(x**2/(sqrt(c*x**2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**2/(sqrt(c*x**2)*(a + b*x)), x), Eq(n, -1)), (-a**2*x*(a + b*x)**n/(b**2*sqrt(c)*n**2*sqrt(x**2) + 3*b**2*sqrt(c)*n*sqrt(x**2) + 2*b**2*sqrt(c)*sqrt(x**2)) + a*b*n*x**2*(a + b*x)**n/(b**2*sqrt(c)*n**2*sqrt(x**2) + 3*b**2*sqrt(c)*n*sqrt(x**2) + 2*b**2*sqrt(c)*sqrt(x**2)) + b**2*n*x**3*(a + b*x)**n/(b**2*sqrt(c)*n**2*sqrt(x**2) + 3*b**2*sqrt(c)*n*sqrt(x**2) + 2*b**2*sqrt(c)*sqrt(x**2)) + b**2*x**3*(a + b*x)**n/(b**2*sqrt(c)*n**2*sqrt(x**2) + 3*b**2*sqrt(c)*n*sqrt(x**2) + 2*b**2*sqrt(c)*sqrt(x**2)), True))","F",0
949,0,0,0,0.000000," ","integrate(x*(b*x+a)**n/(c*x**2)**(1/2),x)","\begin{cases} \frac{x^{2}}{a \sqrt{c} \sqrt{x^{2}}} & \text{for}\: b = 0 \wedge n = -1 \\\frac{a^{n} x^{2}}{\sqrt{c} \sqrt{x^{2}}} & \text{for}\: b = 0 \\\int \frac{x}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{a x \left(a + b x\right)^{n}}{b \sqrt{c} n \sqrt{x^{2}} + b \sqrt{c} \sqrt{x^{2}}} + \frac{b x^{2} \left(a + b x\right)^{n}}{b \sqrt{c} n \sqrt{x^{2}} + b \sqrt{c} \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2/(a*sqrt(c)*sqrt(x**2)), Eq(b, 0) & Eq(n, -1)), (a**n*x**2/(sqrt(c)*sqrt(x**2)), Eq(b, 0)), (Integral(x/(sqrt(c*x**2)*(a + b*x)), x), Eq(n, -1)), (a*x*(a + b*x)**n/(b*sqrt(c)*n*sqrt(x**2) + b*sqrt(c)*sqrt(x**2)) + b*x**2*(a + b*x)**n/(b*sqrt(c)*n*sqrt(x**2) + b*sqrt(c)*sqrt(x**2)), True))","F",0
950,0,0,0,0.000000," ","integrate((b*x+a)**n/(c*x**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{n}}{\sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)**n/sqrt(c*x**2), x)","F",0
951,0,0,0,0.000000," ","integrate((b*x+a)**n/x/(c*x**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{n}}{x \sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)**n/(x*sqrt(c*x**2)), x)","F",0
952,0,0,0,0.000000," ","integrate((b*x+a)**n/x**2/(c*x**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{n}}{x^{2} \sqrt{c x^{2}}}\, dx"," ",0,"Integral((a + b*x)**n/(x**2*sqrt(c*x**2)), x)","F",0
953,0,0,0,0.000000," ","integrate(x**6*(b*x+a)**n/(c*x**2)**(3/2),x)","\begin{cases} \frac{a^{n} x^{7}}{4 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{4}}\, dx & \text{for}\: n = -4 \\\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{6 a^{4} x^{3} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{6 a^{3} b n x^{4} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{3 a^{2} b^{2} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{3 a^{2} b^{2} n x^{5} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{a b^{3} n^{3} x^{6} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{3 a b^{3} n^{2} x^{6} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{2 a b^{3} n x^{6} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b^{4} n^{3} x^{7} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{6 b^{4} n^{2} x^{7} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{11 b^{4} n x^{7} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{6 b^{4} x^{7} \left(a + b x\right)^{n}}{b^{4} c^{\frac{3}{2}} n^{4} \left(x^{2}\right)^{\frac{3}{2}} + 10 b^{4} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 35 b^{4} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 50 b^{4} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 24 b^{4} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**7/(4*c**(3/2)*(x**2)**(3/2)), Eq(b, 0)), (Integral(x**6/((c*x**2)**(3/2)*(a + b*x)**4), x), Eq(n, -4)), (Integral(x**6/((c*x**2)**(3/2)*(a + b*x)**3), x), Eq(n, -3)), (Integral(x**6/((c*x**2)**(3/2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**6/((c*x**2)**(3/2)*(a + b*x)), x), Eq(n, -1)), (-6*a**4*x**3*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + 6*a**3*b*n*x**4*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) - 3*a**2*b**2*n**2*x**5*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) - 3*a**2*b**2*n*x**5*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + a*b**3*n**3*x**6*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + 3*a*b**3*n**2*x**6*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + 2*a*b**3*n*x**6*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + b**4*n**3*x**7*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + 6*b**4*n**2*x**7*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + 11*b**4*n*x**7*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)) + 6*b**4*x**7*(a + b*x)**n/(b**4*c**(3/2)*n**4*(x**2)**(3/2) + 10*b**4*c**(3/2)*n**3*(x**2)**(3/2) + 35*b**4*c**(3/2)*n**2*(x**2)**(3/2) + 50*b**4*c**(3/2)*n*(x**2)**(3/2) + 24*b**4*c**(3/2)*(x**2)**(3/2)), True))","F",0
954,0,0,0,0.000000," ","integrate(x**5*(b*x+a)**n/(c*x**2)**(3/2),x)","\begin{cases} \frac{a^{n} x^{6}}{3 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{5}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{5}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{5}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{2 a^{3} x^{3} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{2 a^{2} b n x^{4} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{a b^{2} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{a b^{2} n x^{5} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b^{3} n^{2} x^{6} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{3 b^{3} n x^{6} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{2 b^{3} x^{6} \left(a + b x\right)^{n}}{b^{3} c^{\frac{3}{2}} n^{3} \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 11 b^{3} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 6 b^{3} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**6/(3*c**(3/2)*(x**2)**(3/2)), Eq(b, 0)), (Integral(x**5/((c*x**2)**(3/2)*(a + b*x)**3), x), Eq(n, -3)), (Integral(x**5/((c*x**2)**(3/2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**5/((c*x**2)**(3/2)*(a + b*x)), x), Eq(n, -1)), (2*a**3*x**3*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)) - 2*a**2*b*n*x**4*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)) + a*b**2*n**2*x**5*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)) + a*b**2*n*x**5*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)) + b**3*n**2*x**6*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)) + 3*b**3*n*x**6*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)) + 2*b**3*x**6*(a + b*x)**n/(b**3*c**(3/2)*n**3*(x**2)**(3/2) + 6*b**3*c**(3/2)*n**2*(x**2)**(3/2) + 11*b**3*c**(3/2)*n*(x**2)**(3/2) + 6*b**3*c**(3/2)*(x**2)**(3/2)), True))","F",0
955,0,0,0,0.000000," ","integrate(x**4*(b*x+a)**n/(c*x**2)**(3/2),x)","\begin{cases} \frac{a^{n} x^{5}}{2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{4}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{4}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{a^{2} x^{3} \left(a + b x\right)^{n}}{b^{2} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 3 b^{2} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 2 b^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{a b n x^{4} \left(a + b x\right)^{n}}{b^{2} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 3 b^{2} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 2 b^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b^{2} n x^{5} \left(a + b x\right)^{n}}{b^{2} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 3 b^{2} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 2 b^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b^{2} x^{5} \left(a + b x\right)^{n}}{b^{2} c^{\frac{3}{2}} n^{2} \left(x^{2}\right)^{\frac{3}{2}} + 3 b^{2} c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + 2 b^{2} c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**5/(2*c**(3/2)*(x**2)**(3/2)), Eq(b, 0)), (Integral(x**4/((c*x**2)**(3/2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**4/((c*x**2)**(3/2)*(a + b*x)), x), Eq(n, -1)), (-a**2*x**3*(a + b*x)**n/(b**2*c**(3/2)*n**2*(x**2)**(3/2) + 3*b**2*c**(3/2)*n*(x**2)**(3/2) + 2*b**2*c**(3/2)*(x**2)**(3/2)) + a*b*n*x**4*(a + b*x)**n/(b**2*c**(3/2)*n**2*(x**2)**(3/2) + 3*b**2*c**(3/2)*n*(x**2)**(3/2) + 2*b**2*c**(3/2)*(x**2)**(3/2)) + b**2*n*x**5*(a + b*x)**n/(b**2*c**(3/2)*n**2*(x**2)**(3/2) + 3*b**2*c**(3/2)*n*(x**2)**(3/2) + 2*b**2*c**(3/2)*(x**2)**(3/2)) + b**2*x**5*(a + b*x)**n/(b**2*c**(3/2)*n**2*(x**2)**(3/2) + 3*b**2*c**(3/2)*n*(x**2)**(3/2) + 2*b**2*c**(3/2)*(x**2)**(3/2)), True))","F",0
956,0,0,0,0.000000," ","integrate(x**3*(b*x+a)**n/(c*x**2)**(3/2),x)","\begin{cases} \frac{x^{4}}{a c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \wedge n = -1 \\\frac{a^{n} x^{4}}{c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{3}}{\left(c x^{2}\right)^{\frac{3}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{a x^{3} \left(a + b x\right)^{n}}{b c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b x^{4} \left(a + b x\right)^{n}}{b c^{\frac{3}{2}} n \left(x^{2}\right)^{\frac{3}{2}} + b c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4/(a*c**(3/2)*(x**2)**(3/2)), Eq(b, 0) & Eq(n, -1)), (a**n*x**4/(c**(3/2)*(x**2)**(3/2)), Eq(b, 0)), (Integral(x**3/((c*x**2)**(3/2)*(a + b*x)), x), Eq(n, -1)), (a*x**3*(a + b*x)**n/(b*c**(3/2)*n*(x**2)**(3/2) + b*c**(3/2)*(x**2)**(3/2)) + b*x**4*(a + b*x)**n/(b*c**(3/2)*n*(x**2)**(3/2) + b*c**(3/2)*(x**2)**(3/2)), True))","F",0
957,0,0,0,0.000000," ","integrate(x**2*(b*x+a)**n/(c*x**2)**(3/2),x)","\int \frac{x^{2} \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x)**n/(c*x**2)**(3/2), x)","F",0
958,0,0,0,0.000000," ","integrate(x*(b*x+a)**n/(c*x**2)**(3/2),x)","\int \frac{x \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*(a + b*x)**n/(c*x**2)**(3/2), x)","F",0
959,0,0,0,0.000000," ","integrate((b*x+a)**n/(c*x**2)**(3/2),x)","\int \frac{\left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)**n/(c*x**2)**(3/2), x)","F",0
960,0,0,0,0.000000," ","integrate((b*x+a)**n/x/(c*x**2)**(3/2),x)","\int \frac{\left(a + b x\right)^{n}}{x \left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)**n/(x*(c*x**2)**(3/2)), x)","F",0
961,0,0,0,0.000000," ","integrate(x**8*(b*x+a)**n/(c*x**2)**(5/2),x)","\begin{cases} \frac{a^{n} x^{9}}{4 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{8}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{4}}\, dx & \text{for}\: n = -4 \\\int \frac{x^{8}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{8}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{8}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{6 a^{4} x^{5} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{6 a^{3} b n x^{6} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{3 a^{2} b^{2} n^{2} x^{7} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{3 a^{2} b^{2} n x^{7} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{a b^{3} n^{3} x^{8} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{3 a b^{3} n^{2} x^{8} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{2 a b^{3} n x^{8} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b^{4} n^{3} x^{9} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{6 b^{4} n^{2} x^{9} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{11 b^{4} n x^{9} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{6 b^{4} x^{9} \left(a + b x\right)^{n}}{b^{4} c^{\frac{5}{2}} n^{4} \left(x^{2}\right)^{\frac{5}{2}} + 10 b^{4} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 35 b^{4} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 50 b^{4} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 24 b^{4} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**9/(4*c**(5/2)*(x**2)**(5/2)), Eq(b, 0)), (Integral(x**8/((c*x**2)**(5/2)*(a + b*x)**4), x), Eq(n, -4)), (Integral(x**8/((c*x**2)**(5/2)*(a + b*x)**3), x), Eq(n, -3)), (Integral(x**8/((c*x**2)**(5/2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**8/((c*x**2)**(5/2)*(a + b*x)), x), Eq(n, -1)), (-6*a**4*x**5*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + 6*a**3*b*n*x**6*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) - 3*a**2*b**2*n**2*x**7*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) - 3*a**2*b**2*n*x**7*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + a*b**3*n**3*x**8*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + 3*a*b**3*n**2*x**8*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + 2*a*b**3*n*x**8*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + b**4*n**3*x**9*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + 6*b**4*n**2*x**9*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + 11*b**4*n*x**9*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)) + 6*b**4*x**9*(a + b*x)**n/(b**4*c**(5/2)*n**4*(x**2)**(5/2) + 10*b**4*c**(5/2)*n**3*(x**2)**(5/2) + 35*b**4*c**(5/2)*n**2*(x**2)**(5/2) + 50*b**4*c**(5/2)*n*(x**2)**(5/2) + 24*b**4*c**(5/2)*(x**2)**(5/2)), True))","F",0
962,0,0,0,0.000000," ","integrate(x**7*(b*x+a)**n/(c*x**2)**(5/2),x)","\begin{cases} \frac{a^{n} x^{8}}{3 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{7}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{3}}\, dx & \text{for}\: n = -3 \\\int \frac{x^{7}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{7}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{2 a^{3} x^{5} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{2 a^{2} b n x^{6} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{a b^{2} n^{2} x^{7} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{a b^{2} n x^{7} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b^{3} n^{2} x^{8} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{3 b^{3} n x^{8} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{2 b^{3} x^{8} \left(a + b x\right)^{n}}{b^{3} c^{\frac{5}{2}} n^{3} \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 11 b^{3} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 6 b^{3} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**8/(3*c**(5/2)*(x**2)**(5/2)), Eq(b, 0)), (Integral(x**7/((c*x**2)**(5/2)*(a + b*x)**3), x), Eq(n, -3)), (Integral(x**7/((c*x**2)**(5/2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**7/((c*x**2)**(5/2)*(a + b*x)), x), Eq(n, -1)), (2*a**3*x**5*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)) - 2*a**2*b*n*x**6*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)) + a*b**2*n**2*x**7*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)) + a*b**2*n*x**7*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)) + b**3*n**2*x**8*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)) + 3*b**3*n*x**8*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)) + 2*b**3*x**8*(a + b*x)**n/(b**3*c**(5/2)*n**3*(x**2)**(5/2) + 6*b**3*c**(5/2)*n**2*(x**2)**(5/2) + 11*b**3*c**(5/2)*n*(x**2)**(5/2) + 6*b**3*c**(5/2)*(x**2)**(5/2)), True))","F",0
963,0,0,0,0.000000," ","integrate(x**6*(b*x+a)**n/(c*x**2)**(5/2),x)","\begin{cases} \frac{a^{n} x^{7}}{2 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)^{2}}\, dx & \text{for}\: n = -2 \\\int \frac{x^{6}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\- \frac{a^{2} x^{5} \left(a + b x\right)^{n}}{b^{2} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 3 b^{2} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 2 b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{a b n x^{6} \left(a + b x\right)^{n}}{b^{2} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 3 b^{2} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 2 b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b^{2} n x^{7} \left(a + b x\right)^{n}}{b^{2} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 3 b^{2} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 2 b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b^{2} x^{7} \left(a + b x\right)^{n}}{b^{2} c^{\frac{5}{2}} n^{2} \left(x^{2}\right)^{\frac{5}{2}} + 3 b^{2} c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + 2 b^{2} c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*x**7/(2*c**(5/2)*(x**2)**(5/2)), Eq(b, 0)), (Integral(x**6/((c*x**2)**(5/2)*(a + b*x)**2), x), Eq(n, -2)), (Integral(x**6/((c*x**2)**(5/2)*(a + b*x)), x), Eq(n, -1)), (-a**2*x**5*(a + b*x)**n/(b**2*c**(5/2)*n**2*(x**2)**(5/2) + 3*b**2*c**(5/2)*n*(x**2)**(5/2) + 2*b**2*c**(5/2)*(x**2)**(5/2)) + a*b*n*x**6*(a + b*x)**n/(b**2*c**(5/2)*n**2*(x**2)**(5/2) + 3*b**2*c**(5/2)*n*(x**2)**(5/2) + 2*b**2*c**(5/2)*(x**2)**(5/2)) + b**2*n*x**7*(a + b*x)**n/(b**2*c**(5/2)*n**2*(x**2)**(5/2) + 3*b**2*c**(5/2)*n*(x**2)**(5/2) + 2*b**2*c**(5/2)*(x**2)**(5/2)) + b**2*x**7*(a + b*x)**n/(b**2*c**(5/2)*n**2*(x**2)**(5/2) + 3*b**2*c**(5/2)*n*(x**2)**(5/2) + 2*b**2*c**(5/2)*(x**2)**(5/2)), True))","F",0
964,0,0,0,0.000000," ","integrate(x**5*(b*x+a)**n/(c*x**2)**(5/2),x)","\begin{cases} \frac{x^{6}}{a c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{for}\: b = 0 \wedge n = -1 \\\frac{a^{n} x^{6}}{c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{for}\: b = 0 \\\int \frac{x^{5}}{\left(c x^{2}\right)^{\frac{5}{2}} \left(a + b x\right)}\, dx & \text{for}\: n = -1 \\\frac{a x^{5} \left(a + b x\right)^{n}}{b c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b x^{6} \left(a + b x\right)^{n}}{b c^{\frac{5}{2}} n \left(x^{2}\right)^{\frac{5}{2}} + b c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6/(a*c**(5/2)*(x**2)**(5/2)), Eq(b, 0) & Eq(n, -1)), (a**n*x**6/(c**(5/2)*(x**2)**(5/2)), Eq(b, 0)), (Integral(x**5/((c*x**2)**(5/2)*(a + b*x)), x), Eq(n, -1)), (a*x**5*(a + b*x)**n/(b*c**(5/2)*n*(x**2)**(5/2) + b*c**(5/2)*(x**2)**(5/2)) + b*x**6*(a + b*x)**n/(b*c**(5/2)*n*(x**2)**(5/2) + b*c**(5/2)*(x**2)**(5/2)), True))","F",0
965,0,0,0,0.000000," ","integrate(x**4*(b*x+a)**n/(c*x**2)**(5/2),x)","\int \frac{x^{4} \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**4*(a + b*x)**n/(c*x**2)**(5/2), x)","F",0
966,0,0,0,0.000000," ","integrate(x**3*(b*x+a)**n/(c*x**2)**(5/2),x)","\int \frac{x^{3} \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3*(a + b*x)**n/(c*x**2)**(5/2), x)","F",0
967,0,0,0,0.000000," ","integrate(x**2*(b*x+a)**n/(c*x**2)**(5/2),x)","\int \frac{x^{2} \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*x)**n/(c*x**2)**(5/2), x)","F",0
968,0,0,0,0.000000," ","integrate(x*(b*x+a)**n/(c*x**2)**(5/2),x)","\int \frac{x \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x*(a + b*x)**n/(c*x**2)**(5/2), x)","F",0
969,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(5/2)*(b*x+a),x)","\begin{cases} \frac{\int \frac{a \left(c x^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx + \int \frac{b \left(c x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx}{d^{7}} & \text{for}\: m = -7 \\\frac{\int \frac{a \left(c x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx + \int \frac{b \left(c x^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx}{d^{6}} & \text{for}\: m = -6 \\\frac{a c^{\frac{5}{2}} d^{m} m x x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{2} + 13 m + 42} + \frac{7 a c^{\frac{5}{2}} d^{m} x x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{2} + 13 m + 42} + \frac{b c^{\frac{5}{2}} d^{m} m x^{2} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{2} + 13 m + 42} + \frac{6 b c^{\frac{5}{2}} d^{m} x^{2} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{2} + 13 m + 42} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(a*(c*x**2)**(5/2)/x**7, x) + Integral(b*(c*x**2)**(5/2)/x**6, x))/d**7, Eq(m, -7)), ((Integral(a*(c*x**2)**(5/2)/x**6, x) + Integral(b*(c*x**2)**(5/2)/x**5, x))/d**6, Eq(m, -6)), (a*c**(5/2)*d**m*m*x*x**m*(x**2)**(5/2)/(m**2 + 13*m + 42) + 7*a*c**(5/2)*d**m*x*x**m*(x**2)**(5/2)/(m**2 + 13*m + 42) + b*c**(5/2)*d**m*m*x**2*x**m*(x**2)**(5/2)/(m**2 + 13*m + 42) + 6*b*c**(5/2)*d**m*x**2*x**m*(x**2)**(5/2)/(m**2 + 13*m + 42), True))","F",0
970,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(3/2)*(b*x+a),x)","\begin{cases} \frac{\int \frac{a \left(c x^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx + \int \frac{b \left(c x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx}{d^{5}} & \text{for}\: m = -5 \\\frac{\int \frac{a \left(c x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx + \int \frac{b \left(c x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx}{d^{4}} & \text{for}\: m = -4 \\\frac{a c^{\frac{3}{2}} d^{m} m x x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{2} + 9 m + 20} + \frac{5 a c^{\frac{3}{2}} d^{m} x x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{2} + 9 m + 20} + \frac{b c^{\frac{3}{2}} d^{m} m x^{2} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{2} + 9 m + 20} + \frac{4 b c^{\frac{3}{2}} d^{m} x^{2} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{2} + 9 m + 20} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(a*(c*x**2)**(3/2)/x**5, x) + Integral(b*(c*x**2)**(3/2)/x**4, x))/d**5, Eq(m, -5)), ((Integral(a*(c*x**2)**(3/2)/x**4, x) + Integral(b*(c*x**2)**(3/2)/x**3, x))/d**4, Eq(m, -4)), (a*c**(3/2)*d**m*m*x*x**m*(x**2)**(3/2)/(m**2 + 9*m + 20) + 5*a*c**(3/2)*d**m*x*x**m*(x**2)**(3/2)/(m**2 + 9*m + 20) + b*c**(3/2)*d**m*m*x**2*x**m*(x**2)**(3/2)/(m**2 + 9*m + 20) + 4*b*c**(3/2)*d**m*x**2*x**m*(x**2)**(3/2)/(m**2 + 9*m + 20), True))","F",0
971,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(1/2)*(b*x+a),x)","\begin{cases} \frac{\int \frac{a \sqrt{c x^{2}}}{x^{3}}\, dx + \int \frac{b \sqrt{c x^{2}}}{x^{2}}\, dx}{d^{3}} & \text{for}\: m = -3 \\\frac{\int \frac{a \sqrt{c x^{2}}}{x^{2}}\, dx + \int \frac{b \sqrt{c x^{2}}}{x}\, dx}{d^{2}} & \text{for}\: m = -2 \\\frac{a \sqrt{c} d^{m} m x x^{m} \sqrt{x^{2}}}{m^{2} + 5 m + 6} + \frac{3 a \sqrt{c} d^{m} x x^{m} \sqrt{x^{2}}}{m^{2} + 5 m + 6} + \frac{b \sqrt{c} d^{m} m x^{2} x^{m} \sqrt{x^{2}}}{m^{2} + 5 m + 6} + \frac{2 b \sqrt{c} d^{m} x^{2} x^{m} \sqrt{x^{2}}}{m^{2} + 5 m + 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(a*sqrt(c*x**2)/x**3, x) + Integral(b*sqrt(c*x**2)/x**2, x))/d**3, Eq(m, -3)), ((Integral(a*sqrt(c*x**2)/x**2, x) + Integral(b*sqrt(c*x**2)/x, x))/d**2, Eq(m, -2)), (a*sqrt(c)*d**m*m*x*x**m*sqrt(x**2)/(m**2 + 5*m + 6) + 3*a*sqrt(c)*d**m*x*x**m*sqrt(x**2)/(m**2 + 5*m + 6) + b*sqrt(c)*d**m*m*x**2*x**m*sqrt(x**2)/(m**2 + 5*m + 6) + 2*b*sqrt(c)*d**m*x**2*x**m*sqrt(x**2)/(m**2 + 5*m + 6), True))","F",0
972,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)/(c*x**2)**(1/2),x)","\begin{cases} \frac{\int \frac{b}{\sqrt{c x^{2}}}\, dx + \int \frac{a}{x \sqrt{c x^{2}}}\, dx}{d} & \text{for}\: m = -1 \\\int \frac{a + b x}{\sqrt{c x^{2}}}\, dx & \text{for}\: m = 0 \\\frac{a d^{m} m x x^{m}}{\sqrt{c} m^{2} \sqrt{x^{2}} + \sqrt{c} m \sqrt{x^{2}}} + \frac{a d^{m} x x^{m}}{\sqrt{c} m^{2} \sqrt{x^{2}} + \sqrt{c} m \sqrt{x^{2}}} + \frac{b d^{m} m x^{2} x^{m}}{\sqrt{c} m^{2} \sqrt{x^{2}} + \sqrt{c} m \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(b/sqrt(c*x**2), x) + Integral(a/(x*sqrt(c*x**2)), x))/d, Eq(m, -1)), (Integral((a + b*x)/sqrt(c*x**2), x), Eq(m, 0)), (a*d**m*m*x*x**m/(sqrt(c)*m**2*sqrt(x**2) + sqrt(c)*m*sqrt(x**2)) + a*d**m*x*x**m/(sqrt(c)*m**2*sqrt(x**2) + sqrt(c)*m*sqrt(x**2)) + b*d**m*m*x**2*x**m/(sqrt(c)*m**2*sqrt(x**2) + sqrt(c)*m*sqrt(x**2)), True))","F",0
973,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)/(c*x**2)**(3/2),x)","\begin{cases} d \left(\int \frac{a x}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx + \int \frac{b x^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx\right) & \text{for}\: m = 1 \\d^{2} \left(\int \frac{a x^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx + \int \frac{b x^{3}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx\right) & \text{for}\: m = 2 \\\frac{a d^{m} m x x^{m}}{c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{a d^{m} x x^{m}}{c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b d^{m} m x^{2} x^{m}}{c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} - \frac{2 b d^{m} x^{2} x^{m}}{c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*(Integral(a*x/(c*x**2)**(3/2), x) + Integral(b*x**2/(c*x**2)**(3/2), x)), Eq(m, 1)), (d**2*(Integral(a*x**2/(c*x**2)**(3/2), x) + Integral(b*x**3/(c*x**2)**(3/2), x)), Eq(m, 2)), (a*d**m*m*x*x**m/(c**(3/2)*m**2*(x**2)**(3/2) - 3*c**(3/2)*m*(x**2)**(3/2) + 2*c**(3/2)*(x**2)**(3/2)) - a*d**m*x*x**m/(c**(3/2)*m**2*(x**2)**(3/2) - 3*c**(3/2)*m*(x**2)**(3/2) + 2*c**(3/2)*(x**2)**(3/2)) + b*d**m*m*x**2*x**m/(c**(3/2)*m**2*(x**2)**(3/2) - 3*c**(3/2)*m*(x**2)**(3/2) + 2*c**(3/2)*(x**2)**(3/2)) - 2*b*d**m*x**2*x**m/(c**(3/2)*m**2*(x**2)**(3/2) - 3*c**(3/2)*m*(x**2)**(3/2) + 2*c**(3/2)*(x**2)**(3/2)), True))","F",0
974,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)/(c*x**2)**(5/2),x)","\begin{cases} d^{3} \left(\int \frac{a x^{3}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{b x^{4}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx\right) & \text{for}\: m = 3 \\d^{4} \left(\int \frac{a x^{4}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{b x^{5}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx\right) & \text{for}\: m = 4 \\\frac{a d^{m} m x x^{m}}{c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} - 7 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} + 12 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{3 a d^{m} x x^{m}}{c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} - 7 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} + 12 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b d^{m} m x^{2} x^{m}}{c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} - 7 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} + 12 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{4 b d^{m} x^{2} x^{m}}{c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} - 7 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} + 12 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**3*(Integral(a*x**3/(c*x**2)**(5/2), x) + Integral(b*x**4/(c*x**2)**(5/2), x)), Eq(m, 3)), (d**4*(Integral(a*x**4/(c*x**2)**(5/2), x) + Integral(b*x**5/(c*x**2)**(5/2), x)), Eq(m, 4)), (a*d**m*m*x*x**m/(c**(5/2)*m**2*(x**2)**(5/2) - 7*c**(5/2)*m*(x**2)**(5/2) + 12*c**(5/2)*(x**2)**(5/2)) - 3*a*d**m*x*x**m/(c**(5/2)*m**2*(x**2)**(5/2) - 7*c**(5/2)*m*(x**2)**(5/2) + 12*c**(5/2)*(x**2)**(5/2)) + b*d**m*m*x**2*x**m/(c**(5/2)*m**2*(x**2)**(5/2) - 7*c**(5/2)*m*(x**2)**(5/2) + 12*c**(5/2)*(x**2)**(5/2)) - 4*b*d**m*x**2*x**m/(c**(5/2)*m**2*(x**2)**(5/2) - 7*c**(5/2)*m*(x**2)**(5/2) + 12*c**(5/2)*(x**2)**(5/2)), True))","F",0
975,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(5/2)*(b*x+a)**2,x)","\begin{cases} \frac{\int \frac{a^{2} \left(c x^{2}\right)^{\frac{5}{2}}}{x^{8}}\, dx + \int \frac{b^{2} \left(c x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx + \int \frac{2 a b \left(c x^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx}{d^{8}} & \text{for}\: m = -8 \\\frac{\int \frac{a^{2} \left(c x^{2}\right)^{\frac{5}{2}}}{x^{7}}\, dx + \int \frac{b^{2} \left(c x^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx + \int \frac{2 a b \left(c x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx}{d^{7}} & \text{for}\: m = -7 \\\frac{\int \frac{a^{2} \left(c x^{2}\right)^{\frac{5}{2}}}{x^{6}}\, dx + \int \frac{b^{2} \left(c x^{2}\right)^{\frac{5}{2}}}{x^{4}}\, dx + \int \frac{2 a b \left(c x^{2}\right)^{\frac{5}{2}}}{x^{5}}\, dx}{d^{6}} & \text{for}\: m = -6 \\\frac{a^{2} c^{\frac{5}{2}} d^{m} m^{2} x x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{15 a^{2} c^{\frac{5}{2}} d^{m} m x x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{56 a^{2} c^{\frac{5}{2}} d^{m} x x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{2 a b c^{\frac{5}{2}} d^{m} m^{2} x^{2} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{28 a b c^{\frac{5}{2}} d^{m} m x^{2} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{96 a b c^{\frac{5}{2}} d^{m} x^{2} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{b^{2} c^{\frac{5}{2}} d^{m} m^{2} x^{3} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{13 b^{2} c^{\frac{5}{2}} d^{m} m x^{3} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} + \frac{42 b^{2} c^{\frac{5}{2}} d^{m} x^{3} x^{m} \left(x^{2}\right)^{\frac{5}{2}}}{m^{3} + 21 m^{2} + 146 m + 336} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(a**2*(c*x**2)**(5/2)/x**8, x) + Integral(b**2*(c*x**2)**(5/2)/x**6, x) + Integral(2*a*b*(c*x**2)**(5/2)/x**7, x))/d**8, Eq(m, -8)), ((Integral(a**2*(c*x**2)**(5/2)/x**7, x) + Integral(b**2*(c*x**2)**(5/2)/x**5, x) + Integral(2*a*b*(c*x**2)**(5/2)/x**6, x))/d**7, Eq(m, -7)), ((Integral(a**2*(c*x**2)**(5/2)/x**6, x) + Integral(b**2*(c*x**2)**(5/2)/x**4, x) + Integral(2*a*b*(c*x**2)**(5/2)/x**5, x))/d**6, Eq(m, -6)), (a**2*c**(5/2)*d**m*m**2*x*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 15*a**2*c**(5/2)*d**m*m*x*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 56*a**2*c**(5/2)*d**m*x*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 2*a*b*c**(5/2)*d**m*m**2*x**2*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 28*a*b*c**(5/2)*d**m*m*x**2*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 96*a*b*c**(5/2)*d**m*x**2*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + b**2*c**(5/2)*d**m*m**2*x**3*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 13*b**2*c**(5/2)*d**m*m*x**3*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336) + 42*b**2*c**(5/2)*d**m*x**3*x**m*(x**2)**(5/2)/(m**3 + 21*m**2 + 146*m + 336), True))","F",0
976,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(3/2)*(b*x+a)**2,x)","\begin{cases} \frac{\int \frac{a^{2} \left(c x^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx + \int \frac{b^{2} \left(c x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx + \int \frac{2 a b \left(c x^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx}{d^{6}} & \text{for}\: m = -6 \\\frac{\int \frac{a^{2} \left(c x^{2}\right)^{\frac{3}{2}}}{x^{5}}\, dx + \int \frac{b^{2} \left(c x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx + \int \frac{2 a b \left(c x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx}{d^{5}} & \text{for}\: m = -5 \\\frac{\int \frac{a^{2} \left(c x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx + \int \frac{b^{2} \left(c x^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx + \int \frac{2 a b \left(c x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx}{d^{4}} & \text{for}\: m = -4 \\\frac{a^{2} c^{\frac{3}{2}} d^{m} m^{2} x x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{11 a^{2} c^{\frac{3}{2}} d^{m} m x x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{30 a^{2} c^{\frac{3}{2}} d^{m} x x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{2 a b c^{\frac{3}{2}} d^{m} m^{2} x^{2} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{20 a b c^{\frac{3}{2}} d^{m} m x^{2} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{48 a b c^{\frac{3}{2}} d^{m} x^{2} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{b^{2} c^{\frac{3}{2}} d^{m} m^{2} x^{3} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{9 b^{2} c^{\frac{3}{2}} d^{m} m x^{3} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} + \frac{20 b^{2} c^{\frac{3}{2}} d^{m} x^{3} x^{m} \left(x^{2}\right)^{\frac{3}{2}}}{m^{3} + 15 m^{2} + 74 m + 120} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(a**2*(c*x**2)**(3/2)/x**6, x) + Integral(b**2*(c*x**2)**(3/2)/x**4, x) + Integral(2*a*b*(c*x**2)**(3/2)/x**5, x))/d**6, Eq(m, -6)), ((Integral(a**2*(c*x**2)**(3/2)/x**5, x) + Integral(b**2*(c*x**2)**(3/2)/x**3, x) + Integral(2*a*b*(c*x**2)**(3/2)/x**4, x))/d**5, Eq(m, -5)), ((Integral(a**2*(c*x**2)**(3/2)/x**4, x) + Integral(b**2*(c*x**2)**(3/2)/x**2, x) + Integral(2*a*b*(c*x**2)**(3/2)/x**3, x))/d**4, Eq(m, -4)), (a**2*c**(3/2)*d**m*m**2*x*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 11*a**2*c**(3/2)*d**m*m*x*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 30*a**2*c**(3/2)*d**m*x*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 2*a*b*c**(3/2)*d**m*m**2*x**2*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 20*a*b*c**(3/2)*d**m*m*x**2*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 48*a*b*c**(3/2)*d**m*x**2*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + b**2*c**(3/2)*d**m*m**2*x**3*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 9*b**2*c**(3/2)*d**m*m*x**3*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120) + 20*b**2*c**(3/2)*d**m*x**3*x**m*(x**2)**(3/2)/(m**3 + 15*m**2 + 74*m + 120), True))","F",0
977,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(1/2)*(b*x+a)**2,x)","\begin{cases} \frac{\int \frac{a^{2} \sqrt{c x^{2}}}{x^{4}}\, dx + \int \frac{b^{2} \sqrt{c x^{2}}}{x^{2}}\, dx + \int \frac{2 a b \sqrt{c x^{2}}}{x^{3}}\, dx}{d^{4}} & \text{for}\: m = -4 \\\frac{\int \frac{a^{2} \sqrt{c x^{2}}}{x^{3}}\, dx + \int \frac{b^{2} \sqrt{c x^{2}}}{x}\, dx + \int \frac{2 a b \sqrt{c x^{2}}}{x^{2}}\, dx}{d^{3}} & \text{for}\: m = -3 \\\frac{\int b^{2} \sqrt{c x^{2}}\, dx + \int \frac{a^{2} \sqrt{c x^{2}}}{x^{2}}\, dx + \int \frac{2 a b \sqrt{c x^{2}}}{x}\, dx}{d^{2}} & \text{for}\: m = -2 \\\frac{a^{2} \sqrt{c} d^{m} m^{2} x x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{7 a^{2} \sqrt{c} d^{m} m x x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{12 a^{2} \sqrt{c} d^{m} x x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{2 a b \sqrt{c} d^{m} m^{2} x^{2} x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{12 a b \sqrt{c} d^{m} m x^{2} x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{16 a b \sqrt{c} d^{m} x^{2} x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{b^{2} \sqrt{c} d^{m} m^{2} x^{3} x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{5 b^{2} \sqrt{c} d^{m} m x^{3} x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} + \frac{6 b^{2} \sqrt{c} d^{m} x^{3} x^{m} \sqrt{x^{2}}}{m^{3} + 9 m^{2} + 26 m + 24} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(a**2*sqrt(c*x**2)/x**4, x) + Integral(b**2*sqrt(c*x**2)/x**2, x) + Integral(2*a*b*sqrt(c*x**2)/x**3, x))/d**4, Eq(m, -4)), ((Integral(a**2*sqrt(c*x**2)/x**3, x) + Integral(b**2*sqrt(c*x**2)/x, x) + Integral(2*a*b*sqrt(c*x**2)/x**2, x))/d**3, Eq(m, -3)), ((Integral(b**2*sqrt(c*x**2), x) + Integral(a**2*sqrt(c*x**2)/x**2, x) + Integral(2*a*b*sqrt(c*x**2)/x, x))/d**2, Eq(m, -2)), (a**2*sqrt(c)*d**m*m**2*x*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 7*a**2*sqrt(c)*d**m*m*x*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 12*a**2*sqrt(c)*d**m*x*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 2*a*b*sqrt(c)*d**m*m**2*x**2*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 12*a*b*sqrt(c)*d**m*m*x**2*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 16*a*b*sqrt(c)*d**m*x**2*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + b**2*sqrt(c)*d**m*m**2*x**3*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 5*b**2*sqrt(c)*d**m*m*x**3*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24) + 6*b**2*sqrt(c)*d**m*x**3*x**m*sqrt(x**2)/(m**3 + 9*m**2 + 26*m + 24), True))","F",0
978,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)**2/(c*x**2)**(1/2),x)","\begin{cases} \frac{\int \frac{b^{2}}{\sqrt{c x^{2}}}\, dx + \int \frac{a^{2}}{x^{2} \sqrt{c x^{2}}}\, dx + \int \frac{2 a b}{x \sqrt{c x^{2}}}\, dx}{d^{2}} & \text{for}\: m = -2 \\\frac{\int \frac{2 a b}{\sqrt{c x^{2}}}\, dx + \int \frac{a^{2}}{x \sqrt{c x^{2}}}\, dx + \int \frac{b^{2} x}{\sqrt{c x^{2}}}\, dx}{d} & \text{for}\: m = -1 \\\int \frac{\left(a + b x\right)^{2}}{\sqrt{c x^{2}}}\, dx & \text{for}\: m = 0 \\\frac{a^{2} d^{m} m^{2} x x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} + \frac{3 a^{2} d^{m} m x x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} + \frac{2 a^{2} d^{m} x x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} + \frac{2 a b d^{m} m^{2} x^{2} x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} + \frac{4 a b d^{m} m x^{2} x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} + \frac{b^{2} d^{m} m^{2} x^{3} x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} + \frac{b^{2} d^{m} m x^{3} x^{m}}{\sqrt{c} m^{3} \sqrt{x^{2}} + 3 \sqrt{c} m^{2} \sqrt{x^{2}} + 2 \sqrt{c} m \sqrt{x^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((Integral(b**2/sqrt(c*x**2), x) + Integral(a**2/(x**2*sqrt(c*x**2)), x) + Integral(2*a*b/(x*sqrt(c*x**2)), x))/d**2, Eq(m, -2)), ((Integral(2*a*b/sqrt(c*x**2), x) + Integral(a**2/(x*sqrt(c*x**2)), x) + Integral(b**2*x/sqrt(c*x**2), x))/d, Eq(m, -1)), (Integral((a + b*x)**2/sqrt(c*x**2), x), Eq(m, 0)), (a**2*d**m*m**2*x*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)) + 3*a**2*d**m*m*x*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)) + 2*a**2*d**m*x*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)) + 2*a*b*d**m*m**2*x**2*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)) + 4*a*b*d**m*m*x**2*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)) + b**2*d**m*m**2*x**3*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)) + b**2*d**m*m*x**3*x**m/(sqrt(c)*m**3*sqrt(x**2) + 3*sqrt(c)*m**2*sqrt(x**2) + 2*sqrt(c)*m*sqrt(x**2)), True))","F",0
979,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)**2/(c*x**2)**(3/2),x)","\begin{cases} \int \frac{\left(a + b x\right)^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx & \text{for}\: m = 0 \\d \left(\int \frac{a^{2} x}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx + \int \frac{b^{2} x^{3}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx + \int \frac{2 a b x^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx\right) & \text{for}\: m = 1 \\d^{2} \left(\int \frac{a^{2} x^{2}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx + \int \frac{b^{2} x^{4}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx + \int \frac{2 a b x^{3}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx\right) & \text{for}\: m = 2 \\\frac{a^{2} d^{m} m^{2} x x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} - \frac{a^{2} d^{m} m x x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} + \frac{2 a b d^{m} m^{2} x^{2} x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} - \frac{4 a b d^{m} m x^{2} x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} + \frac{b^{2} d^{m} m^{2} x^{3} x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} - \frac{3 b^{2} d^{m} m x^{3} x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} + \frac{2 b^{2} d^{m} x^{3} x^{m}}{c^{\frac{3}{2}} m^{3} \left(x^{2}\right)^{\frac{3}{2}} - 3 c^{\frac{3}{2}} m^{2} \left(x^{2}\right)^{\frac{3}{2}} + 2 c^{\frac{3}{2}} m \left(x^{2}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((Integral((a + b*x)**2/(c*x**2)**(3/2), x), Eq(m, 0)), (d*(Integral(a**2*x/(c*x**2)**(3/2), x) + Integral(b**2*x**3/(c*x**2)**(3/2), x) + Integral(2*a*b*x**2/(c*x**2)**(3/2), x)), Eq(m, 1)), (d**2*(Integral(a**2*x**2/(c*x**2)**(3/2), x) + Integral(b**2*x**4/(c*x**2)**(3/2), x) + Integral(2*a*b*x**3/(c*x**2)**(3/2), x)), Eq(m, 2)), (a**2*d**m*m**2*x*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)) - a**2*d**m*m*x*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)) + 2*a*b*d**m*m**2*x**2*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)) - 4*a*b*d**m*m*x**2*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)) + b**2*d**m*m**2*x**3*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)) - 3*b**2*d**m*m*x**3*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)) + 2*b**2*d**m*x**3*x**m/(c**(3/2)*m**3*(x**2)**(3/2) - 3*c**(3/2)*m**2*(x**2)**(3/2) + 2*c**(3/2)*m*(x**2)**(3/2)), True))","F",0
980,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)**2/(c*x**2)**(5/2),x)","\begin{cases} d^{2} \left(\int \frac{a^{2} x^{2}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{b^{2} x^{4}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{2 a b x^{3}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx\right) & \text{for}\: m = 2 \\d^{3} \left(\int \frac{a^{2} x^{3}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{b^{2} x^{5}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{2 a b x^{4}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx\right) & \text{for}\: m = 3 \\d^{4} \left(\int \frac{a^{2} x^{4}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{b^{2} x^{6}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx + \int \frac{2 a b x^{5}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx\right) & \text{for}\: m = 4 \\\frac{a^{2} d^{m} m^{2} x x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{5 a^{2} d^{m} m x x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{6 a^{2} d^{m} x x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{2 a b d^{m} m^{2} x^{2} x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{12 a b d^{m} m x^{2} x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{16 a b d^{m} x^{2} x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{b^{2} d^{m} m^{2} x^{3} x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} - \frac{7 b^{2} d^{m} m x^{3} x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} + \frac{12 b^{2} d^{m} x^{3} x^{m}}{c^{\frac{5}{2}} m^{3} \left(x^{2}\right)^{\frac{5}{2}} - 9 c^{\frac{5}{2}} m^{2} \left(x^{2}\right)^{\frac{5}{2}} + 26 c^{\frac{5}{2}} m \left(x^{2}\right)^{\frac{5}{2}} - 24 c^{\frac{5}{2}} \left(x^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**2*(Integral(a**2*x**2/(c*x**2)**(5/2), x) + Integral(b**2*x**4/(c*x**2)**(5/2), x) + Integral(2*a*b*x**3/(c*x**2)**(5/2), x)), Eq(m, 2)), (d**3*(Integral(a**2*x**3/(c*x**2)**(5/2), x) + Integral(b**2*x**5/(c*x**2)**(5/2), x) + Integral(2*a*b*x**4/(c*x**2)**(5/2), x)), Eq(m, 3)), (d**4*(Integral(a**2*x**4/(c*x**2)**(5/2), x) + Integral(b**2*x**6/(c*x**2)**(5/2), x) + Integral(2*a*b*x**5/(c*x**2)**(5/2), x)), Eq(m, 4)), (a**2*d**m*m**2*x*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) - 5*a**2*d**m*m*x*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) + 6*a**2*d**m*x*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) + 2*a*b*d**m*m**2*x**2*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) - 12*a*b*d**m*m*x**2*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) + 16*a*b*d**m*x**2*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) + b**2*d**m*m**2*x**3*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) - 7*b**2*d**m*m*x**3*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)) + 12*b**2*d**m*x**3*x**m/(c**(5/2)*m**3*(x**2)**(5/2) - 9*c**(5/2)*m**2*(x**2)**(5/2) + 26*c**(5/2)*m*(x**2)**(5/2) - 24*c**(5/2)*(x**2)**(5/2)), True))","F",0
981,-1,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(5/2)*(b*x+a)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
982,-1,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(3/2)*(b*x+a)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
983,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**(1/2)*(b*x+a)**n,x)","\int \sqrt{c x^{2}} \left(d x\right)^{m} \left(a + b x\right)^{n}\, dx"," ",0,"Integral(sqrt(c*x**2)*(d*x)**m*(a + b*x)**n, x)","F",0
984,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)**n/(c*x**2)**(1/2),x)","\int \frac{\left(d x\right)^{m} \left(a + b x\right)^{n}}{\sqrt{c x^{2}}}\, dx"," ",0,"Integral((d*x)**m*(a + b*x)**n/sqrt(c*x**2), x)","F",0
985,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)**n/(c*x**2)**(3/2),x)","\int \frac{\left(d x\right)^{m} \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*x)**m*(a + b*x)**n/(c*x**2)**(3/2), x)","F",0
986,0,0,0,0.000000," ","integrate((d*x)**m*(b*x+a)**n/(c*x**2)**(5/2),x)","\int \frac{\left(d x\right)^{m} \left(a + b x\right)^{n}}{\left(c x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((d*x)**m*(a + b*x)**n/(c*x**2)**(5/2), x)","F",0
987,-1,0,0,0.000000," ","integrate(x**3*(c*x**2)**p*(b*x+a)**(-5-2*p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
988,-1,0,0,0.000000," ","integrate(x**2*(c*x**2)**p*(b*x+a)**(-4-2*p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
989,-1,0,0,0.000000," ","integrate(x*(c*x**2)**p*(b*x+a)**(-3-2*p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
990,0,0,0,0.000000," ","integrate((c*x**2)**p*(b*x+a)**(-2-2*p),x)","\begin{cases} - \frac{b^{- 2 p} c^{p} x^{- 2 p} \left(x^{2}\right)^{p}}{b^{2} x} & \text{for}\: a = 0 \\\frac{0^{- 2 p - 2} c^{p} x \left(x^{2}\right)^{p}}{2 p + 1} & \text{for}\: a = - b x \\\frac{c^{p} x \left(0^{\frac{1}{p}}\right)^{- 2 p - 2} \left(x^{2}\right)^{p}}{2 p + 1} & \text{for}\: a = 0^{\frac{1}{p}} - b x \\\int \frac{1}{\sqrt{c x^{2}} \left(a + b x\right)}\, dx & \text{for}\: p = - \frac{1}{2} \\\frac{a^{3} c^{p} x \left(x^{2}\right)^{p}}{2 a^{5} p \left(a + b x\right)^{2 p} + a^{5} \left(a + b x\right)^{2 p} + 8 a^{4} b p x \left(a + b x\right)^{2 p} + 4 a^{4} b x \left(a + b x\right)^{2 p} + 12 a^{3} b^{2} p x^{2} \left(a + b x\right)^{2 p} + 6 a^{3} b^{2} x^{2} \left(a + b x\right)^{2 p} + 8 a^{2} b^{3} p x^{3} \left(a + b x\right)^{2 p} + 4 a^{2} b^{3} x^{3} \left(a + b x\right)^{2 p} + 2 a b^{4} p x^{4} \left(a + b x\right)^{2 p} + a b^{4} x^{4} \left(a + b x\right)^{2 p}} + \frac{2 a^{2} b c^{p} x^{2} \left(x^{2}\right)^{p}}{2 a^{5} p \left(a + b x\right)^{2 p} + a^{5} \left(a + b x\right)^{2 p} + 8 a^{4} b p x \left(a + b x\right)^{2 p} + 4 a^{4} b x \left(a + b x\right)^{2 p} + 12 a^{3} b^{2} p x^{2} \left(a + b x\right)^{2 p} + 6 a^{3} b^{2} x^{2} \left(a + b x\right)^{2 p} + 8 a^{2} b^{3} p x^{3} \left(a + b x\right)^{2 p} + 4 a^{2} b^{3} x^{3} \left(a + b x\right)^{2 p} + 2 a b^{4} p x^{4} \left(a + b x\right)^{2 p} + a b^{4} x^{4} \left(a + b x\right)^{2 p}} + \frac{a b^{2} c^{p} x^{3} \left(x^{2}\right)^{p}}{2 a^{5} p \left(a + b x\right)^{2 p} + a^{5} \left(a + b x\right)^{2 p} + 8 a^{4} b p x \left(a + b x\right)^{2 p} + 4 a^{4} b x \left(a + b x\right)^{2 p} + 12 a^{3} b^{2} p x^{2} \left(a + b x\right)^{2 p} + 6 a^{3} b^{2} x^{2} \left(a + b x\right)^{2 p} + 8 a^{2} b^{3} p x^{3} \left(a + b x\right)^{2 p} + 4 a^{2} b^{3} x^{3} \left(a + b x\right)^{2 p} + 2 a b^{4} p x^{4} \left(a + b x\right)^{2 p} + a b^{4} x^{4} \left(a + b x\right)^{2 p}} + \frac{b c^{p} x^{2} \left(x^{2}\right)^{p}}{2 a^{3} p \left(a + b x\right)^{2 p} + a^{3} \left(a + b x\right)^{2 p} + 4 a^{2} b p x \left(a + b x\right)^{2 p} + 2 a^{2} b x \left(a + b x\right)^{2 p} + 2 a b^{2} p x^{2} \left(a + b x\right)^{2 p} + a b^{2} x^{2} \left(a + b x\right)^{2 p}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**(-2*p)*c**p*x**(-2*p)*(x**2)**p/(b**2*x), Eq(a, 0)), (0**(-2*p - 2)*c**p*x*(x**2)**p/(2*p + 1), Eq(a, -b*x)), (c**p*x*(0**(1/p))**(-2*p - 2)*(x**2)**p/(2*p + 1), Eq(a, 0**(1/p) - b*x)), (Integral(1/(sqrt(c*x**2)*(a + b*x)), x), Eq(p, -1/2)), (a**3*c**p*x*(x**2)**p/(2*a**5*p*(a + b*x)**(2*p) + a**5*(a + b*x)**(2*p) + 8*a**4*b*p*x*(a + b*x)**(2*p) + 4*a**4*b*x*(a + b*x)**(2*p) + 12*a**3*b**2*p*x**2*(a + b*x)**(2*p) + 6*a**3*b**2*x**2*(a + b*x)**(2*p) + 8*a**2*b**3*p*x**3*(a + b*x)**(2*p) + 4*a**2*b**3*x**3*(a + b*x)**(2*p) + 2*a*b**4*p*x**4*(a + b*x)**(2*p) + a*b**4*x**4*(a + b*x)**(2*p)) + 2*a**2*b*c**p*x**2*(x**2)**p/(2*a**5*p*(a + b*x)**(2*p) + a**5*(a + b*x)**(2*p) + 8*a**4*b*p*x*(a + b*x)**(2*p) + 4*a**4*b*x*(a + b*x)**(2*p) + 12*a**3*b**2*p*x**2*(a + b*x)**(2*p) + 6*a**3*b**2*x**2*(a + b*x)**(2*p) + 8*a**2*b**3*p*x**3*(a + b*x)**(2*p) + 4*a**2*b**3*x**3*(a + b*x)**(2*p) + 2*a*b**4*p*x**4*(a + b*x)**(2*p) + a*b**4*x**4*(a + b*x)**(2*p)) + a*b**2*c**p*x**3*(x**2)**p/(2*a**5*p*(a + b*x)**(2*p) + a**5*(a + b*x)**(2*p) + 8*a**4*b*p*x*(a + b*x)**(2*p) + 4*a**4*b*x*(a + b*x)**(2*p) + 12*a**3*b**2*p*x**2*(a + b*x)**(2*p) + 6*a**3*b**2*x**2*(a + b*x)**(2*p) + 8*a**2*b**3*p*x**3*(a + b*x)**(2*p) + 4*a**2*b**3*x**3*(a + b*x)**(2*p) + 2*a*b**4*p*x**4*(a + b*x)**(2*p) + a*b**4*x**4*(a + b*x)**(2*p)) + b*c**p*x**2*(x**2)**p/(2*a**3*p*(a + b*x)**(2*p) + a**3*(a + b*x)**(2*p) + 4*a**2*b*p*x*(a + b*x)**(2*p) + 2*a**2*b*x*(a + b*x)**(2*p) + 2*a*b**2*p*x**2*(a + b*x)**(2*p) + a*b**2*x**2*(a + b*x)**(2*p)), True))","F",0
991,1,264,0,59.694151," ","integrate((c*x**2)**p*(b*x+a)**(-1-2*p)/x,x)","\begin{cases} - \frac{b^{- 2 p} c^{p} x^{- 2 p} \left(x^{2}\right)^{p}}{b x} & \text{for}\: a = 0 \\\frac{0^{- 2 p - 1} c^{p} \left(x^{2}\right)^{p}}{2 p} & \text{for}\: a = - b x \\\frac{c^{p} \left(0^{\frac{1}{p}}\right)^{- 2 p - 1} \left(x^{2}\right)^{p}}{2 p} & \text{for}\: a = 0^{\frac{1}{p}} - b x \\\frac{\log{\left(x \right)}}{a} - \frac{\log{\left(\frac{a}{b} + x \right)}}{a} & \text{for}\: p = 0 \\\frac{a^{2} c^{p} \left(x^{2}\right)^{p}}{2 a^{3} p \left(a + b x\right)^{2 p} + 4 a^{2} b p x \left(a + b x\right)^{2 p} + 2 a b^{2} p x^{2} \left(a + b x\right)^{2 p}} + \frac{a b c^{p} x \left(x^{2}\right)^{p}}{2 a^{3} p \left(a + b x\right)^{2 p} + 4 a^{2} b p x \left(a + b x\right)^{2 p} + 2 a b^{2} p x^{2} \left(a + b x\right)^{2 p}} + \frac{b c^{p} x \left(x^{2}\right)^{p}}{2 a^{2} p \left(a + b x\right)^{2 p} + 2 a b p x \left(a + b x\right)^{2 p}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**(-2*p)*c**p*x**(-2*p)*(x**2)**p/(b*x), Eq(a, 0)), (0**(-2*p - 1)*c**p*(x**2)**p/(2*p), Eq(a, -b*x)), (c**p*(0**(1/p))**(-2*p - 1)*(x**2)**p/(2*p), Eq(a, 0**(1/p) - b*x)), (log(x)/a - log(a/b + x)/a, Eq(p, 0)), (a**2*c**p*(x**2)**p/(2*a**3*p*(a + b*x)**(2*p) + 4*a**2*b*p*x*(a + b*x)**(2*p) + 2*a*b**2*p*x**2*(a + b*x)**(2*p)) + a*b*c**p*x*(x**2)**p/(2*a**3*p*(a + b*x)**(2*p) + 4*a**2*b*p*x*(a + b*x)**(2*p) + 2*a*b**2*p*x**2*(a + b*x)**(2*p)) + b*c**p*x*(x**2)**p/(2*a**2*p*(a + b*x)**(2*p) + 2*a*b*p*x*(a + b*x)**(2*p)), True))","A",0
992,0,0,0,0.000000," ","integrate((c*x**2)**p/x**2/((b*x+a)**(2*p)),x)","\begin{cases} - \frac{\sqrt{c} \sqrt{x^{2}}}{b x^{2}} & \text{for}\: a = 0 \wedge p = \frac{1}{2} \\- \frac{b^{- 2 p} c^{p} x^{- 2 p} \left(x^{2}\right)^{p}}{x} & \text{for}\: a = 0 \\\int \frac{\sqrt{c x^{2}}}{x^{2} \left(a + b x\right)}\, dx & \text{for}\: p = \frac{1}{2} \\\frac{a c^{p} \left(x^{2}\right)^{p}}{2 a p x \left(a + b x\right)^{2 p} - a x \left(a + b x\right)^{2 p}} + \frac{b c^{p} x \left(x^{2}\right)^{p}}{2 a p x \left(a + b x\right)^{2 p} - a x \left(a + b x\right)^{2 p}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(c)*sqrt(x**2)/(b*x**2), Eq(a, 0) & Eq(p, 1/2)), (-b**(-2*p)*c**p*x**(-2*p)*(x**2)**p/x, Eq(a, 0)), (Integral(sqrt(c*x**2)/(x**2*(a + b*x)), x), Eq(p, 1/2)), (a*c**p*(x**2)**p/(2*a*p*x*(a + b*x)**(2*p) - a*x*(a + b*x)**(2*p)) + b*c**p*x*(x**2)**p/(2*a*p*x*(a + b*x)**(2*p) - a*x*(a + b*x)**(2*p)), True))","F",0
993,0,0,0,0.000000," ","integrate((c*x**2)**p*(b*x+a)**(1-2*p)/x**3,x)","\int \frac{\left(c x^{2}\right)^{p} \left(a + b x\right)^{1 - 2 p}}{x^{3}}\, dx"," ",0,"Integral((c*x**2)**p*(a + b*x)**(1 - 2*p)/x**3, x)","F",0
994,-1,0,0,0.000000," ","integrate((c*x**2)**p*(b*x+a)**(2-2*p)/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
995,-1,0,0,0.000000," ","integrate(x**m*(c*x**2)**p*(b*x+a)**(-2-m-2*p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
996,-1,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**p*(b*x+a)**(-2-m-2*p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
997,0,0,0,0.000000," ","integrate(x**m*(c*x**2)**p*(b*x+a)**n,x)","\int x^{m} \left(c x^{2}\right)^{p} \left(a + b x\right)^{n}\, dx"," ",0,"Integral(x**m*(c*x**2)**p*(a + b*x)**n, x)","F",0
998,0,0,0,0.000000," ","integrate((d*x)**m*(c*x**2)**p*(b*x+a)**n,x)","\int \left(c x^{2}\right)^{p} \left(d x\right)^{m} \left(a + b x\right)^{n}\, dx"," ",0,"Integral((c*x**2)**p*(d*x)**m*(a + b*x)**n, x)","F",0
999,1,34,0,0.120538," ","integrate((b*x+a)**5/(a*d/b+d*x)**3,x)","\frac{a^{2} b^{3} x}{d^{3}} + \frac{a b^{4} x^{2}}{d^{3}} + \frac{b^{5} x^{3}}{3 d^{3}}"," ",0,"a**2*b**3*x/d**3 + a*b**4*x**2/d**3 + b**5*x**3/(3*d**3)","B",0
1000,1,20,0,0.118790," ","integrate((b*x+a)**4/(a*d/b+d*x)**3,x)","\frac{a b^{3} x}{d^{3}} + \frac{b^{4} x^{2}}{2 d^{3}}"," ",0,"a*b**3*x/d**3 + b**4*x**2/(2*d**3)","A",0
1001,1,7,0,0.107213," ","integrate((b*x+a)**3/(a*d/b+d*x)**3,x)","\frac{b^{3} x}{d^{3}}"," ",0,"b**3*x/d**3","A",0
1002,1,19,0,0.112325," ","integrate((b*x+a)**2/(a*d/b+d*x)**3,x)","\frac{b^{2} \log{\left(a d^{3} + b d^{3} x \right)}}{d^{3}}"," ",0,"b**2*log(a*d**3 + b*d**3*x)/d**3","A",0
1003,1,19,0,0.177213," ","integrate((b*x+a)/(a*d/b+d*x)**3,x)","- \frac{b^{3}}{a b d^{3} + b^{2} d^{3} x}"," ",0,"-b**3/(a*b*d**3 + b**2*d**3*x)","A",0
1004,1,53,0,0.288310," ","integrate(1/(b*x+a)/(a*d/b+d*x)**3,x)","- \frac{b^{3}}{3 a^{3} b d^{3} + 9 a^{2} b^{2} d^{3} x + 9 a b^{3} d^{3} x^{2} + 3 b^{4} d^{3} x^{3}}"," ",0,"-b**3/(3*a**3*b*d**3 + 9*a**2*b**2*d**3*x + 9*a*b**3*d**3*x**2 + 3*b**4*d**3*x**3)","B",0
1005,1,68,0,0.362865," ","integrate(1/(b*x+a)**2/(a*d/b+d*x)**3,x)","- \frac{b^{3}}{4 a^{4} b d^{3} + 16 a^{3} b^{2} d^{3} x + 24 a^{2} b^{3} d^{3} x^{2} + 16 a b^{4} d^{3} x^{3} + 4 b^{5} d^{3} x^{4}}"," ",0,"-b**3/(4*a**4*b*d**3 + 16*a**3*b**2*d**3*x + 24*a**2*b**3*d**3*x**2 + 16*a*b**4*d**3*x**3 + 4*b**5*d**3*x**4)","B",0
1006,1,83,0,0.421994," ","integrate(1/(b*x+a)**3/(a*d/b+d*x)**3,x)","- \frac{b^{3}}{5 a^{5} b d^{3} + 25 a^{4} b^{2} d^{3} x + 50 a^{3} b^{3} d^{3} x^{2} + 50 a^{2} b^{4} d^{3} x^{3} + 25 a b^{5} d^{3} x^{4} + 5 b^{6} d^{3} x^{5}}"," ",0,"-b**3/(5*a**5*b*d**3 + 25*a**4*b**2*d**3*x + 50*a**3*b**3*d**3*x**2 + 50*a**2*b**4*d**3*x**3 + 25*a*b**5*d**3*x**4 + 5*b**6*d**3*x**5)","B",0
1007,1,34,0,0.129658," ","integrate((b*c/d+b*x)**5/(d*x+c)**3,x)","\frac{b^{5} c^{2} x}{d^{5}} + \frac{b^{5} c x^{2}}{d^{4}} + \frac{b^{5} x^{3}}{3 d^{3}}"," ",0,"b**5*c**2*x/d**5 + b**5*c*x**2/d**4 + b**5*x**3/(3*d**3)","B",0
1008,1,20,0,0.117575," ","integrate((b*c/d+b*x)**4/(d*x+c)**3,x)","\frac{b^{4} c x}{d^{4}} + \frac{b^{4} x^{2}}{2 d^{3}}"," ",0,"b**4*c*x/d**4 + b**4*x**2/(2*d**3)","A",0
1009,1,7,0,0.103761," ","integrate((b*c/d+b*x)**3/(d*x+c)**3,x)","\frac{b^{3} x}{d^{3}}"," ",0,"b**3*x/d**3","A",0
1010,1,17,0,0.104103," ","integrate((b*c/d+b*x)**2/(d*x+c)**3,x)","\frac{b^{2} \log{\left(c d^{2} + d^{3} x \right)}}{d^{3}}"," ",0,"b**2*log(c*d**2 + d**3*x)/d**3","A",0
1011,1,12,0,0.153636," ","integrate((b*c/d+b*x)/(d*x+c)**3,x)","- \frac{b}{c d^{2} + d^{3} x}"," ",0,"-b/(c*d**2 + d**3*x)","A",0
1012,1,44,0,0.280195," ","integrate(1/(b*c/d+b*x)/(d*x+c)**3,x)","- \frac{d}{3 b c^{3} d + 9 b c^{2} d^{2} x + 9 b c d^{3} x^{2} + 3 b d^{4} x^{3}}"," ",0,"-d/(3*b*c**3*d + 9*b*c**2*d**2*x + 9*b*c*d**3*x**2 + 3*b*d**4*x**3)","B",0
1013,1,68,0,0.362055," ","integrate(1/(b*c/d+b*x)**2/(d*x+c)**3,x)","- \frac{d^{2}}{4 b^{2} c^{4} d + 16 b^{2} c^{3} d^{2} x + 24 b^{2} c^{2} d^{3} x^{2} + 16 b^{2} c d^{4} x^{3} + 4 b^{2} d^{5} x^{4}}"," ",0,"-d**2/(4*b**2*c**4*d + 16*b**2*c**3*d**2*x + 24*b**2*c**2*d**3*x**2 + 16*b**2*c*d**4*x**3 + 4*b**2*d**5*x**4)","B",0
1014,1,83,0,0.418730," ","integrate(1/(b*c/d+b*x)**3/(d*x+c)**3,x)","- \frac{d^{3}}{5 b^{3} c^{5} d + 25 b^{3} c^{4} d^{2} x + 50 b^{3} c^{3} d^{3} x^{2} + 50 b^{3} c^{2} d^{4} x^{3} + 25 b^{3} c d^{5} x^{4} + 5 b^{3} d^{6} x^{5}}"," ",0,"-d**3/(5*b**3*c**5*d + 25*b**3*c**4*d**2*x + 50*b**3*c**3*d**3*x**2 + 50*b**3*c**2*d**4*x**3 + 25*b**3*c*d**5*x**4 + 5*b**3*d**6*x**5)","B",0
1015,1,212,0,2.292952," ","integrate((b*x+a)**5*(b*c*x+a*c)**n,x)","\begin{cases} \frac{x}{a c^{6}} & \text{for}\: b = 0 \wedge n = -6 \\a^{5} x \left(a c\right)^{n} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + x \right)}}{b c^{6}} & \text{for}\: n = -6 \\\frac{a^{6} \left(a c + b c x\right)^{n}}{b n + 6 b} + \frac{6 a^{5} b x \left(a c + b c x\right)^{n}}{b n + 6 b} + \frac{15 a^{4} b^{2} x^{2} \left(a c + b c x\right)^{n}}{b n + 6 b} + \frac{20 a^{3} b^{3} x^{3} \left(a c + b c x\right)^{n}}{b n + 6 b} + \frac{15 a^{2} b^{4} x^{4} \left(a c + b c x\right)^{n}}{b n + 6 b} + \frac{6 a b^{5} x^{5} \left(a c + b c x\right)^{n}}{b n + 6 b} + \frac{b^{6} x^{6} \left(a c + b c x\right)^{n}}{b n + 6 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(a*c**6), Eq(b, 0) & Eq(n, -6)), (a**5*x*(a*c)**n, Eq(b, 0)), (log(a/b + x)/(b*c**6), Eq(n, -6)), (a**6*(a*c + b*c*x)**n/(b*n + 6*b) + 6*a**5*b*x*(a*c + b*c*x)**n/(b*n + 6*b) + 15*a**4*b**2*x**2*(a*c + b*c*x)**n/(b*n + 6*b) + 20*a**3*b**3*x**3*(a*c + b*c*x)**n/(b*n + 6*b) + 15*a**2*b**4*x**4*(a*c + b*c*x)**n/(b*n + 6*b) + 6*a*b**5*x**5*(a*c + b*c*x)**n/(b*n + 6*b) + b**6*x**6*(a*c + b*c*x)**n/(b*n + 6*b), True))","A",0
1016,1,124,0,0.098836," ","integrate((b*x+a)**5*(b*c*x+a*c)**3,x)","a^{8} c^{3} x + 4 a^{7} b c^{3} x^{2} + \frac{28 a^{6} b^{2} c^{3} x^{3}}{3} + 14 a^{5} b^{3} c^{3} x^{4} + 14 a^{4} b^{4} c^{3} x^{5} + \frac{28 a^{3} b^{5} c^{3} x^{6}}{3} + 4 a^{2} b^{6} c^{3} x^{7} + a b^{7} c^{3} x^{8} + \frac{b^{8} c^{3} x^{9}}{9}"," ",0,"a**8*c**3*x + 4*a**7*b*c**3*x**2 + 28*a**6*b**2*c**3*x**3/3 + 14*a**5*b**3*c**3*x**4 + 14*a**4*b**4*c**3*x**5 + 28*a**3*b**5*c**3*x**6/3 + 4*a**2*b**6*c**3*x**7 + a*b**7*c**3*x**8 + b**8*c**3*x**9/9","B",0
1017,1,110,0,0.095256," ","integrate((b*x+a)**5*(b*c*x+a*c)**2,x)","a^{7} c^{2} x + \frac{7 a^{6} b c^{2} x^{2}}{2} + 7 a^{5} b^{2} c^{2} x^{3} + \frac{35 a^{4} b^{3} c^{2} x^{4}}{4} + 7 a^{3} b^{4} c^{2} x^{5} + \frac{7 a^{2} b^{5} c^{2} x^{6}}{2} + a b^{6} c^{2} x^{7} + \frac{b^{7} c^{2} x^{8}}{8}"," ",0,"a**7*c**2*x + 7*a**6*b*c**2*x**2/2 + 7*a**5*b**2*c**2*x**3 + 35*a**4*b**3*c**2*x**4/4 + 7*a**3*b**4*c**2*x**5 + 7*a**2*b**5*c**2*x**6/2 + a*b**6*c**2*x**7 + b**7*c**2*x**8/8","B",0
1018,1,78,0,0.083936," ","integrate((b*x+a)**5*(b*c*x+a*c),x)","a^{6} c x + 3 a^{5} b c x^{2} + 5 a^{4} b^{2} c x^{3} + 5 a^{3} b^{3} c x^{4} + 3 a^{2} b^{4} c x^{5} + a b^{5} c x^{6} + \frac{b^{6} c x^{7}}{7}"," ",0,"a**6*c*x + 3*a**5*b*c*x**2 + 5*a**4*b**2*c*x**3 + 5*a**3*b**3*c*x**4 + 3*a**2*b**4*c*x**5 + a*b**5*c*x**6 + b**6*c*x**7/7","B",0
1019,1,51,0,0.102085," ","integrate((b*x+a)**5/(b*c*x+a*c),x)","\frac{a^{4} x}{c} + \frac{2 a^{3} b x^{2}}{c} + \frac{2 a^{2} b^{2} x^{3}}{c} + \frac{a b^{3} x^{4}}{c} + \frac{b^{4} x^{5}}{5 c}"," ",0,"a**4*x/c + 2*a**3*b*x**2/c + 2*a**2*b**2*x**3/c + a*b**3*x**4/c + b**4*x**5/(5*c)","B",0
1020,1,46,0,0.107445," ","integrate((b*x+a)**5/(b*c*x+a*c)**2,x)","\frac{a^{3} x}{c^{2}} + \frac{3 a^{2} b x^{2}}{2 c^{2}} + \frac{a b^{2} x^{3}}{c^{2}} + \frac{b^{3} x^{4}}{4 c^{2}}"," ",0,"a**3*x/c**2 + 3*a**2*b*x**2/(2*c**2) + a*b**2*x**3/c**2 + b**3*x**4/(4*c**2)","B",0
1021,1,29,0,0.108687," ","integrate((b*x+a)**5/(b*c*x+a*c)**3,x)","\frac{a^{2} x}{c^{3}} + \frac{a b x^{2}}{c^{3}} + \frac{b^{2} x^{3}}{3 c^{3}}"," ",0,"a**2*x/c**3 + a*b*x**2/c**3 + b**2*x**3/(3*c**3)","B",0
1022,1,15,0,0.109058," ","integrate((b*x+a)**5/(b*c*x+a*c)**4,x)","\frac{a x}{c^{4}} + \frac{b x^{2}}{2 c^{4}}"," ",0,"a*x/c**4 + b*x**2/(2*c**4)","A",0
1023,1,3,0,0.107115," ","integrate((b*x+a)**5/(b*c*x+a*c)**5,x)","\frac{x}{c^{5}}"," ",0,"x/c**5","A",0
1024,1,17,0,0.123442," ","integrate((b*x+a)**5/(b*c*x+a*c)**6,x)","\frac{\log{\left(a c^{6} + b c^{6} x \right)}}{b c^{6}}"," ",0,"log(a*c**6 + b*c**6*x)/(b*c**6)","A",0
1025,1,17,0,0.200456," ","integrate((b*x+a)**5/(b*c*x+a*c)**7,x)","- \frac{1}{a b c^{7} + b^{2} c^{7} x}"," ",0,"-1/(a*b*c**7 + b**2*c**7*x)","A",0
1026,1,36,0,0.260386," ","integrate((b*x+a)**5/(b*c*x+a*c)**8,x)","- \frac{1}{2 a^{2} b c^{8} + 4 a b^{2} c^{8} x + 2 b^{3} c^{8} x^{2}}"," ",0,"-1/(2*a**2*b*c**8 + 4*a*b**2*c**8*x + 2*b**3*c**8*x**2)","B",0
1027,1,53,0,1.460602," ","integrate(1/(-2-3*x)**(1/2)/(2+3*x)**(1/2),x)","\begin{cases} - \frac{i \log{\left(x + \frac{2}{3} \right)}}{3} & \text{for}\: \left|{x + \frac{2}{3}}\right| < 1 \\\frac{i \log{\left(\frac{1}{x + \frac{2}{3}} \right)}}{3} & \text{for}\: \frac{1}{\left|{x + \frac{2}{3}}\right|} < 1 \\\frac{i {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x + \frac{2}{3}} \right)}}{3} - \frac{i {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x + \frac{2}{3}} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*log(x + 2/3)/3, Abs(x + 2/3) < 1), (I*log(1/(x + 2/3))/3, 1/Abs(x + 2/3) < 1), (I*meijerg(((), (1, 1)), ((0, 0), ()), x + 2/3)/3 - I*meijerg(((1, 1), ()), ((), (0, 0)), x + 2/3)/3, True))","C",0
1028,1,44,0,0.079538," ","integrate((b*x+a)*(-b*c*x+a*c)**3,x)","a^{4} c^{3} x - a^{3} b c^{3} x^{2} + \frac{a b^{3} c^{3} x^{4}}{2} - \frac{b^{4} c^{3} x^{5}}{5}"," ",0,"a**4*c**3*x - a**3*b*c**3*x**2 + a*b**3*c**3*x**4/2 - b**4*c**3*x**5/5","A",0
1029,1,46,0,0.074330," ","integrate((b*x+a)*(-b*c*x+a*c)**2,x)","a^{3} c^{2} x - \frac{a^{2} b c^{2} x^{2}}{2} - \frac{a b^{2} c^{2} x^{3}}{3} + \frac{b^{3} c^{2} x^{4}}{4}"," ",0,"a**3*c**2*x - a**2*b*c**2*x**2/2 - a*b**2*c**2*x**3/3 + b**3*c**2*x**4/4","A",0
1030,1,15,0,0.062763," ","integrate((b*x+a)*(-b*c*x+a*c),x)","a^{2} c x - \frac{b^{2} c x^{3}}{3}"," ",0,"a**2*c*x - b**2*c*x**3/3","A",0
1031,1,8,0,0.057688," ","integrate(b*x+a,x)","a x + \frac{b x^{2}}{2}"," ",0,"a*x + b*x**2/2","A",0
1032,1,17,0,0.140255," ","integrate((b*x+a)/(-b*c*x+a*c),x)","- \frac{2 a \log{\left(- a + b x \right)}}{b c} - \frac{x}{c}"," ",0,"-2*a*log(-a + b*x)/(b*c) - x/c","A",0
1033,1,29,0,0.187326," ","integrate((b*x+a)/(-b*c*x+a*c)**2,x)","- \frac{2 a}{- a b c^{2} + b^{2} c^{2} x} + \frac{\log{\left(- a + b x \right)}}{b c^{2}}"," ",0,"-2*a/(-a*b*c**2 + b**2*c**2*x) + log(-a + b*x)/(b*c**2)","A",0
1034,1,27,0,0.241364," ","integrate((b*x+a)/(-b*c*x+a*c)**3,x)","\frac{x}{a^{2} c^{3} - 2 a b c^{3} x + b^{2} c^{3} x^{2}}"," ",0,"x/(a**2*c**3 - 2*a*b*c**3*x + b**2*c**3*x**2)","B",0
1035,1,56,0,0.307313," ","integrate((b*x+a)/(-b*c*x+a*c)**4,x)","\frac{- a - 3 b x}{- 6 a^{3} b c^{4} + 18 a^{2} b^{2} c^{4} x - 18 a b^{3} c^{4} x^{2} + 6 b^{4} c^{4} x^{3}}"," ",0,"(-a - 3*b*x)/(-6*a**3*b*c**4 + 18*a**2*b**2*c**4*x - 18*a*b**3*c**4*x**2 + 6*b**4*c**4*x**3)","A",0
1036,1,73,0,0.391746," ","integrate((b*x+a)/(-b*c*x+a*c)**5,x)","- \frac{- a - 2 b x}{6 a^{4} b c^{5} - 24 a^{3} b^{2} c^{5} x + 36 a^{2} b^{3} c^{5} x^{2} - 24 a b^{4} c^{5} x^{3} + 6 b^{5} c^{5} x^{4}}"," ",0,"-(-a - 2*b*x)/(6*a**4*b*c**5 - 24*a**3*b**2*c**5*x + 36*a**2*b**3*c**5*x**2 - 24*a*b**4*c**5*x**3 + 6*b**5*c**5*x**4)","B",0
1037,1,88,0,0.462509," ","integrate((b*x+a)/(-b*c*x+a*c)**6,x)","\frac{- 3 a - 5 b x}{- 20 a^{5} b c^{6} + 100 a^{4} b^{2} c^{6} x - 200 a^{3} b^{3} c^{6} x^{2} + 200 a^{2} b^{4} c^{6} x^{3} - 100 a b^{5} c^{6} x^{4} + 20 b^{6} c^{6} x^{5}}"," ",0,"(-3*a - 5*b*x)/(-20*a**5*b*c**6 + 100*a**4*b**2*c**6*x - 200*a**3*b**3*c**6*x**2 + 200*a**2*b**4*c**6*x**3 - 100*a*b**5*c**6*x**4 + 20*b**6*c**6*x**5)","B",0
1038,1,78,0,0.086144," ","integrate((b*x+a)**2*(-b*c*x+a*c)**3,x)","a^{5} c^{3} x - \frac{a^{4} b c^{3} x^{2}}{2} - \frac{2 a^{3} b^{2} c^{3} x^{3}}{3} + \frac{a^{2} b^{3} c^{3} x^{4}}{2} + \frac{a b^{4} c^{3} x^{5}}{5} - \frac{b^{5} c^{3} x^{6}}{6}"," ",0,"a**5*c**3*x - a**4*b*c**3*x**2/2 - 2*a**3*b**2*c**3*x**3/3 + a**2*b**3*c**3*x**4/2 + a*b**4*c**3*x**5/5 - b**5*c**3*x**6/6","A",0
1039,1,36,0,0.078005," ","integrate((b*x+a)**2*(-b*c*x+a*c)**2,x)","a^{4} c^{2} x - \frac{2 a^{2} b^{2} c^{2} x^{3}}{3} + \frac{b^{4} c^{2} x^{5}}{5}"," ",0,"a**4*c**2*x - 2*a**2*b**2*c**2*x**3/3 + b**4*c**2*x**5/5","A",0
1040,1,39,0,0.074235," ","integrate((b*x+a)**2*(-b*c*x+a*c),x)","a^{3} c x + \frac{a^{2} b c x^{2}}{2} - \frac{a b^{2} c x^{3}}{3} - \frac{b^{3} c x^{4}}{4}"," ",0,"a**3*c*x + a**2*b*c*x**2/2 - a*b**2*c*x**3/3 - b**3*c*x**4/4","A",0
1041,1,19,0,0.064444," ","integrate((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","B",0
1042,1,31,0,0.165486," ","integrate((b*x+a)**2/(-b*c*x+a*c),x)","- \frac{4 a^{2} \log{\left(- a + b x \right)}}{b c} - \frac{3 a x}{c} - \frac{b x^{2}}{2 c}"," ",0,"-4*a**2*log(-a + b*x)/(b*c) - 3*a*x/c - b*x**2/(2*c)","A",0
1043,1,39,0,0.198646," ","integrate((b*x+a)**2/(-b*c*x+a*c)**2,x)","- \frac{4 a^{2}}{- a b c^{2} + b^{2} c^{2} x} + \frac{4 a \log{\left(- a + b x \right)}}{b c^{2}} + \frac{x}{c^{2}}"," ",0,"-4*a**2/(-a*b*c**2 + b**2*c**2*x) + 4*a*log(-a + b*x)/(b*c**2) + x/c**2","A",0
1044,1,54,0,0.306299," ","integrate((b*x+a)**2/(-b*c*x+a*c)**3,x)","- \frac{2 a^{2} - 4 a b x}{a^{2} b c^{3} - 2 a b^{2} c^{3} x + b^{3} c^{3} x^{2}} - \frac{\log{\left(- a + b x \right)}}{b c^{3}}"," ",0,"-(2*a**2 - 4*a*b*x)/(a**2*b*c**3 - 2*a*b**2*c**3*x + b**3*c**3*x**2) - log(-a + b*x)/(b*c**3)","A",0
1045,1,61,0,0.350541," ","integrate((b*x+a)**2/(-b*c*x+a*c)**4,x)","\frac{- a^{2} - 3 b^{2} x^{2}}{- 3 a^{3} b c^{4} + 9 a^{2} b^{2} c^{4} x - 9 a b^{3} c^{4} x^{2} + 3 b^{4} c^{4} x^{3}}"," ",0,"(-a**2 - 3*b**2*x**2)/(-3*a**3*b*c**4 + 9*a**2*b**2*c**4*x - 9*a*b**3*c**4*x**2 + 3*b**4*c**4*x**3)","B",0
1046,1,85,0,0.438549," ","integrate((b*x+a)**2/(-b*c*x+a*c)**5,x)","- \frac{- a^{2} - 2 a b x - 3 b^{2} x^{2}}{6 a^{4} b c^{5} - 24 a^{3} b^{2} c^{5} x + 36 a^{2} b^{3} c^{5} x^{2} - 24 a b^{4} c^{5} x^{3} + 6 b^{5} c^{5} x^{4}}"," ",0,"-(-a**2 - 2*a*b*x - 3*b**2*x**2)/(6*a**4*b*c**5 - 24*a**3*b**2*c**5*x + 36*a**2*b**3*c**5*x**2 - 24*a*b**4*c**5*x**3 + 6*b**5*c**5*x**4)","A",0
1047,1,100,0,0.505268," ","integrate((b*x+a)**2/(-b*c*x+a*c)**6,x)","\frac{- 2 a^{2} - 5 a b x - 5 b^{2} x^{2}}{- 15 a^{5} b c^{6} + 75 a^{4} b^{2} c^{6} x - 150 a^{3} b^{3} c^{6} x^{2} + 150 a^{2} b^{4} c^{6} x^{3} - 75 a b^{5} c^{6} x^{4} + 15 b^{6} c^{6} x^{5}}"," ",0,"(-2*a**2 - 5*a*b*x - 5*b**2*x**2)/(-15*a**5*b*c**6 + 75*a**4*b**2*c**6*x - 150*a**3*b**3*c**6*x**2 + 150*a**2*b**4*c**6*x**3 - 75*a*b**5*c**6*x**4 + 15*b**6*c**6*x**5)","B",0
1048,1,117,0,0.599502," ","integrate((b*x+a)**2/(-b*c*x+a*c)**7,x)","- \frac{- 7 a^{2} - 18 a b x - 15 b^{2} x^{2}}{60 a^{6} b c^{7} - 360 a^{5} b^{2} c^{7} x + 900 a^{4} b^{3} c^{7} x^{2} - 1200 a^{3} b^{4} c^{7} x^{3} + 900 a^{2} b^{5} c^{7} x^{4} - 360 a b^{6} c^{7} x^{5} + 60 b^{7} c^{7} x^{6}}"," ",0,"-(-7*a**2 - 18*a*b*x - 15*b**2*x**2)/(60*a**6*b*c**7 - 360*a**5*b**2*c**7*x + 900*a**4*b**3*c**7*x**2 - 1200*a**3*b**4*c**7*x**3 + 900*a**2*b**5*c**7*x**4 - 360*a*b**6*c**7*x**5 + 60*b**7*c**7*x**6)","B",0
1049,1,49,0,0.180841," ","integrate((-b*c*x+a*c)**3/(b*x+a),x)","\frac{8 a^{3} c^{3} \log{\left(a + b x \right)}}{b} - 7 a^{2} c^{3} x + 2 a b c^{3} x^{2} - \frac{b^{2} c^{3} x^{3}}{3}"," ",0,"8*a**3*c**3*log(a + b*x)/b - 7*a**2*c**3*x + 2*a*b*c**3*x**2 - b**2*c**3*x**3/3","A",0
1050,1,34,0,0.152603," ","integrate((-b*c*x+a*c)**2/(b*x+a),x)","\frac{4 a^{2} c^{2} \log{\left(a + b x \right)}}{b} - 3 a c^{2} x + \frac{b c^{2} x^{2}}{2}"," ",0,"4*a**2*c**2*log(a + b*x)/b - 3*a*c**2*x + b*c**2*x**2/2","A",0
1051,1,15,0,0.121923," ","integrate((-b*c*x+a*c)/(b*x+a),x)","\frac{2 a c \log{\left(a + b x \right)}}{b} - c x"," ",0,"2*a*c*log(a + b*x)/b - c*x","A",0
1052,1,7,0,0.065560," ","integrate(1/(b*x+a),x)","\frac{\log{\left(a + b x \right)}}{b}"," ",0,"log(a + b*x)/b","A",0
1053,1,22,0,0.170547," ","integrate(1/(b*x+a)/(-b*c*x+a*c),x)","- \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{2} - \frac{\log{\left(\frac{a}{b} + x \right)}}{2}}{a b c}"," ",0,"-(log(-a/b + x)/2 - log(a/b + x)/2)/(a*b*c)","B",0
1054,1,48,0,0.283458," ","integrate(1/(b*x+a)/(-b*c*x+a*c)**2,x)","- \frac{1}{- 2 a^{2} b c^{2} + 2 a b^{2} c^{2} x} + \frac{- \frac{\log{\left(- \frac{a}{b} + x \right)}}{4} + \frac{\log{\left(\frac{a}{b} + x \right)}}{4}}{a^{2} b c^{2}}"," ",0,"-1/(-2*a**2*b*c**2 + 2*a*b**2*c**2*x) + (-log(-a/b + x)/4 + log(a/b + x)/4)/(a**2*b*c**2)","A",0
1055,1,71,0,0.381033," ","integrate(1/(b*x+a)/(-b*c*x+a*c)**3,x)","- \frac{- 2 a + b x}{4 a^{4} b c^{3} - 8 a^{3} b^{2} c^{3} x + 4 a^{2} b^{3} c^{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 c^{3}}"," ",0,"-(-2*a + b*x)/(4*a**4*b*c**3 - 8*a**3*b**2*c**3*x + 4*a**2*b**3*c**3*x**2) - (log(-a/b + x)/8 - log(a/b + x)/8)/(a**3*b*c**3)","A",0
1056,1,51,0,0.246308," ","integrate((-b*c*x+a*c)**3/(b*x+a)**2,x)","- \frac{8 a^{3} c^{3}}{a b + b^{2} x} - \frac{12 a^{2} c^{3} \log{\left(a + b x \right)}}{b} + 5 a c^{3} x - \frac{b c^{3} x^{2}}{2}"," ",0,"-8*a**3*c**3/(a*b + b**2*x) - 12*a**2*c**3*log(a + b*x)/b + 5*a*c**3*x - b*c**3*x**2/2","A",0
1057,1,36,0,0.193691," ","integrate((-b*c*x+a*c)**2/(b*x+a)**2,x)","- \frac{4 a^{2} c^{2}}{a b + b^{2} x} - \frac{4 a c^{2} \log{\left(a + b x \right)}}{b} + c^{2} x"," ",0,"-4*a**2*c**2/(a*b + b**2*x) - 4*a*c**2*log(a + b*x)/b + c**2*x","A",0
1058,1,24,0,0.172220," ","integrate((-b*c*x+a*c)/(b*x+a)**2,x)","- \frac{2 a c}{a b + b^{2} x} - \frac{c \log{\left(a + b x \right)}}{b}"," ",0,"-2*a*c/(a*b + b**2*x) - c*log(a + b*x)/b","A",0
1059,1,10,0,0.137464," ","integrate(1/(b*x+a)**2,x)","- \frac{1}{a b + b^{2} x}"," ",0,"-1/(a*b + b**2*x)","A",0
1060,1,44,0,0.283518," ","integrate(1/(b*x+a)**2/(-b*c*x+a*c),x)","- \frac{1}{2 a^{2} b c + 2 a b^{2} c x} - \frac{\frac{\log{\left(- \frac{a}{b} + x \right)}}{4} - \frac{\log{\left(\frac{a}{b} + x \right)}}{4}}{a^{2} b c}"," ",0,"-1/(2*a**2*b*c + 2*a*b**2*c*x) - (log(-a/b + x)/4 - log(a/b + x)/4)/(a**2*b*c)","A",0
1061,1,49,0,0.272883," ","integrate(1/(b*x+a)**2/(-b*c*x+a*c)**2,x)","- \frac{x}{- 2 a^{4} c^{2} + 2 a^{2} b^{2} c^{2} x^{2}} + \frac{- \frac{\log{\left(- \frac{a}{b} + x \right)}}{4} + \frac{\log{\left(\frac{a}{b} + x \right)}}{4}}{a^{3} b c^{2}}"," ",0,"-x/(-2*a**4*c**2 + 2*a**2*b**2*c**2*x**2) + (-log(-a/b + x)/4 + log(a/b + x)/4)/(a**3*b*c**2)","A",0
1062,1,104,0,0.512312," ","integrate(1/(b*x+a)**2/(-b*c*x+a*c)**3,x)","- \frac{- 2 a^{2} - 3 a b x + 3 b^{2} x^{2}}{8 a^{6} b c^{3} - 8 a^{5} b^{2} c^{3} x - 8 a^{4} b^{3} c^{3} x^{2} + 8 a^{3} b^{4} c^{3} 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 c^{3}}"," ",0,"-(-2*a**2 - 3*a*b*x + 3*b**2*x**2)/(8*a**6*b*c**3 - 8*a**5*b**2*c**3*x - 8*a**4*b**3*c**3*x**2 + 8*a**3*b**4*c**3*x**3) - (3*log(-a/b + x)/16 - 3*log(a/b + x)/16)/(a**4*b*c**3)","A",0
1063,1,289,0,48.588659," ","integrate((1-x)**(9/2)*(1+x)**(1/2),x)","\begin{cases} - \frac{21 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} + \frac{i \left(x + 1\right)^{\frac{13}{2}}}{6 \sqrt{x - 1}} - \frac{59 i \left(x + 1\right)^{\frac{11}{2}}}{30 \sqrt{x - 1}} + \frac{1151 i \left(x + 1\right)^{\frac{9}{2}}}{120 \sqrt{x - 1}} - \frac{2947 i \left(x + 1\right)^{\frac{7}{2}}}{120 \sqrt{x - 1}} + \frac{8171 i \left(x + 1\right)^{\frac{5}{2}}}{240 \sqrt{x - 1}} - \frac{1045 i \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{x - 1}} + \frac{21 i \sqrt{x + 1}}{8 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{21 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} - \frac{\left(x + 1\right)^{\frac{13}{2}}}{6 \sqrt{1 - x}} + \frac{59 \left(x + 1\right)^{\frac{11}{2}}}{30 \sqrt{1 - x}} - \frac{1151 \left(x + 1\right)^{\frac{9}{2}}}{120 \sqrt{1 - x}} + \frac{2947 \left(x + 1\right)^{\frac{7}{2}}}{120 \sqrt{1 - x}} - \frac{8171 \left(x + 1\right)^{\frac{5}{2}}}{240 \sqrt{1 - x}} + \frac{1045 \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{1 - x}} - \frac{21 \sqrt{x + 1}}{8 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-21*I*acosh(sqrt(2)*sqrt(x + 1)/2)/8 + I*(x + 1)**(13/2)/(6*sqrt(x - 1)) - 59*I*(x + 1)**(11/2)/(30*sqrt(x - 1)) + 1151*I*(x + 1)**(9/2)/(120*sqrt(x - 1)) - 2947*I*(x + 1)**(7/2)/(120*sqrt(x - 1)) + 8171*I*(x + 1)**(5/2)/(240*sqrt(x - 1)) - 1045*I*(x + 1)**(3/2)/(48*sqrt(x - 1)) + 21*I*sqrt(x + 1)/(8*sqrt(x - 1)), Abs(x + 1)/2 > 1), (21*asin(sqrt(2)*sqrt(x + 1)/2)/8 - (x + 1)**(13/2)/(6*sqrt(1 - x)) + 59*(x + 1)**(11/2)/(30*sqrt(1 - x)) - 1151*(x + 1)**(9/2)/(120*sqrt(1 - x)) + 2947*(x + 1)**(7/2)/(120*sqrt(1 - x)) - 8171*(x + 1)**(5/2)/(240*sqrt(1 - x)) + 1045*(x + 1)**(3/2)/(48*sqrt(1 - x)) - 21*sqrt(x + 1)/(8*sqrt(1 - x)), True))","A",0
1064,1,253,0,21.066665," ","integrate((1-x)**(7/2)*(1+x)**(1/2),x)","\begin{cases} - \frac{7 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{i \left(x + 1\right)^{\frac{11}{2}}}{5 \sqrt{x - 1}} + \frac{39 i \left(x + 1\right)^{\frac{9}{2}}}{20 \sqrt{x - 1}} - \frac{449 i \left(x + 1\right)^{\frac{7}{2}}}{60 \sqrt{x - 1}} + \frac{1657 i \left(x + 1\right)^{\frac{5}{2}}}{120 \sqrt{x - 1}} - \frac{263 i \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{x - 1}} + \frac{7 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{7 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{\left(x + 1\right)^{\frac{11}{2}}}{5 \sqrt{1 - x}} - \frac{39 \left(x + 1\right)^{\frac{9}{2}}}{20 \sqrt{1 - x}} + \frac{449 \left(x + 1\right)^{\frac{7}{2}}}{60 \sqrt{1 - x}} - \frac{1657 \left(x + 1\right)^{\frac{5}{2}}}{120 \sqrt{1 - x}} + \frac{263 \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{1 - x}} - \frac{7 \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-7*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 - I*(x + 1)**(11/2)/(5*sqrt(x - 1)) + 39*I*(x + 1)**(9/2)/(20*sqrt(x - 1)) - 449*I*(x + 1)**(7/2)/(60*sqrt(x - 1)) + 1657*I*(x + 1)**(5/2)/(120*sqrt(x - 1)) - 263*I*(x + 1)**(3/2)/(24*sqrt(x - 1)) + 7*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (7*asin(sqrt(2)*sqrt(x + 1)/2)/4 + (x + 1)**(11/2)/(5*sqrt(1 - x)) - 39*(x + 1)**(9/2)/(20*sqrt(1 - x)) + 449*(x + 1)**(7/2)/(60*sqrt(1 - x)) - 1657*(x + 1)**(5/2)/(120*sqrt(1 - x)) + 263*(x + 1)**(3/2)/(24*sqrt(1 - x)) - 7*sqrt(x + 1)/(4*sqrt(1 - x)), True))","A",0
1065,1,218,0,9.030941," ","integrate((1-x)**(5/2)*(1+x)**(1/2),x)","\begin{cases} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{i \left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{x - 1}} - \frac{23 i \left(x + 1\right)^{\frac{7}{2}}}{12 \sqrt{x - 1}} + \frac{127 i \left(x + 1\right)^{\frac{5}{2}}}{24 \sqrt{x - 1}} - \frac{133 i \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{x - 1}} + \frac{5 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{\left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{1 - x}} + \frac{23 \left(x + 1\right)^{\frac{7}{2}}}{12 \sqrt{1 - x}} - \frac{127 \left(x + 1\right)^{\frac{5}{2}}}{24 \sqrt{1 - x}} + \frac{133 \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{1 - x}} - \frac{5 \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 + I*(x + 1)**(9/2)/(4*sqrt(x - 1)) - 23*I*(x + 1)**(7/2)/(12*sqrt(x - 1)) + 127*I*(x + 1)**(5/2)/(24*sqrt(x - 1)) - 133*I*(x + 1)**(3/2)/(24*sqrt(x - 1)) + 5*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (5*asin(sqrt(2)*sqrt(x + 1)/2)/4 - (x + 1)**(9/2)/(4*sqrt(1 - x)) + 23*(x + 1)**(7/2)/(12*sqrt(1 - x)) - 127*(x + 1)**(5/2)/(24*sqrt(1 - x)) + 133*(x + 1)**(3/2)/(24*sqrt(1 - x)) - 5*sqrt(x + 1)/(4*sqrt(1 - x)), True))","A",0
1066,1,168,0,4.493535," ","integrate((1-x)**(3/2)*(1+x)**(1/2),x)","\begin{cases} - i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{x - 1}} + \frac{11 i \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{x - 1}} - \frac{17 i \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{x - 1}} + \frac{i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{1 - x}} - \frac{11 \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{1 - x}} + \frac{17 \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{1 - x}} - \frac{\sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(7/2)/(3*sqrt(x - 1)) + 11*I*(x + 1)**(5/2)/(6*sqrt(x - 1)) - 17*I*(x + 1)**(3/2)/(6*sqrt(x - 1)) + I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(7/2)/(3*sqrt(1 - x)) - 11*(x + 1)**(5/2)/(6*sqrt(1 - x)) + 17*(x + 1)**(3/2)/(6*sqrt(1 - x)) - sqrt(x + 1)/sqrt(1 - x), True))","B",0
1067,1,133,0,2.728252," ","integrate((1-x)**(1/2)*(1+x)**(1/2),x)","\begin{cases} - i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{x - 1}} - \frac{3 i \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{x - 1}} + \frac{i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{1 - x}} + \frac{3 \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{1 - x}} - \frac{\sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(5/2)/(2*sqrt(x - 1)) - 3*I*(x + 1)**(3/2)/(2*sqrt(x - 1)) + I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(5/2)/(2*sqrt(1 - x)) + 3*(x + 1)**(3/2)/(2*sqrt(1 - x)) - sqrt(x + 1)/sqrt(1 - x), True))","B",0
1068,1,100,0,1.842852," ","integrate((1+x)**(1/2)/(1-x)**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{\sqrt{x - 1}} + \frac{2 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{1 - x}} - \frac{2 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(3/2)/sqrt(x - 1) + 2*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (2*asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(3/2)/sqrt(1 - x) - 2*sqrt(x + 1)/sqrt(1 - x), True))","B",0
1069,1,71,0,1.618511," ","integrate((1+x)**(1/2)/(1-x)**(3/2),x)","\begin{cases} 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{2 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{2 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(sqrt(2)*sqrt(x + 1)/2) - 2*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (-2*asin(sqrt(2)*sqrt(x + 1)/2) + 2*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1070,1,61,0,1.674484," ","integrate((1+x)**(1/2)/(1-x)**(5/2),x)","\begin{cases} \frac{i \left(x + 1\right)^{\frac{3}{2}}}{3 \sqrt{x - 1} \left(x + 1\right) - 6 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{\left(x + 1\right)^{\frac{3}{2}}}{3 \sqrt{1 - x} \left(x + 1\right) - 6 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*(x + 1)**(3/2)/(3*sqrt(x - 1)*(x + 1) - 6*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-(x + 1)**(3/2)/(3*sqrt(1 - x)*(x + 1) - 6*sqrt(1 - x)), True))","A",0
1071,1,173,0,6.547471," ","integrate((1+x)**(1/2)/(1-x)**(7/2),x)","\begin{cases} \frac{i \left(x + 1\right)^{\frac{5}{2}}}{15 \sqrt{x - 1} \left(x + 1\right)^{2} - 60 \sqrt{x - 1} \left(x + 1\right) + 60 \sqrt{x - 1}} - \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{15 \sqrt{x - 1} \left(x + 1\right)^{2} - 60 \sqrt{x - 1} \left(x + 1\right) + 60 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{\left(x + 1\right)^{\frac{5}{2}}}{15 \sqrt{1 - x} \left(x + 1\right)^{2} - 60 \sqrt{1 - x} \left(x + 1\right) + 60 \sqrt{1 - x}} + \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{15 \sqrt{1 - x} \left(x + 1\right)^{2} - 60 \sqrt{1 - x} \left(x + 1\right) + 60 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*(x + 1)**(5/2)/(15*sqrt(x - 1)*(x + 1)**2 - 60*sqrt(x - 1)*(x + 1) + 60*sqrt(x - 1)) - 5*I*(x + 1)**(3/2)/(15*sqrt(x - 1)*(x + 1)**2 - 60*sqrt(x - 1)*(x + 1) + 60*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-(x + 1)**(5/2)/(15*sqrt(1 - x)*(x + 1)**2 - 60*sqrt(1 - x)*(x + 1) + 60*sqrt(1 - x)) + 5*(x + 1)**(3/2)/(15*sqrt(1 - x)*(x + 1)**2 - 60*sqrt(1 - x)*(x + 1) + 60*sqrt(1 - x)), True))","B",0
1072,1,568,0,19.922572," ","integrate((1+x)**(1/2)/(1-x)**(9/2),x)","\begin{cases} \frac{2 i \left(x + 1\right)^{\frac{9}{2}}}{105 \sqrt{x - 1} \left(x + 1\right)^{4} - 840 \sqrt{x - 1} \left(x + 1\right)^{3} + 2520 \sqrt{x - 1} \left(x + 1\right)^{2} - 3360 \sqrt{x - 1} \left(x + 1\right) + 1680 \sqrt{x - 1}} - \frac{18 i \left(x + 1\right)^{\frac{7}{2}}}{105 \sqrt{x - 1} \left(x + 1\right)^{4} - 840 \sqrt{x - 1} \left(x + 1\right)^{3} + 2520 \sqrt{x - 1} \left(x + 1\right)^{2} - 3360 \sqrt{x - 1} \left(x + 1\right) + 1680 \sqrt{x - 1}} + \frac{63 i \left(x + 1\right)^{\frac{5}{2}}}{105 \sqrt{x - 1} \left(x + 1\right)^{4} - 840 \sqrt{x - 1} \left(x + 1\right)^{3} + 2520 \sqrt{x - 1} \left(x + 1\right)^{2} - 3360 \sqrt{x - 1} \left(x + 1\right) + 1680 \sqrt{x - 1}} - \frac{70 i \left(x + 1\right)^{\frac{3}{2}}}{105 \sqrt{x - 1} \left(x + 1\right)^{4} - 840 \sqrt{x - 1} \left(x + 1\right)^{3} + 2520 \sqrt{x - 1} \left(x + 1\right)^{2} - 3360 \sqrt{x - 1} \left(x + 1\right) + 1680 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{2 \left(x + 1\right)^{\frac{9}{2}}}{105 \sqrt{1 - x} \left(x + 1\right)^{4} - 840 \sqrt{1 - x} \left(x + 1\right)^{3} + 2520 \sqrt{1 - x} \left(x + 1\right)^{2} - 3360 \sqrt{1 - x} \left(x + 1\right) + 1680 \sqrt{1 - x}} + \frac{18 \left(x + 1\right)^{\frac{7}{2}}}{105 \sqrt{1 - x} \left(x + 1\right)^{4} - 840 \sqrt{1 - x} \left(x + 1\right)^{3} + 2520 \sqrt{1 - x} \left(x + 1\right)^{2} - 3360 \sqrt{1 - x} \left(x + 1\right) + 1680 \sqrt{1 - x}} - \frac{63 \left(x + 1\right)^{\frac{5}{2}}}{105 \sqrt{1 - x} \left(x + 1\right)^{4} - 840 \sqrt{1 - x} \left(x + 1\right)^{3} + 2520 \sqrt{1 - x} \left(x + 1\right)^{2} - 3360 \sqrt{1 - x} \left(x + 1\right) + 1680 \sqrt{1 - x}} + \frac{70 \left(x + 1\right)^{\frac{3}{2}}}{105 \sqrt{1 - x} \left(x + 1\right)^{4} - 840 \sqrt{1 - x} \left(x + 1\right)^{3} + 2520 \sqrt{1 - x} \left(x + 1\right)^{2} - 3360 \sqrt{1 - x} \left(x + 1\right) + 1680 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*(x + 1)**(9/2)/(105*sqrt(x - 1)*(x + 1)**4 - 840*sqrt(x - 1)*(x + 1)**3 + 2520*sqrt(x - 1)*(x + 1)**2 - 3360*sqrt(x - 1)*(x + 1) + 1680*sqrt(x - 1)) - 18*I*(x + 1)**(7/2)/(105*sqrt(x - 1)*(x + 1)**4 - 840*sqrt(x - 1)*(x + 1)**3 + 2520*sqrt(x - 1)*(x + 1)**2 - 3360*sqrt(x - 1)*(x + 1) + 1680*sqrt(x - 1)) + 63*I*(x + 1)**(5/2)/(105*sqrt(x - 1)*(x + 1)**4 - 840*sqrt(x - 1)*(x + 1)**3 + 2520*sqrt(x - 1)*(x + 1)**2 - 3360*sqrt(x - 1)*(x + 1) + 1680*sqrt(x - 1)) - 70*I*(x + 1)**(3/2)/(105*sqrt(x - 1)*(x + 1)**4 - 840*sqrt(x - 1)*(x + 1)**3 + 2520*sqrt(x - 1)*(x + 1)**2 - 3360*sqrt(x - 1)*(x + 1) + 1680*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-2*(x + 1)**(9/2)/(105*sqrt(1 - x)*(x + 1)**4 - 840*sqrt(1 - x)*(x + 1)**3 + 2520*sqrt(1 - x)*(x + 1)**2 - 3360*sqrt(1 - x)*(x + 1) + 1680*sqrt(1 - x)) + 18*(x + 1)**(7/2)/(105*sqrt(1 - x)*(x + 1)**4 - 840*sqrt(1 - x)*(x + 1)**3 + 2520*sqrt(1 - x)*(x + 1)**2 - 3360*sqrt(1 - x)*(x + 1) + 1680*sqrt(1 - x)) - 63*(x + 1)**(5/2)/(105*sqrt(1 - x)*(x + 1)**4 - 840*sqrt(1 - x)*(x + 1)**3 + 2520*sqrt(1 - x)*(x + 1)**2 - 3360*sqrt(1 - x)*(x + 1) + 1680*sqrt(1 - x)) + 70*(x + 1)**(3/2)/(105*sqrt(1 - x)*(x + 1)**4 - 840*sqrt(1 - x)*(x + 1)**3 + 2520*sqrt(1 - x)*(x + 1)**2 - 3360*sqrt(1 - x)*(x + 1) + 1680*sqrt(1 - x)), True))","B",0
1073,1,1562,0,53.780192," ","integrate((1+x)**(1/2)/(1-x)**(11/2),x)","\begin{cases} \frac{2 i \left(x + 1\right)^{\frac{15}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} - \frac{30 i \left(x + 1\right)^{\frac{13}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} + \frac{195 i \left(x + 1\right)^{\frac{11}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} - \frac{715 i \left(x + 1\right)^{\frac{9}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} + \frac{1530 i \left(x + 1\right)^{\frac{7}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} - \frac{1764 i \left(x + 1\right)^{\frac{5}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} + \frac{840 i \left(x + 1\right)^{\frac{3}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{7} - 4410 \sqrt{x - 1} \left(x + 1\right)^{6} + 26460 \sqrt{x - 1} \left(x + 1\right)^{5} - 88200 \sqrt{x - 1} \left(x + 1\right)^{4} + 176400 \sqrt{x - 1} \left(x + 1\right)^{3} - 211680 \sqrt{x - 1} \left(x + 1\right)^{2} + 141120 \sqrt{x - 1} \left(x + 1\right) - 40320 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{2 \left(x + 1\right)^{\frac{15}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} + \frac{30 \left(x + 1\right)^{\frac{13}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} - \frac{195 \left(x + 1\right)^{\frac{11}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} + \frac{715 \left(x + 1\right)^{\frac{9}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} - \frac{1530 \left(x + 1\right)^{\frac{7}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} + \frac{1764 \left(x + 1\right)^{\frac{5}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} - \frac{840 \left(x + 1\right)^{\frac{3}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{7} - 4410 \sqrt{1 - x} \left(x + 1\right)^{6} + 26460 \sqrt{1 - x} \left(x + 1\right)^{5} - 88200 \sqrt{1 - x} \left(x + 1\right)^{4} + 176400 \sqrt{1 - x} \left(x + 1\right)^{3} - 211680 \sqrt{1 - x} \left(x + 1\right)^{2} + 141120 \sqrt{1 - x} \left(x + 1\right) - 40320 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*(x + 1)**(15/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)) - 30*I*(x + 1)**(13/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)) + 195*I*(x + 1)**(11/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)) - 715*I*(x + 1)**(9/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)) + 1530*I*(x + 1)**(7/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)) - 1764*I*(x + 1)**(5/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)) + 840*I*(x + 1)**(3/2)/(315*sqrt(x - 1)*(x + 1)**7 - 4410*sqrt(x - 1)*(x + 1)**6 + 26460*sqrt(x - 1)*(x + 1)**5 - 88200*sqrt(x - 1)*(x + 1)**4 + 176400*sqrt(x - 1)*(x + 1)**3 - 211680*sqrt(x - 1)*(x + 1)**2 + 141120*sqrt(x - 1)*(x + 1) - 40320*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-2*(x + 1)**(15/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)) + 30*(x + 1)**(13/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)) - 195*(x + 1)**(11/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)) + 715*(x + 1)**(9/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)) - 1530*(x + 1)**(7/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)) + 1764*(x + 1)**(5/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)) - 840*(x + 1)**(3/2)/(315*sqrt(1 - x)*(x + 1)**7 - 4410*sqrt(1 - x)*(x + 1)**6 + 26460*sqrt(1 - x)*(x + 1)**5 - 88200*sqrt(1 - x)*(x + 1)**4 + 176400*sqrt(1 - x)*(x + 1)**3 - 211680*sqrt(1 - x)*(x + 1)**2 + 141120*sqrt(1 - x)*(x + 1) - 40320*sqrt(1 - x)), True))","B",0
1074,1,3650,0,135.085455," ","integrate((1+x)**(1/2)/(1-x)**(13/2),x)","\begin{cases} \frac{8 i \left(x + 1\right)^{\frac{23}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} - \frac{184 i \left(x + 1\right)^{\frac{21}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} + \frac{1932 i \left(x + 1\right)^{\frac{19}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} - \frac{12236 i \left(x + 1\right)^{\frac{17}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} + \frac{52003 i \left(x + 1\right)^{\frac{15}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} - \frac{155316 i \left(x + 1\right)^{\frac{13}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} + \frac{329588 i \left(x + 1\right)^{\frac{11}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} - \frac{488224 i \left(x + 1\right)^{\frac{9}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} + \frac{479952 i \left(x + 1\right)^{\frac{7}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} - \frac{280896 i \left(x + 1\right)^{\frac{5}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} + \frac{73920 i \left(x + 1\right)^{\frac{3}{2}}}{3465 \sqrt{x - 1} \left(x + 1\right)^{11} - 76230 \sqrt{x - 1} \left(x + 1\right)^{10} + 762300 \sqrt{x - 1} \left(x + 1\right)^{9} - 4573800 \sqrt{x - 1} \left(x + 1\right)^{8} + 18295200 \sqrt{x - 1} \left(x + 1\right)^{7} - 51226560 \sqrt{x - 1} \left(x + 1\right)^{6} + 102453120 \sqrt{x - 1} \left(x + 1\right)^{5} - 146361600 \sqrt{x - 1} \left(x + 1\right)^{4} + 146361600 \sqrt{x - 1} \left(x + 1\right)^{3} - 97574400 \sqrt{x - 1} \left(x + 1\right)^{2} + 39029760 \sqrt{x - 1} \left(x + 1\right) - 7096320 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{8 \left(x + 1\right)^{\frac{23}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} + \frac{184 \left(x + 1\right)^{\frac{21}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} - \frac{1932 \left(x + 1\right)^{\frac{19}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} + \frac{12236 \left(x + 1\right)^{\frac{17}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} - \frac{52003 \left(x + 1\right)^{\frac{15}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} + \frac{155316 \left(x + 1\right)^{\frac{13}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} - \frac{329588 \left(x + 1\right)^{\frac{11}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} + \frac{488224 \left(x + 1\right)^{\frac{9}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} - \frac{479952 \left(x + 1\right)^{\frac{7}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} + \frac{280896 \left(x + 1\right)^{\frac{5}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} - \frac{73920 \left(x + 1\right)^{\frac{3}{2}}}{3465 \sqrt{1 - x} \left(x + 1\right)^{11} - 76230 \sqrt{1 - x} \left(x + 1\right)^{10} + 762300 \sqrt{1 - x} \left(x + 1\right)^{9} - 4573800 \sqrt{1 - x} \left(x + 1\right)^{8} + 18295200 \sqrt{1 - x} \left(x + 1\right)^{7} - 51226560 \sqrt{1 - x} \left(x + 1\right)^{6} + 102453120 \sqrt{1 - x} \left(x + 1\right)^{5} - 146361600 \sqrt{1 - x} \left(x + 1\right)^{4} + 146361600 \sqrt{1 - x} \left(x + 1\right)^{3} - 97574400 \sqrt{1 - x} \left(x + 1\right)^{2} + 39029760 \sqrt{1 - x} \left(x + 1\right) - 7096320 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*I*(x + 1)**(23/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 184*I*(x + 1)**(21/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 1932*I*(x + 1)**(19/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 12236*I*(x + 1)**(17/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 52003*I*(x + 1)**(15/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 155316*I*(x + 1)**(13/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 329588*I*(x + 1)**(11/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 488224*I*(x + 1)**(9/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 479952*I*(x + 1)**(7/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 280896*I*(x + 1)**(5/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 73920*I*(x + 1)**(3/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-8*(x + 1)**(23/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 184*(x + 1)**(21/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 1932*(x + 1)**(19/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 12236*(x + 1)**(17/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 52003*(x + 1)**(15/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 155316*(x + 1)**(13/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 329588*(x + 1)**(11/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 488224*(x + 1)**(9/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 479952*(x + 1)**(7/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 280896*(x + 1)**(5/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 73920*(x + 1)**(3/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)), True))","B",0
1075,1,325,0,75.197627," ","integrate((1-x)**(9/2)*(1+x)**(3/2),x)","\begin{cases} - \frac{9 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} + \frac{i \left(x + 1\right)^{\frac{15}{2}}}{7 \sqrt{x - 1}} - \frac{23 i \left(x + 1\right)^{\frac{13}{2}}}{14 \sqrt{x - 1}} + \frac{541 i \left(x + 1\right)^{\frac{11}{2}}}{70 \sqrt{x - 1}} - \frac{5249 i \left(x + 1\right)^{\frac{9}{2}}}{280 \sqrt{x - 1}} + \frac{6653 i \left(x + 1\right)^{\frac{7}{2}}}{280 \sqrt{x - 1}} - \frac{1027 i \left(x + 1\right)^{\frac{5}{2}}}{80 \sqrt{x - 1}} - \frac{3 i \left(x + 1\right)^{\frac{3}{2}}}{16 \sqrt{x - 1}} + \frac{9 i \sqrt{x + 1}}{8 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{9 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} - \frac{\left(x + 1\right)^{\frac{15}{2}}}{7 \sqrt{1 - x}} + \frac{23 \left(x + 1\right)^{\frac{13}{2}}}{14 \sqrt{1 - x}} - \frac{541 \left(x + 1\right)^{\frac{11}{2}}}{70 \sqrt{1 - x}} + \frac{5249 \left(x + 1\right)^{\frac{9}{2}}}{280 \sqrt{1 - x}} - \frac{6653 \left(x + 1\right)^{\frac{7}{2}}}{280 \sqrt{1 - x}} + \frac{1027 \left(x + 1\right)^{\frac{5}{2}}}{80 \sqrt{1 - x}} + \frac{3 \left(x + 1\right)^{\frac{3}{2}}}{16 \sqrt{1 - x}} - \frac{9 \sqrt{x + 1}}{8 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*I*acosh(sqrt(2)*sqrt(x + 1)/2)/8 + I*(x + 1)**(15/2)/(7*sqrt(x - 1)) - 23*I*(x + 1)**(13/2)/(14*sqrt(x - 1)) + 541*I*(x + 1)**(11/2)/(70*sqrt(x - 1)) - 5249*I*(x + 1)**(9/2)/(280*sqrt(x - 1)) + 6653*I*(x + 1)**(7/2)/(280*sqrt(x - 1)) - 1027*I*(x + 1)**(5/2)/(80*sqrt(x - 1)) - 3*I*(x + 1)**(3/2)/(16*sqrt(x - 1)) + 9*I*sqrt(x + 1)/(8*sqrt(x - 1)), Abs(x + 1)/2 > 1), (9*asin(sqrt(2)*sqrt(x + 1)/2)/8 - (x + 1)**(15/2)/(7*sqrt(1 - x)) + 23*(x + 1)**(13/2)/(14*sqrt(1 - x)) - 541*(x + 1)**(11/2)/(70*sqrt(1 - x)) + 5249*(x + 1)**(9/2)/(280*sqrt(1 - x)) - 6653*(x + 1)**(7/2)/(280*sqrt(1 - x)) + 1027*(x + 1)**(5/2)/(80*sqrt(1 - x)) + 3*(x + 1)**(3/2)/(16*sqrt(1 - x)) - 9*sqrt(x + 1)/(8*sqrt(1 - x)), True))","A",0
1076,1,289,0,32.987253," ","integrate((1-x)**(7/2)*(1+x)**(3/2),x)","\begin{cases} - \frac{7 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} - \frac{i \left(x + 1\right)^{\frac{13}{2}}}{6 \sqrt{x - 1}} + \frac{47 i \left(x + 1\right)^{\frac{11}{2}}}{30 \sqrt{x - 1}} - \frac{683 i \left(x + 1\right)^{\frac{9}{2}}}{120 \sqrt{x - 1}} + \frac{1151 i \left(x + 1\right)^{\frac{7}{2}}}{120 \sqrt{x - 1}} - \frac{1543 i \left(x + 1\right)^{\frac{5}{2}}}{240 \sqrt{x - 1}} - \frac{7 i \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{x - 1}} + \frac{7 i \sqrt{x + 1}}{8 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{7 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} + \frac{\left(x + 1\right)^{\frac{13}{2}}}{6 \sqrt{1 - x}} - \frac{47 \left(x + 1\right)^{\frac{11}{2}}}{30 \sqrt{1 - x}} + \frac{683 \left(x + 1\right)^{\frac{9}{2}}}{120 \sqrt{1 - x}} - \frac{1151 \left(x + 1\right)^{\frac{7}{2}}}{120 \sqrt{1 - x}} + \frac{1543 \left(x + 1\right)^{\frac{5}{2}}}{240 \sqrt{1 - x}} + \frac{7 \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{1 - x}} - \frac{7 \sqrt{x + 1}}{8 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-7*I*acosh(sqrt(2)*sqrt(x + 1)/2)/8 - I*(x + 1)**(13/2)/(6*sqrt(x - 1)) + 47*I*(x + 1)**(11/2)/(30*sqrt(x - 1)) - 683*I*(x + 1)**(9/2)/(120*sqrt(x - 1)) + 1151*I*(x + 1)**(7/2)/(120*sqrt(x - 1)) - 1543*I*(x + 1)**(5/2)/(240*sqrt(x - 1)) - 7*I*(x + 1)**(3/2)/(48*sqrt(x - 1)) + 7*I*sqrt(x + 1)/(8*sqrt(x - 1)), Abs(x + 1)/2 > 1), (7*asin(sqrt(2)*sqrt(x + 1)/2)/8 + (x + 1)**(13/2)/(6*sqrt(1 - x)) - 47*(x + 1)**(11/2)/(30*sqrt(1 - x)) + 683*(x + 1)**(9/2)/(120*sqrt(1 - x)) - 1151*(x + 1)**(7/2)/(120*sqrt(1 - x)) + 1543*(x + 1)**(5/2)/(240*sqrt(1 - x)) + 7*(x + 1)**(3/2)/(48*sqrt(1 - x)) - 7*sqrt(x + 1)/(8*sqrt(1 - x)), True))","A",0
1077,1,250,0,15.248204," ","integrate((1-x)**(5/2)*(1+x)**(3/2),x)","\begin{cases} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{i \left(x + 1\right)^{\frac{11}{2}}}{5 \sqrt{x - 1}} - \frac{29 i \left(x + 1\right)^{\frac{9}{2}}}{20 \sqrt{x - 1}} + \frac{73 i \left(x + 1\right)^{\frac{7}{2}}}{20 \sqrt{x - 1}} - \frac{129 i \left(x + 1\right)^{\frac{5}{2}}}{40 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{x - 1}} + \frac{3 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{\left(x + 1\right)^{\frac{11}{2}}}{5 \sqrt{1 - x}} + \frac{29 \left(x + 1\right)^{\frac{9}{2}}}{20 \sqrt{1 - x}} - \frac{73 \left(x + 1\right)^{\frac{7}{2}}}{20 \sqrt{1 - x}} + \frac{129 \left(x + 1\right)^{\frac{5}{2}}}{40 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{1 - x}} - \frac{3 \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 + I*(x + 1)**(11/2)/(5*sqrt(x - 1)) - 29*I*(x + 1)**(9/2)/(20*sqrt(x - 1)) + 73*I*(x + 1)**(7/2)/(20*sqrt(x - 1)) - 129*I*(x + 1)**(5/2)/(40*sqrt(x - 1)) - I*(x + 1)**(3/2)/(8*sqrt(x - 1)) + 3*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (3*asin(sqrt(2)*sqrt(x + 1)/2)/4 - (x + 1)**(11/2)/(5*sqrt(1 - x)) + 29*(x + 1)**(9/2)/(20*sqrt(1 - x)) - 73*(x + 1)**(7/2)/(20*sqrt(1 - x)) + 129*(x + 1)**(5/2)/(40*sqrt(1 - x)) + (x + 1)**(3/2)/(8*sqrt(1 - x)) - 3*sqrt(x + 1)/(4*sqrt(1 - x)), True))","B",0
1078,1,214,0,7.461130," ","integrate((1-x)**(3/2)*(1+x)**(3/2),x)","\begin{cases} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{i \left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{x - 1}} + \frac{5 i \left(x + 1\right)^{\frac{7}{2}}}{4 \sqrt{x - 1}} - \frac{13 i \left(x + 1\right)^{\frac{5}{2}}}{8 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{x - 1}} + \frac{3 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{\left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{1 - x}} - \frac{5 \left(x + 1\right)^{\frac{7}{2}}}{4 \sqrt{1 - x}} + \frac{13 \left(x + 1\right)^{\frac{5}{2}}}{8 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{1 - x}} - \frac{3 \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 - I*(x + 1)**(9/2)/(4*sqrt(x - 1)) + 5*I*(x + 1)**(7/2)/(4*sqrt(x - 1)) - 13*I*(x + 1)**(5/2)/(8*sqrt(x - 1)) - I*(x + 1)**(3/2)/(8*sqrt(x - 1)) + 3*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (3*asin(sqrt(2)*sqrt(x + 1)/2)/4 + (x + 1)**(9/2)/(4*sqrt(1 - x)) - 5*(x + 1)**(7/2)/(4*sqrt(1 - x)) + 13*(x + 1)**(5/2)/(8*sqrt(1 - x)) + (x + 1)**(3/2)/(8*sqrt(1 - x)) - 3*sqrt(x + 1)/(4*sqrt(1 - x)), True))","B",0
1079,1,165,0,4.819672," ","integrate((1-x)**(1/2)*(1+x)**(3/2),x)","\begin{cases} - i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{x - 1}} - \frac{5 i \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{x - 1}} + \frac{i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{1 - x}} + \frac{5 \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{1 - x}} - \frac{\sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(7/2)/(3*sqrt(x - 1)) - 5*I*(x + 1)**(5/2)/(6*sqrt(x - 1)) - I*(x + 1)**(3/2)/(6*sqrt(x - 1)) + I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(7/2)/(3*sqrt(1 - x)) + 5*(x + 1)**(5/2)/(6*sqrt(1 - x)) + (x + 1)**(3/2)/(6*sqrt(1 - x)) - sqrt(x + 1)/sqrt(1 - x), True))","B",0
1080,1,136,0,3.275429," ","integrate((1+x)**(3/2)/(1-x)**(1/2),x)","\begin{cases} - 3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{x - 1}} + \frac{3 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{1 - x}} - \frac{3 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(5/2)/(2*sqrt(x - 1)) - I*(x + 1)**(3/2)/(2*sqrt(x - 1)) + 3*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (3*asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(5/2)/(2*sqrt(1 - x)) + (x + 1)**(3/2)/(2*sqrt(1 - x)) - 3*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1081,1,100,0,2.920189," ","integrate((1+x)**(3/2)/(1-x)**(3/2),x)","\begin{cases} 6 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{3}{2}}}{\sqrt{x - 1}} - \frac{6 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 6 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{1 - x}} + \frac{6 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(3/2)/sqrt(x - 1) - 6*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (-6*asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(3/2)/sqrt(1 - x) + 6*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1082,1,500,0,3.697551," ","integrate((1+x)**(3/2)/(1-x)**(5/2),x)","\begin{cases} \frac{6 i \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}} - \frac{3 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}} - \frac{12 i \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}} + \frac{6 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}} - \frac{8 i \left(x + 1\right)^{8}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}} + \frac{12 i \left(x + 1\right)^{7}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{15}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{13}{2}}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{6 \sqrt{1 - x} \left(x + 1\right)^{\frac{15}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{15}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{13}{2}}} - \frac{12 \sqrt{1 - x} \left(x + 1\right)^{\frac{13}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{15}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{13}{2}}} - \frac{8 \left(x + 1\right)^{8}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{15}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{13}{2}}} + \frac{12 \left(x + 1\right)^{7}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{15}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{13}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*I*sqrt(x - 1)*(x + 1)**(15/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(-3*sqrt(x - 1)*(x + 1)**(15/2) + 6*sqrt(x - 1)*(x + 1)**(13/2)) - 3*pi*sqrt(x - 1)*(x + 1)**(15/2)/(-3*sqrt(x - 1)*(x + 1)**(15/2) + 6*sqrt(x - 1)*(x + 1)**(13/2)) - 12*I*sqrt(x - 1)*(x + 1)**(13/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(-3*sqrt(x - 1)*(x + 1)**(15/2) + 6*sqrt(x - 1)*(x + 1)**(13/2)) + 6*pi*sqrt(x - 1)*(x + 1)**(13/2)/(-3*sqrt(x - 1)*(x + 1)**(15/2) + 6*sqrt(x - 1)*(x + 1)**(13/2)) - 8*I*(x + 1)**8/(-3*sqrt(x - 1)*(x + 1)**(15/2) + 6*sqrt(x - 1)*(x + 1)**(13/2)) + 12*I*(x + 1)**7/(-3*sqrt(x - 1)*(x + 1)**(15/2) + 6*sqrt(x - 1)*(x + 1)**(13/2)), Abs(x + 1)/2 > 1), (6*sqrt(1 - x)*(x + 1)**(15/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(3*sqrt(1 - x)*(x + 1)**(15/2) - 6*sqrt(1 - x)*(x + 1)**(13/2)) - 12*sqrt(1 - x)*(x + 1)**(13/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(3*sqrt(1 - x)*(x + 1)**(15/2) - 6*sqrt(1 - x)*(x + 1)**(13/2)) - 8*(x + 1)**8/(3*sqrt(1 - x)*(x + 1)**(15/2) - 6*sqrt(1 - x)*(x + 1)**(13/2)) + 12*(x + 1)**7/(3*sqrt(1 - x)*(x + 1)**(15/2) - 6*sqrt(1 - x)*(x + 1)**(13/2)), True))","B",0
1083,1,88,0,6.256490," ","integrate((1+x)**(3/2)/(1-x)**(7/2),x)","\begin{cases} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{5 \sqrt{x - 1} \left(x + 1\right)^{2} - 20 \sqrt{x - 1} \left(x + 1\right) + 20 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{\left(x + 1\right)^{\frac{5}{2}}}{5 \sqrt{1 - x} \left(x + 1\right)^{2} - 20 \sqrt{1 - x} \left(x + 1\right) + 20 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*(x + 1)**(5/2)/(5*sqrt(x - 1)*(x + 1)**2 - 20*sqrt(x - 1)*(x + 1) + 20*sqrt(x - 1)), Abs(x + 1)/2 > 1), ((x + 1)**(5/2)/(5*sqrt(1 - x)*(x + 1)**2 - 20*sqrt(1 - x)*(x + 1) + 20*sqrt(1 - x)), True))","B",0
1084,1,228,0,19.081224," ","integrate((1+x)**(3/2)/(1-x)**(9/2),x)","\begin{cases} - \frac{i \left(x + 1\right)^{\frac{7}{2}}}{35 \sqrt{x - 1} \left(x + 1\right)^{3} - 210 \sqrt{x - 1} \left(x + 1\right)^{2} + 420 \sqrt{x - 1} \left(x + 1\right) - 280 \sqrt{x - 1}} + \frac{7 i \left(x + 1\right)^{\frac{5}{2}}}{35 \sqrt{x - 1} \left(x + 1\right)^{3} - 210 \sqrt{x - 1} \left(x + 1\right)^{2} + 420 \sqrt{x - 1} \left(x + 1\right) - 280 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{\left(x + 1\right)^{\frac{7}{2}}}{35 \sqrt{1 - x} \left(x + 1\right)^{3} - 210 \sqrt{1 - x} \left(x + 1\right)^{2} + 420 \sqrt{1 - x} \left(x + 1\right) - 280 \sqrt{1 - x}} - \frac{7 \left(x + 1\right)^{\frac{5}{2}}}{35 \sqrt{1 - x} \left(x + 1\right)^{3} - 210 \sqrt{1 - x} \left(x + 1\right)^{2} + 420 \sqrt{1 - x} \left(x + 1\right) - 280 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*(x + 1)**(7/2)/(35*sqrt(x - 1)*(x + 1)**3 - 210*sqrt(x - 1)*(x + 1)**2 + 420*sqrt(x - 1)*(x + 1) - 280*sqrt(x - 1)) + 7*I*(x + 1)**(5/2)/(35*sqrt(x - 1)*(x + 1)**3 - 210*sqrt(x - 1)*(x + 1)**2 + 420*sqrt(x - 1)*(x + 1) - 280*sqrt(x - 1)), Abs(x + 1)/2 > 1), ((x + 1)**(7/2)/(35*sqrt(1 - x)*(x + 1)**3 - 210*sqrt(1 - x)*(x + 1)**2 + 420*sqrt(1 - x)*(x + 1) - 280*sqrt(1 - x)) - 7*(x + 1)**(5/2)/(35*sqrt(1 - x)*(x + 1)**3 - 210*sqrt(1 - x)*(x + 1)**2 + 420*sqrt(1 - x)*(x + 1) - 280*sqrt(1 - x)), True))","B",0
1085,1,677,0,51.652410," ","integrate((1+x)**(3/2)/(1-x)**(11/2),x)","\begin{cases} - \frac{2 i \left(x + 1\right)^{\frac{11}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{5} - 3150 \sqrt{x - 1} \left(x + 1\right)^{4} + 12600 \sqrt{x - 1} \left(x + 1\right)^{3} - 25200 \sqrt{x - 1} \left(x + 1\right)^{2} + 25200 \sqrt{x - 1} \left(x + 1\right) - 10080 \sqrt{x - 1}} + \frac{22 i \left(x + 1\right)^{\frac{9}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{5} - 3150 \sqrt{x - 1} \left(x + 1\right)^{4} + 12600 \sqrt{x - 1} \left(x + 1\right)^{3} - 25200 \sqrt{x - 1} \left(x + 1\right)^{2} + 25200 \sqrt{x - 1} \left(x + 1\right) - 10080 \sqrt{x - 1}} - \frac{99 i \left(x + 1\right)^{\frac{7}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{5} - 3150 \sqrt{x - 1} \left(x + 1\right)^{4} + 12600 \sqrt{x - 1} \left(x + 1\right)^{3} - 25200 \sqrt{x - 1} \left(x + 1\right)^{2} + 25200 \sqrt{x - 1} \left(x + 1\right) - 10080 \sqrt{x - 1}} + \frac{126 i \left(x + 1\right)^{\frac{5}{2}}}{315 \sqrt{x - 1} \left(x + 1\right)^{5} - 3150 \sqrt{x - 1} \left(x + 1\right)^{4} + 12600 \sqrt{x - 1} \left(x + 1\right)^{3} - 25200 \sqrt{x - 1} \left(x + 1\right)^{2} + 25200 \sqrt{x - 1} \left(x + 1\right) - 10080 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{2 \left(x + 1\right)^{\frac{11}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{5} - 3150 \sqrt{1 - x} \left(x + 1\right)^{4} + 12600 \sqrt{1 - x} \left(x + 1\right)^{3} - 25200 \sqrt{1 - x} \left(x + 1\right)^{2} + 25200 \sqrt{1 - x} \left(x + 1\right) - 10080 \sqrt{1 - x}} - \frac{22 \left(x + 1\right)^{\frac{9}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{5} - 3150 \sqrt{1 - x} \left(x + 1\right)^{4} + 12600 \sqrt{1 - x} \left(x + 1\right)^{3} - 25200 \sqrt{1 - x} \left(x + 1\right)^{2} + 25200 \sqrt{1 - x} \left(x + 1\right) - 10080 \sqrt{1 - x}} + \frac{99 \left(x + 1\right)^{\frac{7}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{5} - 3150 \sqrt{1 - x} \left(x + 1\right)^{4} + 12600 \sqrt{1 - x} \left(x + 1\right)^{3} - 25200 \sqrt{1 - x} \left(x + 1\right)^{2} + 25200 \sqrt{1 - x} \left(x + 1\right) - 10080 \sqrt{1 - x}} - \frac{126 \left(x + 1\right)^{\frac{5}{2}}}{315 \sqrt{1 - x} \left(x + 1\right)^{5} - 3150 \sqrt{1 - x} \left(x + 1\right)^{4} + 12600 \sqrt{1 - x} \left(x + 1\right)^{3} - 25200 \sqrt{1 - x} \left(x + 1\right)^{2} + 25200 \sqrt{1 - x} \left(x + 1\right) - 10080 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*(x + 1)**(11/2)/(315*sqrt(x - 1)*(x + 1)**5 - 3150*sqrt(x - 1)*(x + 1)**4 + 12600*sqrt(x - 1)*(x + 1)**3 - 25200*sqrt(x - 1)*(x + 1)**2 + 25200*sqrt(x - 1)*(x + 1) - 10080*sqrt(x - 1)) + 22*I*(x + 1)**(9/2)/(315*sqrt(x - 1)*(x + 1)**5 - 3150*sqrt(x - 1)*(x + 1)**4 + 12600*sqrt(x - 1)*(x + 1)**3 - 25200*sqrt(x - 1)*(x + 1)**2 + 25200*sqrt(x - 1)*(x + 1) - 10080*sqrt(x - 1)) - 99*I*(x + 1)**(7/2)/(315*sqrt(x - 1)*(x + 1)**5 - 3150*sqrt(x - 1)*(x + 1)**4 + 12600*sqrt(x - 1)*(x + 1)**3 - 25200*sqrt(x - 1)*(x + 1)**2 + 25200*sqrt(x - 1)*(x + 1) - 10080*sqrt(x - 1)) + 126*I*(x + 1)**(5/2)/(315*sqrt(x - 1)*(x + 1)**5 - 3150*sqrt(x - 1)*(x + 1)**4 + 12600*sqrt(x - 1)*(x + 1)**3 - 25200*sqrt(x - 1)*(x + 1)**2 + 25200*sqrt(x - 1)*(x + 1) - 10080*sqrt(x - 1)), Abs(x + 1)/2 > 1), (2*(x + 1)**(11/2)/(315*sqrt(1 - x)*(x + 1)**5 - 3150*sqrt(1 - x)*(x + 1)**4 + 12600*sqrt(1 - x)*(x + 1)**3 - 25200*sqrt(1 - x)*(x + 1)**2 + 25200*sqrt(1 - x)*(x + 1) - 10080*sqrt(1 - x)) - 22*(x + 1)**(9/2)/(315*sqrt(1 - x)*(x + 1)**5 - 3150*sqrt(1 - x)*(x + 1)**4 + 12600*sqrt(1 - x)*(x + 1)**3 - 25200*sqrt(1 - x)*(x + 1)**2 + 25200*sqrt(1 - x)*(x + 1) - 10080*sqrt(1 - x)) + 99*(x + 1)**(7/2)/(315*sqrt(1 - x)*(x + 1)**5 - 3150*sqrt(1 - x)*(x + 1)**4 + 12600*sqrt(1 - x)*(x + 1)**3 - 25200*sqrt(1 - x)*(x + 1)**2 + 25200*sqrt(1 - x)*(x + 1) - 10080*sqrt(1 - x)) - 126*(x + 1)**(5/2)/(315*sqrt(1 - x)*(x + 1)**5 - 3150*sqrt(1 - x)*(x + 1)**4 + 12600*sqrt(1 - x)*(x + 1)**3 - 25200*sqrt(1 - x)*(x + 1)**2 + 25200*sqrt(1 - x)*(x + 1) - 10080*sqrt(1 - x)), True))","B",0
1086,1,1753,0,132.964950," ","integrate((1+x)**(3/2)/(1-x)**(13/2),x)","\begin{cases} - \frac{2 i \left(x + 1\right)^{\frac{17}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} + \frac{34 i \left(x + 1\right)^{\frac{15}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} - \frac{255 i \left(x + 1\right)^{\frac{13}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} + \frac{1105 i \left(x + 1\right)^{\frac{11}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} - \frac{2750 i \left(x + 1\right)^{\frac{9}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} + \frac{3564 i \left(x + 1\right)^{\frac{7}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} - \frac{1848 i \left(x + 1\right)^{\frac{5}{2}}}{1155 \sqrt{x - 1} \left(x + 1\right)^{8} - 18480 \sqrt{x - 1} \left(x + 1\right)^{7} + 129360 \sqrt{x - 1} \left(x + 1\right)^{6} - 517440 \sqrt{x - 1} \left(x + 1\right)^{5} + 1293600 \sqrt{x - 1} \left(x + 1\right)^{4} - 2069760 \sqrt{x - 1} \left(x + 1\right)^{3} + 2069760 \sqrt{x - 1} \left(x + 1\right)^{2} - 1182720 \sqrt{x - 1} \left(x + 1\right) + 295680 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{2 \left(x + 1\right)^{\frac{17}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} - \frac{34 \left(x + 1\right)^{\frac{15}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} + \frac{255 \left(x + 1\right)^{\frac{13}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} - \frac{1105 \left(x + 1\right)^{\frac{11}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} + \frac{2750 \left(x + 1\right)^{\frac{9}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} - \frac{3564 \left(x + 1\right)^{\frac{7}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} + \frac{1848 \left(x + 1\right)^{\frac{5}{2}}}{1155 \sqrt{1 - x} \left(x + 1\right)^{8} - 18480 \sqrt{1 - x} \left(x + 1\right)^{7} + 129360 \sqrt{1 - x} \left(x + 1\right)^{6} - 517440 \sqrt{1 - x} \left(x + 1\right)^{5} + 1293600 \sqrt{1 - x} \left(x + 1\right)^{4} - 2069760 \sqrt{1 - x} \left(x + 1\right)^{3} + 2069760 \sqrt{1 - x} \left(x + 1\right)^{2} - 1182720 \sqrt{1 - x} \left(x + 1\right) + 295680 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*(x + 1)**(17/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)) + 34*I*(x + 1)**(15/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)) - 255*I*(x + 1)**(13/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)) + 1105*I*(x + 1)**(11/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)) - 2750*I*(x + 1)**(9/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)) + 3564*I*(x + 1)**(7/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)) - 1848*I*(x + 1)**(5/2)/(1155*sqrt(x - 1)*(x + 1)**8 - 18480*sqrt(x - 1)*(x + 1)**7 + 129360*sqrt(x - 1)*(x + 1)**6 - 517440*sqrt(x - 1)*(x + 1)**5 + 1293600*sqrt(x - 1)*(x + 1)**4 - 2069760*sqrt(x - 1)*(x + 1)**3 + 2069760*sqrt(x - 1)*(x + 1)**2 - 1182720*sqrt(x - 1)*(x + 1) + 295680*sqrt(x - 1)), Abs(x + 1)/2 > 1), (2*(x + 1)**(17/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)) - 34*(x + 1)**(15/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)) + 255*(x + 1)**(13/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)) - 1105*(x + 1)**(11/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)) + 2750*(x + 1)**(9/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)) - 3564*(x + 1)**(7/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)) + 1848*(x + 1)**(5/2)/(1155*sqrt(1 - x)*(x + 1)**8 - 18480*sqrt(1 - x)*(x + 1)**7 + 129360*sqrt(1 - x)*(x + 1)**6 - 517440*sqrt(1 - x)*(x + 1)**5 + 1293600*sqrt(1 - x)*(x + 1)**4 - 2069760*sqrt(1 - x)*(x + 1)**3 + 2069760*sqrt(1 - x)*(x + 1)**2 - 1182720*sqrt(1 - x)*(x + 1) + 295680*sqrt(1 - x)), True))","B",0
1087,-1,0,0,0.000000," ","integrate((1+x)**(3/2)/(1-x)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,-1,0,0,0.000000," ","integrate((1-x)**(11/2)*(1+x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1089,1,360,0,117.569459," ","integrate((1-x)**(9/2)*(1+x)**(5/2),x)","\begin{cases} - \frac{45 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{64} + \frac{i \left(x + 1\right)^{\frac{17}{2}}}{8 \sqrt{x - 1}} - \frac{79 i \left(x + 1\right)^{\frac{15}{2}}}{56 \sqrt{x - 1}} + \frac{725 i \left(x + 1\right)^{\frac{13}{2}}}{112 \sqrt{x - 1}} - \frac{1699 i \left(x + 1\right)^{\frac{11}{2}}}{112 \sqrt{x - 1}} + \frac{8191 i \left(x + 1\right)^{\frac{9}{2}}}{448 \sqrt{x - 1}} - \frac{4099 i \left(x + 1\right)^{\frac{7}{2}}}{448 \sqrt{x - 1}} - \frac{3 i \left(x + 1\right)^{\frac{5}{2}}}{128 \sqrt{x - 1}} - \frac{15 i \left(x + 1\right)^{\frac{3}{2}}}{128 \sqrt{x - 1}} + \frac{45 i \sqrt{x + 1}}{64 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{45 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{64} - \frac{\left(x + 1\right)^{\frac{17}{2}}}{8 \sqrt{1 - x}} + \frac{79 \left(x + 1\right)^{\frac{15}{2}}}{56 \sqrt{1 - x}} - \frac{725 \left(x + 1\right)^{\frac{13}{2}}}{112 \sqrt{1 - x}} + \frac{1699 \left(x + 1\right)^{\frac{11}{2}}}{112 \sqrt{1 - x}} - \frac{8191 \left(x + 1\right)^{\frac{9}{2}}}{448 \sqrt{1 - x}} + \frac{4099 \left(x + 1\right)^{\frac{7}{2}}}{448 \sqrt{1 - x}} + \frac{3 \left(x + 1\right)^{\frac{5}{2}}}{128 \sqrt{1 - x}} + \frac{15 \left(x + 1\right)^{\frac{3}{2}}}{128 \sqrt{1 - x}} - \frac{45 \sqrt{x + 1}}{64 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-45*I*acosh(sqrt(2)*sqrt(x + 1)/2)/64 + I*(x + 1)**(17/2)/(8*sqrt(x - 1)) - 79*I*(x + 1)**(15/2)/(56*sqrt(x - 1)) + 725*I*(x + 1)**(13/2)/(112*sqrt(x - 1)) - 1699*I*(x + 1)**(11/2)/(112*sqrt(x - 1)) + 8191*I*(x + 1)**(9/2)/(448*sqrt(x - 1)) - 4099*I*(x + 1)**(7/2)/(448*sqrt(x - 1)) - 3*I*(x + 1)**(5/2)/(128*sqrt(x - 1)) - 15*I*(x + 1)**(3/2)/(128*sqrt(x - 1)) + 45*I*sqrt(x + 1)/(64*sqrt(x - 1)), Abs(x + 1)/2 > 1), (45*asin(sqrt(2)*sqrt(x + 1)/2)/64 - (x + 1)**(17/2)/(8*sqrt(1 - x)) + 79*(x + 1)**(15/2)/(56*sqrt(1 - x)) - 725*(x + 1)**(13/2)/(112*sqrt(1 - x)) + 1699*(x + 1)**(11/2)/(112*sqrt(1 - x)) - 8191*(x + 1)**(9/2)/(448*sqrt(1 - x)) + 4099*(x + 1)**(7/2)/(448*sqrt(1 - x)) + 3*(x + 1)**(5/2)/(128*sqrt(1 - x)) + 15*(x + 1)**(3/2)/(128*sqrt(1 - x)) - 45*sqrt(x + 1)/(64*sqrt(1 - x)), True))","A",0
1090,1,321,0,53.580407," ","integrate((1-x)**(7/2)*(1+x)**(5/2),x)","\begin{cases} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} - \frac{i \left(x + 1\right)^{\frac{15}{2}}}{7 \sqrt{x - 1}} + \frac{55 i \left(x + 1\right)^{\frac{13}{2}}}{42 \sqrt{x - 1}} - \frac{193 i \left(x + 1\right)^{\frac{11}{2}}}{42 \sqrt{x - 1}} + \frac{1237 i \left(x + 1\right)^{\frac{9}{2}}}{168 \sqrt{x - 1}} - \frac{769 i \left(x + 1\right)^{\frac{7}{2}}}{168 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{48 \sqrt{x - 1}} - \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{x - 1}} + \frac{5 i \sqrt{x + 1}}{8 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} + \frac{\left(x + 1\right)^{\frac{15}{2}}}{7 \sqrt{1 - x}} - \frac{55 \left(x + 1\right)^{\frac{13}{2}}}{42 \sqrt{1 - x}} + \frac{193 \left(x + 1\right)^{\frac{11}{2}}}{42 \sqrt{1 - x}} - \frac{1237 \left(x + 1\right)^{\frac{9}{2}}}{168 \sqrt{1 - x}} + \frac{769 \left(x + 1\right)^{\frac{7}{2}}}{168 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{48 \sqrt{1 - x}} + \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{1 - x}} - \frac{5 \sqrt{x + 1}}{8 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*acosh(sqrt(2)*sqrt(x + 1)/2)/8 - I*(x + 1)**(15/2)/(7*sqrt(x - 1)) + 55*I*(x + 1)**(13/2)/(42*sqrt(x - 1)) - 193*I*(x + 1)**(11/2)/(42*sqrt(x - 1)) + 1237*I*(x + 1)**(9/2)/(168*sqrt(x - 1)) - 769*I*(x + 1)**(7/2)/(168*sqrt(x - 1)) - I*(x + 1)**(5/2)/(48*sqrt(x - 1)) - 5*I*(x + 1)**(3/2)/(48*sqrt(x - 1)) + 5*I*sqrt(x + 1)/(8*sqrt(x - 1)), Abs(x + 1)/2 > 1), (5*asin(sqrt(2)*sqrt(x + 1)/2)/8 + (x + 1)**(15/2)/(7*sqrt(1 - x)) - 55*(x + 1)**(13/2)/(42*sqrt(1 - x)) + 193*(x + 1)**(11/2)/(42*sqrt(1 - x)) - 1237*(x + 1)**(9/2)/(168*sqrt(1 - x)) + 769*(x + 1)**(7/2)/(168*sqrt(1 - x)) + (x + 1)**(5/2)/(48*sqrt(1 - x)) + 5*(x + 1)**(3/2)/(48*sqrt(1 - x)) - 5*sqrt(x + 1)/(8*sqrt(1 - x)), True))","A",0
1091,1,286,0,25.760769," ","integrate((1-x)**(5/2)*(1+x)**(5/2),x)","\begin{cases} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} + \frac{i \left(x + 1\right)^{\frac{13}{2}}}{6 \sqrt{x - 1}} - \frac{7 i \left(x + 1\right)^{\frac{11}{2}}}{6 \sqrt{x - 1}} + \frac{67 i \left(x + 1\right)^{\frac{9}{2}}}{24 \sqrt{x - 1}} - \frac{55 i \left(x + 1\right)^{\frac{7}{2}}}{24 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{48 \sqrt{x - 1}} - \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{x - 1}} + \frac{5 i \sqrt{x + 1}}{8 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{8} - \frac{\left(x + 1\right)^{\frac{13}{2}}}{6 \sqrt{1 - x}} + \frac{7 \left(x + 1\right)^{\frac{11}{2}}}{6 \sqrt{1 - x}} - \frac{67 \left(x + 1\right)^{\frac{9}{2}}}{24 \sqrt{1 - x}} + \frac{55 \left(x + 1\right)^{\frac{7}{2}}}{24 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{48 \sqrt{1 - x}} + \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{48 \sqrt{1 - x}} - \frac{5 \sqrt{x + 1}}{8 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*acosh(sqrt(2)*sqrt(x + 1)/2)/8 + I*(x + 1)**(13/2)/(6*sqrt(x - 1)) - 7*I*(x + 1)**(11/2)/(6*sqrt(x - 1)) + 67*I*(x + 1)**(9/2)/(24*sqrt(x - 1)) - 55*I*(x + 1)**(7/2)/(24*sqrt(x - 1)) - I*(x + 1)**(5/2)/(48*sqrt(x - 1)) - 5*I*(x + 1)**(3/2)/(48*sqrt(x - 1)) + 5*I*sqrt(x + 1)/(8*sqrt(x - 1)), Abs(x + 1)/2 > 1), (5*asin(sqrt(2)*sqrt(x + 1)/2)/8 - (x + 1)**(13/2)/(6*sqrt(1 - x)) + 7*(x + 1)**(11/2)/(6*sqrt(1 - x)) - 67*(x + 1)**(9/2)/(24*sqrt(1 - x)) + 55*(x + 1)**(7/2)/(24*sqrt(1 - x)) + (x + 1)**(5/2)/(48*sqrt(1 - x)) + 5*(x + 1)**(3/2)/(48*sqrt(1 - x)) - 5*sqrt(x + 1)/(8*sqrt(1 - x)), True))","B",0
1092,1,246,0,16.531002," ","integrate((1-x)**(3/2)*(1+x)**(5/2),x)","\begin{cases} - \frac{3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{i \left(x + 1\right)^{\frac{11}{2}}}{5 \sqrt{x - 1}} + \frac{19 i \left(x + 1\right)^{\frac{9}{2}}}{20 \sqrt{x - 1}} - \frac{23 i \left(x + 1\right)^{\frac{7}{2}}}{20 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{40 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{x - 1}} + \frac{3 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{\left(x + 1\right)^{\frac{11}{2}}}{5 \sqrt{1 - x}} - \frac{19 \left(x + 1\right)^{\frac{9}{2}}}{20 \sqrt{1 - x}} + \frac{23 \left(x + 1\right)^{\frac{7}{2}}}{20 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{40 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{8 \sqrt{1 - x}} - \frac{3 \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 - I*(x + 1)**(11/2)/(5*sqrt(x - 1)) + 19*I*(x + 1)**(9/2)/(20*sqrt(x - 1)) - 23*I*(x + 1)**(7/2)/(20*sqrt(x - 1)) - I*(x + 1)**(5/2)/(40*sqrt(x - 1)) - I*(x + 1)**(3/2)/(8*sqrt(x - 1)) + 3*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (3*asin(sqrt(2)*sqrt(x + 1)/2)/4 + (x + 1)**(11/2)/(5*sqrt(1 - x)) - 19*(x + 1)**(9/2)/(20*sqrt(1 - x)) + 23*(x + 1)**(7/2)/(20*sqrt(1 - x)) + (x + 1)**(5/2)/(40*sqrt(1 - x)) + (x + 1)**(3/2)/(8*sqrt(1 - x)) - 3*sqrt(x + 1)/(4*sqrt(1 - x)), True))","B",0
1093,1,214,0,9.886453," ","integrate((1-x)**(1/2)*(1+x)**(5/2),x)","\begin{cases} - \frac{5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} + \frac{i \left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{x - 1}} - \frac{7 i \left(x + 1\right)^{\frac{7}{2}}}{12 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{24 \sqrt{x - 1}} - \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{x - 1}} + \frac{5 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{\left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{1 - x}} + \frac{7 \left(x + 1\right)^{\frac{7}{2}}}{12 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{24 \sqrt{1 - x}} + \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{1 - x}} - \frac{5 \sqrt{x + 1}}{4 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 + I*(x + 1)**(9/2)/(4*sqrt(x - 1)) - 7*I*(x + 1)**(7/2)/(12*sqrt(x - 1)) - I*(x + 1)**(5/2)/(24*sqrt(x - 1)) - 5*I*(x + 1)**(3/2)/(24*sqrt(x - 1)) + 5*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (5*asin(sqrt(2)*sqrt(x + 1)/2)/4 - (x + 1)**(9/2)/(4*sqrt(1 - x)) + 7*(x + 1)**(7/2)/(12*sqrt(1 - x)) + (x + 1)**(5/2)/(24*sqrt(1 - x)) + 5*(x + 1)**(3/2)/(24*sqrt(1 - x)) - 5*sqrt(x + 1)/(4*sqrt(1 - x)), True))","A",0
1094,1,172,0,7.502717," ","integrate((1+x)**(5/2)/(1-x)**(1/2),x)","\begin{cases} - 5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{x - 1}} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{x - 1}} - \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{x - 1}} + \frac{5 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{1 - x}} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{1 - x}} + \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{1 - x}} - \frac{5 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(7/2)/(3*sqrt(x - 1)) - I*(x + 1)**(5/2)/(6*sqrt(x - 1)) - 5*I*(x + 1)**(3/2)/(6*sqrt(x - 1)) + 5*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (5*asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(7/2)/(3*sqrt(1 - x)) + (x + 1)**(5/2)/(6*sqrt(1 - x)) + 5*(x + 1)**(3/2)/(6*sqrt(1 - x)) - 5*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1095,1,139,0,7.762128," ","integrate((1+x)**(5/2)/(1-x)**(3/2),x)","\begin{cases} 15 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{x - 1}} + \frac{5 i \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{x - 1}} - \frac{15 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 15 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{1 - x}} - \frac{5 \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{1 - x}} + \frac{15 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(5/2)/(2*sqrt(x - 1)) + 5*I*(x + 1)**(3/2)/(2*sqrt(x - 1)) - 15*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (-15*asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(5/2)/(2*sqrt(1 - x)) - 5*(x + 1)**(3/2)/(2*sqrt(1 - x)) + 15*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1096,1,576,0,7.472907," ","integrate((1+x)**(5/2)/(1-x)**(5/2),x)","\begin{cases} \frac{30 i \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} - \frac{15 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} - \frac{60 i \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} + \frac{30 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} + \frac{3 i \left(x + 1\right)^{15}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} - \frac{40 i \left(x + 1\right)^{14}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} + \frac{60 i \left(x + 1\right)^{13}}{- 3 \sqrt{x - 1} \left(x + 1\right)^{\frac{27}{2}} + 6 \sqrt{x - 1} \left(x + 1\right)^{\frac{25}{2}}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{30 \sqrt{1 - x} \left(x + 1\right)^{\frac{27}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{27}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{25}{2}}} - \frac{60 \sqrt{1 - x} \left(x + 1\right)^{\frac{25}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{27}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{25}{2}}} + \frac{3 \left(x + 1\right)^{15}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{27}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{25}{2}}} - \frac{40 \left(x + 1\right)^{14}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{27}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{25}{2}}} + \frac{60 \left(x + 1\right)^{13}}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{27}{2}} - 6 \sqrt{1 - x} \left(x + 1\right)^{\frac{25}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*I*sqrt(x - 1)*(x + 1)**(27/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)) - 15*pi*sqrt(x - 1)*(x + 1)**(27/2)/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)) - 60*I*sqrt(x - 1)*(x + 1)**(25/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)) + 30*pi*sqrt(x - 1)*(x + 1)**(25/2)/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)) + 3*I*(x + 1)**15/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)) - 40*I*(x + 1)**14/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)) + 60*I*(x + 1)**13/(-3*sqrt(x - 1)*(x + 1)**(27/2) + 6*sqrt(x - 1)*(x + 1)**(25/2)), Abs(x + 1)/2 > 1), (30*sqrt(1 - x)*(x + 1)**(27/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(3*sqrt(1 - x)*(x + 1)**(27/2) - 6*sqrt(1 - x)*(x + 1)**(25/2)) - 60*sqrt(1 - x)*(x + 1)**(25/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(3*sqrt(1 - x)*(x + 1)**(27/2) - 6*sqrt(1 - x)*(x + 1)**(25/2)) + 3*(x + 1)**15/(3*sqrt(1 - x)*(x + 1)**(27/2) - 6*sqrt(1 - x)*(x + 1)**(25/2)) - 40*(x + 1)**14/(3*sqrt(1 - x)*(x + 1)**(27/2) - 6*sqrt(1 - x)*(x + 1)**(25/2)) + 60*(x + 1)**13/(3*sqrt(1 - x)*(x + 1)**(27/2) - 6*sqrt(1 - x)*(x + 1)**(25/2)), True))","B",0
1097,1,1608,0,11.212630," ","integrate((1+x)**(5/2)/(1-x)**(7/2),x)","\begin{cases} \frac{30 i \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} - \frac{15 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} - \frac{180 i \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} + \frac{90 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} + \frac{360 i \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} - \frac{180 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} - \frac{240 i \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}} \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} + \frac{120 \pi \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} - \frac{46 i \left(x + 1\right)^{18}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} + \frac{232 i \left(x + 1\right)^{17}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} - \frac{400 i \left(x + 1\right)^{16}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} + \frac{240 i \left(x + 1\right)^{15}}{15 \sqrt{x - 1} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{x - 1} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{x - 1} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{x - 1} \left(x + 1\right)^{\frac{29}{2}}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{30 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} + \frac{180 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} - \frac{360 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} + \frac{240 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}} \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} + \frac{46 \left(x + 1\right)^{18}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} - \frac{232 \left(x + 1\right)^{17}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} + \frac{400 \left(x + 1\right)^{16}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} - \frac{240 \left(x + 1\right)^{15}}{15 \sqrt{1 - x} \left(x + 1\right)^{\frac{35}{2}} - 90 \sqrt{1 - x} \left(x + 1\right)^{\frac{33}{2}} + 180 \sqrt{1 - x} \left(x + 1\right)^{\frac{31}{2}} - 120 \sqrt{1 - x} \left(x + 1\right)^{\frac{29}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*I*sqrt(x - 1)*(x + 1)**(35/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) - 15*pi*sqrt(x - 1)*(x + 1)**(35/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) - 180*I*sqrt(x - 1)*(x + 1)**(33/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) + 90*pi*sqrt(x - 1)*(x + 1)**(33/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) + 360*I*sqrt(x - 1)*(x + 1)**(31/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) - 180*pi*sqrt(x - 1)*(x + 1)**(31/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) - 240*I*sqrt(x - 1)*(x + 1)**(29/2)*acosh(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) + 120*pi*sqrt(x - 1)*(x + 1)**(29/2)/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) - 46*I*(x + 1)**18/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) + 232*I*(x + 1)**17/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) - 400*I*(x + 1)**16/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)) + 240*I*(x + 1)**15/(15*sqrt(x - 1)*(x + 1)**(35/2) - 90*sqrt(x - 1)*(x + 1)**(33/2) + 180*sqrt(x - 1)*(x + 1)**(31/2) - 120*sqrt(x - 1)*(x + 1)**(29/2)), Abs(x + 1)/2 > 1), (-30*sqrt(1 - x)*(x + 1)**(35/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) + 180*sqrt(1 - x)*(x + 1)**(33/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) - 360*sqrt(1 - x)*(x + 1)**(31/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) + 240*sqrt(1 - x)*(x + 1)**(29/2)*asin(sqrt(2)*sqrt(x + 1)/2)/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) + 46*(x + 1)**18/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) - 232*(x + 1)**17/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) + 400*(x + 1)**16/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)) - 240*(x + 1)**15/(15*sqrt(1 - x)*(x + 1)**(35/2) - 90*sqrt(1 - x)*(x + 1)**(33/2) + 180*sqrt(1 - x)*(x + 1)**(31/2) - 120*sqrt(1 - x)*(x + 1)**(29/2)), True))","B",0
1098,1,116,0,19.493738," ","integrate((1+x)**(5/2)/(1-x)**(9/2),x)","\begin{cases} \frac{i \left(x + 1\right)^{\frac{7}{2}}}{7 \sqrt{x - 1} \left(x + 1\right)^{3} - 42 \sqrt{x - 1} \left(x + 1\right)^{2} + 84 \sqrt{x - 1} \left(x + 1\right) - 56 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{\left(x + 1\right)^{\frac{7}{2}}}{7 \sqrt{1 - x} \left(x + 1\right)^{3} - 42 \sqrt{1 - x} \left(x + 1\right)^{2} + 84 \sqrt{1 - x} \left(x + 1\right) - 56 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*(x + 1)**(7/2)/(7*sqrt(x - 1)*(x + 1)**3 - 42*sqrt(x - 1)*(x + 1)**2 + 84*sqrt(x - 1)*(x + 1) - 56*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-(x + 1)**(7/2)/(7*sqrt(1 - x)*(x + 1)**3 - 42*sqrt(1 - x)*(x + 1)**2 + 84*sqrt(1 - x)*(x + 1) - 56*sqrt(1 - x)), True))","B",0
1099,1,282,0,53.144899," ","integrate((1+x)**(5/2)/(1-x)**(11/2),x)","\begin{cases} \frac{i \left(x + 1\right)^{\frac{9}{2}}}{63 \sqrt{x - 1} \left(x + 1\right)^{4} - 504 \sqrt{x - 1} \left(x + 1\right)^{3} + 1512 \sqrt{x - 1} \left(x + 1\right)^{2} - 2016 \sqrt{x - 1} \left(x + 1\right) + 1008 \sqrt{x - 1}} - \frac{9 i \left(x + 1\right)^{\frac{7}{2}}}{63 \sqrt{x - 1} \left(x + 1\right)^{4} - 504 \sqrt{x - 1} \left(x + 1\right)^{3} + 1512 \sqrt{x - 1} \left(x + 1\right)^{2} - 2016 \sqrt{x - 1} \left(x + 1\right) + 1008 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{\left(x + 1\right)^{\frac{9}{2}}}{63 \sqrt{1 - x} \left(x + 1\right)^{4} - 504 \sqrt{1 - x} \left(x + 1\right)^{3} + 1512 \sqrt{1 - x} \left(x + 1\right)^{2} - 2016 \sqrt{1 - x} \left(x + 1\right) + 1008 \sqrt{1 - x}} + \frac{9 \left(x + 1\right)^{\frac{7}{2}}}{63 \sqrt{1 - x} \left(x + 1\right)^{4} - 504 \sqrt{1 - x} \left(x + 1\right)^{3} + 1512 \sqrt{1 - x} \left(x + 1\right)^{2} - 2016 \sqrt{1 - x} \left(x + 1\right) + 1008 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*(x + 1)**(9/2)/(63*sqrt(x - 1)*(x + 1)**4 - 504*sqrt(x - 1)*(x + 1)**3 + 1512*sqrt(x - 1)*(x + 1)**2 - 2016*sqrt(x - 1)*(x + 1) + 1008*sqrt(x - 1)) - 9*I*(x + 1)**(7/2)/(63*sqrt(x - 1)*(x + 1)**4 - 504*sqrt(x - 1)*(x + 1)**3 + 1512*sqrt(x - 1)*(x + 1)**2 - 2016*sqrt(x - 1)*(x + 1) + 1008*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-(x + 1)**(9/2)/(63*sqrt(1 - x)*(x + 1)**4 - 504*sqrt(1 - x)*(x + 1)**3 + 1512*sqrt(1 - x)*(x + 1)**2 - 2016*sqrt(1 - x)*(x + 1) + 1008*sqrt(1 - x)) + 9*(x + 1)**(7/2)/(63*sqrt(1 - x)*(x + 1)**4 - 504*sqrt(1 - x)*(x + 1)**3 + 1512*sqrt(1 - x)*(x + 1)**2 - 2016*sqrt(1 - x)*(x + 1) + 1008*sqrt(1 - x)), True))","B",0
1100,1,785,0,133.938040," ","integrate((1+x)**(5/2)/(1-x)**(13/2),x)","\begin{cases} \frac{2 i \left(x + 1\right)^{\frac{13}{2}}}{693 \sqrt{x - 1} \left(x + 1\right)^{6} - 8316 \sqrt{x - 1} \left(x + 1\right)^{5} + 41580 \sqrt{x - 1} \left(x + 1\right)^{4} - 110880 \sqrt{x - 1} \left(x + 1\right)^{3} + 166320 \sqrt{x - 1} \left(x + 1\right)^{2} - 133056 \sqrt{x - 1} \left(x + 1\right) + 44352 \sqrt{x - 1}} - \frac{26 i \left(x + 1\right)^{\frac{11}{2}}}{693 \sqrt{x - 1} \left(x + 1\right)^{6} - 8316 \sqrt{x - 1} \left(x + 1\right)^{5} + 41580 \sqrt{x - 1} \left(x + 1\right)^{4} - 110880 \sqrt{x - 1} \left(x + 1\right)^{3} + 166320 \sqrt{x - 1} \left(x + 1\right)^{2} - 133056 \sqrt{x - 1} \left(x + 1\right) + 44352 \sqrt{x - 1}} + \frac{143 i \left(x + 1\right)^{\frac{9}{2}}}{693 \sqrt{x - 1} \left(x + 1\right)^{6} - 8316 \sqrt{x - 1} \left(x + 1\right)^{5} + 41580 \sqrt{x - 1} \left(x + 1\right)^{4} - 110880 \sqrt{x - 1} \left(x + 1\right)^{3} + 166320 \sqrt{x - 1} \left(x + 1\right)^{2} - 133056 \sqrt{x - 1} \left(x + 1\right) + 44352 \sqrt{x - 1}} - \frac{198 i \left(x + 1\right)^{\frac{7}{2}}}{693 \sqrt{x - 1} \left(x + 1\right)^{6} - 8316 \sqrt{x - 1} \left(x + 1\right)^{5} + 41580 \sqrt{x - 1} \left(x + 1\right)^{4} - 110880 \sqrt{x - 1} \left(x + 1\right)^{3} + 166320 \sqrt{x - 1} \left(x + 1\right)^{2} - 133056 \sqrt{x - 1} \left(x + 1\right) + 44352 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{2 \left(x + 1\right)^{\frac{13}{2}}}{693 \sqrt{1 - x} \left(x + 1\right)^{6} - 8316 \sqrt{1 - x} \left(x + 1\right)^{5} + 41580 \sqrt{1 - x} \left(x + 1\right)^{4} - 110880 \sqrt{1 - x} \left(x + 1\right)^{3} + 166320 \sqrt{1 - x} \left(x + 1\right)^{2} - 133056 \sqrt{1 - x} \left(x + 1\right) + 44352 \sqrt{1 - x}} + \frac{26 \left(x + 1\right)^{\frac{11}{2}}}{693 \sqrt{1 - x} \left(x + 1\right)^{6} - 8316 \sqrt{1 - x} \left(x + 1\right)^{5} + 41580 \sqrt{1 - x} \left(x + 1\right)^{4} - 110880 \sqrt{1 - x} \left(x + 1\right)^{3} + 166320 \sqrt{1 - x} \left(x + 1\right)^{2} - 133056 \sqrt{1 - x} \left(x + 1\right) + 44352 \sqrt{1 - x}} - \frac{143 \left(x + 1\right)^{\frac{9}{2}}}{693 \sqrt{1 - x} \left(x + 1\right)^{6} - 8316 \sqrt{1 - x} \left(x + 1\right)^{5} + 41580 \sqrt{1 - x} \left(x + 1\right)^{4} - 110880 \sqrt{1 - x} \left(x + 1\right)^{3} + 166320 \sqrt{1 - x} \left(x + 1\right)^{2} - 133056 \sqrt{1 - x} \left(x + 1\right) + 44352 \sqrt{1 - x}} + \frac{198 \left(x + 1\right)^{\frac{7}{2}}}{693 \sqrt{1 - x} \left(x + 1\right)^{6} - 8316 \sqrt{1 - x} \left(x + 1\right)^{5} + 41580 \sqrt{1 - x} \left(x + 1\right)^{4} - 110880 \sqrt{1 - x} \left(x + 1\right)^{3} + 166320 \sqrt{1 - x} \left(x + 1\right)^{2} - 133056 \sqrt{1 - x} \left(x + 1\right) + 44352 \sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*(x + 1)**(13/2)/(693*sqrt(x - 1)*(x + 1)**6 - 8316*sqrt(x - 1)*(x + 1)**5 + 41580*sqrt(x - 1)*(x + 1)**4 - 110880*sqrt(x - 1)*(x + 1)**3 + 166320*sqrt(x - 1)*(x + 1)**2 - 133056*sqrt(x - 1)*(x + 1) + 44352*sqrt(x - 1)) - 26*I*(x + 1)**(11/2)/(693*sqrt(x - 1)*(x + 1)**6 - 8316*sqrt(x - 1)*(x + 1)**5 + 41580*sqrt(x - 1)*(x + 1)**4 - 110880*sqrt(x - 1)*(x + 1)**3 + 166320*sqrt(x - 1)*(x + 1)**2 - 133056*sqrt(x - 1)*(x + 1) + 44352*sqrt(x - 1)) + 143*I*(x + 1)**(9/2)/(693*sqrt(x - 1)*(x + 1)**6 - 8316*sqrt(x - 1)*(x + 1)**5 + 41580*sqrt(x - 1)*(x + 1)**4 - 110880*sqrt(x - 1)*(x + 1)**3 + 166320*sqrt(x - 1)*(x + 1)**2 - 133056*sqrt(x - 1)*(x + 1) + 44352*sqrt(x - 1)) - 198*I*(x + 1)**(7/2)/(693*sqrt(x - 1)*(x + 1)**6 - 8316*sqrt(x - 1)*(x + 1)**5 + 41580*sqrt(x - 1)*(x + 1)**4 - 110880*sqrt(x - 1)*(x + 1)**3 + 166320*sqrt(x - 1)*(x + 1)**2 - 133056*sqrt(x - 1)*(x + 1) + 44352*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-2*(x + 1)**(13/2)/(693*sqrt(1 - x)*(x + 1)**6 - 8316*sqrt(1 - x)*(x + 1)**5 + 41580*sqrt(1 - x)*(x + 1)**4 - 110880*sqrt(1 - x)*(x + 1)**3 + 166320*sqrt(1 - x)*(x + 1)**2 - 133056*sqrt(1 - x)*(x + 1) + 44352*sqrt(1 - x)) + 26*(x + 1)**(11/2)/(693*sqrt(1 - x)*(x + 1)**6 - 8316*sqrt(1 - x)*(x + 1)**5 + 41580*sqrt(1 - x)*(x + 1)**4 - 110880*sqrt(1 - x)*(x + 1)**3 + 166320*sqrt(1 - x)*(x + 1)**2 - 133056*sqrt(1 - x)*(x + 1) + 44352*sqrt(1 - x)) - 143*(x + 1)**(9/2)/(693*sqrt(1 - x)*(x + 1)**6 - 8316*sqrt(1 - x)*(x + 1)**5 + 41580*sqrt(1 - x)*(x + 1)**4 - 110880*sqrt(1 - x)*(x + 1)**3 + 166320*sqrt(1 - x)*(x + 1)**2 - 133056*sqrt(1 - x)*(x + 1) + 44352*sqrt(1 - x)) + 198*(x + 1)**(7/2)/(693*sqrt(1 - x)*(x + 1)**6 - 8316*sqrt(1 - x)*(x + 1)**5 + 41580*sqrt(1 - x)*(x + 1)**4 - 110880*sqrt(1 - x)*(x + 1)**3 + 166320*sqrt(1 - x)*(x + 1)**2 - 133056*sqrt(1 - x)*(x + 1) + 44352*sqrt(1 - x)), True))","B",0
1101,-1,0,0,0.000000," ","integrate((1+x)**(5/2)/(1-x)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,-1,0,0,0.000000," ","integrate((1+x)**(5/2)/(1-x)**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1103,-1,0,0,0.000000," ","integrate((1+x)**(5/2)/(1-x)**(19/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1104,1,75,0,33.751117," ","integrate((a*x+1)**(3/2)/(-a*x+1)**(1/2),x)","\begin{cases} \frac{2 \left(\begin{cases} - \frac{a x \sqrt{- a x + 1} \sqrt{a x + 1}}{4} - \sqrt{- a x + 1} \sqrt{a x + 1} + \frac{3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{a x + 1}}{2} \right)}}{2} & \text{for}\: a x - 1 \geq -2 \wedge a x - 1 < 0 \end{cases}\right)}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*Piecewise((-a*x*sqrt(-a*x + 1)*sqrt(a*x + 1)/4 - sqrt(-a*x + 1)*sqrt(a*x + 1) + 3*asin(sqrt(2)*sqrt(a*x + 1)/2)/2, (a*x - 1 >= -2) & (a*x - 1 < 0)))/a, Ne(a, 0)), (x, True))","A",0
1105,1,76,0,7.083145," ","integrate((a*x+1)*(-a**2*x**2+1)**(1/2)/(-a*x+1),x)","- \begin{cases} - \frac{- \sqrt{- a^{2} x^{2} + 1} + \operatorname{asin}{\left(a x \right)}}{a} & \text{for}\: a x > -1 \wedge a x < 1 \end{cases} - \begin{cases} - \frac{- \frac{a x \sqrt{- a^{2} x^{2} + 1}}{2} - \sqrt{- a^{2} x^{2} + 1} + \frac{\operatorname{asin}{\left(a x \right)}}{2}}{a} & \text{for}\: a x > -1 \wedge a x < 1 \end{cases}"," ",0,"-Piecewise((-(-sqrt(-a**2*x**2 + 1) + asin(a*x))/a, (a*x > -1) & (a*x < 1))) - Piecewise((-(-a*x*sqrt(-a**2*x**2 + 1)/2 - sqrt(-a**2*x**2 + 1) + asin(a*x)/2)/a, (a*x > -1) & (a*x < 1)))","A",0
1106,1,201,0,14.675749," ","integrate((1-x)**(7/2)/(1+x)**(1/2),x)","\begin{cases} - \frac{35 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} - \frac{i \left(x + 1\right)^{\frac{9}{2}}}{4 \sqrt{x - 1}} + \frac{31 i \left(x + 1\right)^{\frac{7}{2}}}{12 \sqrt{x - 1}} - \frac{263 i \left(x + 1\right)^{\frac{5}{2}}}{24 \sqrt{x - 1}} + \frac{605 i \left(x + 1\right)^{\frac{3}{2}}}{24 \sqrt{x - 1}} - \frac{93 i \sqrt{x + 1}}{4 \sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- \frac{\sqrt{1 - x} \left(x + 1\right)^{\frac{7}{2}}}{4} + \frac{25 \sqrt{1 - x} \left(x + 1\right)^{\frac{5}{2}}}{12} - \frac{163 \sqrt{1 - x} \left(x + 1\right)^{\frac{3}{2}}}{24} + \frac{93 \sqrt{1 - x} \sqrt{x + 1}}{8} + \frac{35 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-35*I*acosh(sqrt(2)*sqrt(x + 1)/2)/4 - I*(x + 1)**(9/2)/(4*sqrt(x - 1)) + 31*I*(x + 1)**(7/2)/(12*sqrt(x - 1)) - 263*I*(x + 1)**(5/2)/(24*sqrt(x - 1)) + 605*I*(x + 1)**(3/2)/(24*sqrt(x - 1)) - 93*I*sqrt(x + 1)/(4*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-sqrt(1 - x)*(x + 1)**(7/2)/4 + 25*sqrt(1 - x)*(x + 1)**(5/2)/12 - 163*sqrt(1 - x)*(x + 1)**(3/2)/24 + 93*sqrt(1 - x)*sqrt(x + 1)/8 + 35*asin(sqrt(2)*sqrt(x + 1)/2)/4, True))","A",0
1107,1,175,0,5.643120," ","integrate((1-x)**(5/2)/(1+x)**(1/2),x)","\begin{cases} - 5 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{x - 1}} - \frac{17 i \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{x - 1}} + \frac{59 i \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{x - 1}} - \frac{11 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\5 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{1 - x}} + \frac{17 \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{1 - x}} - \frac{59 \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{1 - x}} + \frac{11 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(7/2)/(3*sqrt(x - 1)) - 17*I*(x + 1)**(5/2)/(6*sqrt(x - 1)) + 59*I*(x + 1)**(3/2)/(6*sqrt(x - 1)) - 11*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (5*asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(7/2)/(3*sqrt(1 - x)) + 17*(x + 1)**(5/2)/(6*sqrt(1 - x)) - 59*(x + 1)**(3/2)/(6*sqrt(1 - x)) + 11*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1108,1,139,0,2.585656," ","integrate((1-x)**(3/2)/(1+x)**(1/2),x)","\begin{cases} - 3 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{x - 1}} + \frac{7 i \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{x - 1}} - \frac{5 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\3 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{1 - x}} - \frac{7 \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{1 - x}} + \frac{5 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(5/2)/(2*sqrt(x - 1)) + 7*I*(x + 1)**(3/2)/(2*sqrt(x - 1)) - 5*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (3*asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(5/2)/(2*sqrt(1 - x)) - 7*(x + 1)**(3/2)/(2*sqrt(1 - x)) + 5*sqrt(x + 1)/sqrt(1 - x), True))","A",0
1109,1,100,0,1.547370," ","integrate((1-x)**(1/2)/(1+x)**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{3}{2}}}{\sqrt{x - 1}} - \frac{2 i \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{1 - x}} + \frac{2 \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(3/2)/sqrt(x - 1) - 2*I*sqrt(x + 1)/sqrt(x - 1), Abs(x + 1)/2 > 1), (2*asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(3/2)/sqrt(1 - x) + 2*sqrt(x + 1)/sqrt(1 - x), True))","B",0
1110,1,41,0,1.035229," ","integrate(1/(1-x)**(1/2)/(1+x)**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(2)*sqrt(x + 1)/2), Abs(x + 1)/2 > 1), (2*asin(sqrt(2)*sqrt(x + 1)/2), True))","B",0
1111,1,29,0,0.937201," ","integrate(1/(1-x)**(3/2)/(1+x)**(1/2),x)","\begin{cases} \frac{1}{\sqrt{-1 + \frac{2}{x + 1}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{i}{\sqrt{1 - \frac{2}{x + 1}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/sqrt(-1 + 2/(x + 1)), 2/Abs(x + 1) > 1), (-I/sqrt(1 - 2/(x + 1)), True))","A",0
1112,1,139,0,2.245976," ","integrate(1/(1-x)**(5/2)/(1+x)**(1/2),x)","\begin{cases} \frac{i \left(x + 1\right)}{3 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 6 i \sqrt{-1 + \frac{2}{x + 1}}} - \frac{3 i}{3 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 6 i \sqrt{-1 + \frac{2}{x + 1}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{x + 1}{- 3 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 6 i \sqrt{1 - \frac{2}{x + 1}}} + \frac{3}{- 3 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 6 i \sqrt{1 - \frac{2}{x + 1}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*(x + 1)/(3*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 6*I*sqrt(-1 + 2/(x + 1))) - 3*I/(3*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 6*I*sqrt(-1 + 2/(x + 1))), 2/Abs(x + 1) > 1), (-(x + 1)/(-3*I*sqrt(1 - 2/(x + 1))*(x + 1) + 6*I*sqrt(1 - 2/(x + 1))) + 3/(-3*I*sqrt(1 - 2/(x + 1))*(x + 1) + 6*I*sqrt(1 - 2/(x + 1))), True))","C",0
1113,1,332,0,7.892367," ","integrate(1/(1-x)**(7/2)/(1+x)**(1/2),x)","\begin{cases} - \frac{2 i \left(x + 1\right)^{2}}{- 15 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 60 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 60 i \sqrt{-1 + \frac{2}{x + 1}}} + \frac{10 i \left(x + 1\right)}{- 15 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 60 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 60 i \sqrt{-1 + \frac{2}{x + 1}}} - \frac{15 i}{- 15 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 60 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 60 i \sqrt{-1 + \frac{2}{x + 1}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{2 \left(x + 1\right)^{2}}{15 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 60 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 60 i \sqrt{1 - \frac{2}{x + 1}}} - \frac{10 \left(x + 1\right)}{15 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 60 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 60 i \sqrt{1 - \frac{2}{x + 1}}} + \frac{15}{15 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 60 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 60 i \sqrt{1 - \frac{2}{x + 1}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*(x + 1)**2/(-15*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 60*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 60*I*sqrt(-1 + 2/(x + 1))) + 10*I*(x + 1)/(-15*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 60*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 60*I*sqrt(-1 + 2/(x + 1))) - 15*I/(-15*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 60*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 60*I*sqrt(-1 + 2/(x + 1))), 2/Abs(x + 1) > 1), (2*(x + 1)**2/(15*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 60*I*sqrt(1 - 2/(x + 1))*(x + 1) + 60*I*sqrt(1 - 2/(x + 1))) - 10*(x + 1)/(15*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 60*I*sqrt(1 - 2/(x + 1))*(x + 1) + 60*I*sqrt(1 - 2/(x + 1))) + 15/(15*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 60*I*sqrt(1 - 2/(x + 1))*(x + 1) + 60*I*sqrt(1 - 2/(x + 1))), True))","C",0
1114,1,595,0,22.133085," ","integrate(1/(1-x)**(9/2)/(1+x)**(1/2),x)","\begin{cases} \frac{2 i \left(x + 1\right)^{3}}{35 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 210 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 420 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 280 i \sqrt{-1 + \frac{2}{x + 1}}} - \frac{14 i \left(x + 1\right)^{2}}{35 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 210 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 420 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 280 i \sqrt{-1 + \frac{2}{x + 1}}} + \frac{35 i \left(x + 1\right)}{35 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 210 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 420 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 280 i \sqrt{-1 + \frac{2}{x + 1}}} - \frac{35 i}{35 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 210 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 420 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 280 i \sqrt{-1 + \frac{2}{x + 1}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{2 \left(x + 1\right)^{3}}{- 35 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 210 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 420 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 280 i \sqrt{1 - \frac{2}{x + 1}}} + \frac{14 \left(x + 1\right)^{2}}{- 35 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 210 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 420 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 280 i \sqrt{1 - \frac{2}{x + 1}}} - \frac{35 \left(x + 1\right)}{- 35 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 210 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 420 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 280 i \sqrt{1 - \frac{2}{x + 1}}} + \frac{35}{- 35 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 210 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 420 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 280 i \sqrt{1 - \frac{2}{x + 1}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*(x + 1)**3/(35*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 210*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 420*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 280*I*sqrt(-1 + 2/(x + 1))) - 14*I*(x + 1)**2/(35*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 210*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 420*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 280*I*sqrt(-1 + 2/(x + 1))) + 35*I*(x + 1)/(35*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 210*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 420*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 280*I*sqrt(-1 + 2/(x + 1))) - 35*I/(35*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 210*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 420*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 280*I*sqrt(-1 + 2/(x + 1))), 2/Abs(x + 1) > 1), (-2*(x + 1)**3/(-35*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 210*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 420*I*sqrt(1 - 2/(x + 1))*(x + 1) + 280*I*sqrt(1 - 2/(x + 1))) + 14*(x + 1)**2/(-35*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 210*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 420*I*sqrt(1 - 2/(x + 1))*(x + 1) + 280*I*sqrt(1 - 2/(x + 1))) - 35*(x + 1)/(-35*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 210*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 420*I*sqrt(1 - 2/(x + 1))*(x + 1) + 280*I*sqrt(1 - 2/(x + 1))) + 35/(-35*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 210*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 420*I*sqrt(1 - 2/(x + 1))*(x + 1) + 280*I*sqrt(1 - 2/(x + 1))), True))","C",0
1115,1,933,0,58.394766," ","integrate(1/(1-x)**(11/2)/(1+x)**(1/2),x)","\begin{cases} - \frac{8 i \left(x + 1\right)^{4}}{- 315 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4} + 2520 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 7560 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 10080 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 5040 i \sqrt{-1 + \frac{2}{x + 1}}} + \frac{72 i \left(x + 1\right)^{3}}{- 315 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4} + 2520 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 7560 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 10080 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 5040 i \sqrt{-1 + \frac{2}{x + 1}}} - \frac{252 i \left(x + 1\right)^{2}}{- 315 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4} + 2520 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 7560 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 10080 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 5040 i \sqrt{-1 + \frac{2}{x + 1}}} + \frac{420 i \left(x + 1\right)}{- 315 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4} + 2520 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 7560 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 10080 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 5040 i \sqrt{-1 + \frac{2}{x + 1}}} - \frac{315 i}{- 315 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4} + 2520 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3} - 7560 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2} + 10080 i \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) - 5040 i \sqrt{-1 + \frac{2}{x + 1}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{8 \left(x + 1\right)^{4}}{315 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4} - 2520 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 7560 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 10080 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 5040 i \sqrt{1 - \frac{2}{x + 1}}} - \frac{72 \left(x + 1\right)^{3}}{315 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4} - 2520 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 7560 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 10080 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 5040 i \sqrt{1 - \frac{2}{x + 1}}} + \frac{252 \left(x + 1\right)^{2}}{315 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4} - 2520 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 7560 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 10080 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 5040 i \sqrt{1 - \frac{2}{x + 1}}} - \frac{420 \left(x + 1\right)}{315 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4} - 2520 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 7560 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 10080 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 5040 i \sqrt{1 - \frac{2}{x + 1}}} + \frac{315}{315 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4} - 2520 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3} + 7560 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2} - 10080 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + 5040 i \sqrt{1 - \frac{2}{x + 1}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*I*(x + 1)**4/(-315*I*sqrt(-1 + 2/(x + 1))*(x + 1)**4 + 2520*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 7560*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 10080*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 5040*I*sqrt(-1 + 2/(x + 1))) + 72*I*(x + 1)**3/(-315*I*sqrt(-1 + 2/(x + 1))*(x + 1)**4 + 2520*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 7560*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 10080*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 5040*I*sqrt(-1 + 2/(x + 1))) - 252*I*(x + 1)**2/(-315*I*sqrt(-1 + 2/(x + 1))*(x + 1)**4 + 2520*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 7560*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 10080*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 5040*I*sqrt(-1 + 2/(x + 1))) + 420*I*(x + 1)/(-315*I*sqrt(-1 + 2/(x + 1))*(x + 1)**4 + 2520*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 7560*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 10080*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 5040*I*sqrt(-1 + 2/(x + 1))) - 315*I/(-315*I*sqrt(-1 + 2/(x + 1))*(x + 1)**4 + 2520*I*sqrt(-1 + 2/(x + 1))*(x + 1)**3 - 7560*I*sqrt(-1 + 2/(x + 1))*(x + 1)**2 + 10080*I*sqrt(-1 + 2/(x + 1))*(x + 1) - 5040*I*sqrt(-1 + 2/(x + 1))), 2/Abs(x + 1) > 1), (8*(x + 1)**4/(315*I*sqrt(1 - 2/(x + 1))*(x + 1)**4 - 2520*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 7560*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 10080*I*sqrt(1 - 2/(x + 1))*(x + 1) + 5040*I*sqrt(1 - 2/(x + 1))) - 72*(x + 1)**3/(315*I*sqrt(1 - 2/(x + 1))*(x + 1)**4 - 2520*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 7560*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 10080*I*sqrt(1 - 2/(x + 1))*(x + 1) + 5040*I*sqrt(1 - 2/(x + 1))) + 252*(x + 1)**2/(315*I*sqrt(1 - 2/(x + 1))*(x + 1)**4 - 2520*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 7560*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 10080*I*sqrt(1 - 2/(x + 1))*(x + 1) + 5040*I*sqrt(1 - 2/(x + 1))) - 420*(x + 1)/(315*I*sqrt(1 - 2/(x + 1))*(x + 1)**4 - 2520*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 7560*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 10080*I*sqrt(1 - 2/(x + 1))*(x + 1) + 5040*I*sqrt(1 - 2/(x + 1))) + 315/(315*I*sqrt(1 - 2/(x + 1))*(x + 1)**4 - 2520*I*sqrt(1 - 2/(x + 1))*(x + 1)**3 + 7560*I*sqrt(1 - 2/(x + 1))*(x + 1)**2 - 10080*I*sqrt(1 - 2/(x + 1))*(x + 1) + 5040*I*sqrt(1 - 2/(x + 1))), True))","C",0
1116,1,207,0,17.475163," ","integrate((1-x)**(7/2)/(1+x)**(3/2),x)","\begin{cases} 35 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{x - 1}} + \frac{23 i \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{x - 1}} - \frac{125 i \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{x - 1}} + \frac{13 i \sqrt{x + 1}}{\sqrt{x - 1}} + \frac{32 i}{\sqrt{x - 1} \sqrt{x + 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 35 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{1 - x}} - \frac{23 \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{1 - x}} + \frac{125 \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{1 - x}} - \frac{13 \sqrt{x + 1}}{\sqrt{1 - x}} - \frac{32}{\sqrt{1 - x} \sqrt{x + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(7/2)/(3*sqrt(x - 1)) + 23*I*(x + 1)**(5/2)/(6*sqrt(x - 1)) - 125*I*(x + 1)**(3/2)/(6*sqrt(x - 1)) + 13*I*sqrt(x + 1)/sqrt(x - 1) + 32*I/(sqrt(x - 1)*sqrt(x + 1)), Abs(x + 1)/2 > 1), (-35*asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(7/2)/(3*sqrt(1 - x)) - 23*(x + 1)**(5/2)/(6*sqrt(1 - x)) + 125*(x + 1)**(3/2)/(6*sqrt(1 - x)) - 13*sqrt(x + 1)/sqrt(1 - x) - 32/(sqrt(1 - x)*sqrt(x + 1)), True))","A",0
1117,1,168,0,6.987274," ","integrate((1-x)**(5/2)/(1+x)**(3/2),x)","\begin{cases} 15 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{x - 1}} - \frac{11 i \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{x - 1}} + \frac{i \sqrt{x + 1}}{\sqrt{x - 1}} + \frac{16 i}{\sqrt{x - 1} \sqrt{x + 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 15 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{5}{2}}}{2 \sqrt{1 - x}} + \frac{11 \left(x + 1\right)^{\frac{3}{2}}}{2 \sqrt{1 - x}} - \frac{\sqrt{x + 1}}{\sqrt{1 - x}} - \frac{16}{\sqrt{1 - x} \sqrt{x + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(5/2)/(2*sqrt(x - 1)) - 11*I*(x + 1)**(3/2)/(2*sqrt(x - 1)) + I*sqrt(x + 1)/sqrt(x - 1) + 16*I/(sqrt(x - 1)*sqrt(x + 1)), Abs(x + 1)/2 > 1), (-15*asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(5/2)/(2*sqrt(1 - x)) + 11*(x + 1)**(3/2)/(2*sqrt(1 - x)) - sqrt(x + 1)/sqrt(1 - x) - 16/(sqrt(1 - x)*sqrt(x + 1)), True))","A",0
1118,1,133,0,2.484581," ","integrate((1-x)**(3/2)/(1+x)**(3/2),x)","\begin{cases} 6 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{\sqrt{x - 1}} - \frac{2 i \sqrt{x + 1}}{\sqrt{x - 1}} + \frac{8 i}{\sqrt{x - 1} \sqrt{x + 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 6 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{1 - x}} + \frac{2 \sqrt{x + 1}}{\sqrt{1 - x}} - \frac{8}{\sqrt{1 - x} \sqrt{x + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*I*acosh(sqrt(2)*sqrt(x + 1)/2) - I*(x + 1)**(3/2)/sqrt(x - 1) - 2*I*sqrt(x + 1)/sqrt(x - 1) + 8*I/(sqrt(x - 1)*sqrt(x + 1)), Abs(x + 1)/2 > 1), (-6*asin(sqrt(2)*sqrt(x + 1)/2) + (x + 1)**(3/2)/sqrt(1 - x) + 2*sqrt(x + 1)/sqrt(1 - x) - 8/(sqrt(1 - x)*sqrt(x + 1)), True))","A",0
1119,1,104,0,1.538031," ","integrate((1-x)**(1/2)/(1+x)**(3/2),x)","\begin{cases} 2 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{2 i \sqrt{x + 1}}{\sqrt{x - 1}} + \frac{4 i}{\sqrt{x - 1} \sqrt{x + 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{2 \sqrt{x + 1}}{\sqrt{1 - x}} - \frac{4}{\sqrt{1 - x} \sqrt{x + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*acosh(sqrt(2)*sqrt(x + 1)/2) - 2*I*sqrt(x + 1)/sqrt(x - 1) + 4*I/(sqrt(x - 1)*sqrt(x + 1)), Abs(x + 1)/2 > 1), (-2*asin(sqrt(2)*sqrt(x + 1)/2) + 2*sqrt(x + 1)/sqrt(1 - x) - 4/(sqrt(1 - x)*sqrt(x + 1)), True))","B",0
1120,1,29,0,1.199335," ","integrate(1/(1-x)**(1/2)/(1+x)**(3/2),x)","\begin{cases} - \sqrt{-1 + \frac{2}{x + 1}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- i \sqrt{1 - \frac{2}{x + 1}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(-1 + 2/(x + 1)), 2/Abs(x + 1) > 1), (-I*sqrt(1 - 2/(x + 1)), True))","A",0
1121,1,65,0,1.857354," ","integrate(1/(1-x)**(3/2)/(1+x)**(3/2),x)","\begin{cases} \frac{1}{\sqrt{-1 + \frac{2}{x + 1}}} - \frac{1}{\sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{x - 1} + \frac{i \sqrt{1 - \frac{2}{x + 1}}}{x - 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/sqrt(-1 + 2/(x + 1)) - 1/(sqrt(-1 + 2/(x + 1))*(x + 1)), 2/Abs(x + 1) > 1), (-I*sqrt(1 - 2/(x + 1))*(x + 1)/(x - 1) + I*sqrt(1 - 2/(x + 1))/(x - 1), True))","A",0
1122,1,158,0,5.278658," ","integrate(1/(1-x)**(5/2)/(1+x)**(3/2),x)","\begin{cases} - \frac{2 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 12 x + 3 \left(x + 1\right)^{2}} + \frac{6 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 12 x + 3 \left(x + 1\right)^{2}} - \frac{3 \sqrt{-1 + \frac{2}{x + 1}}}{- 12 x + 3 \left(x + 1\right)^{2}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{2 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 12 x + 3 \left(x + 1\right)^{2}} + \frac{6 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 12 x + 3 \left(x + 1\right)^{2}} - \frac{3 i \sqrt{1 - \frac{2}{x + 1}}}{- 12 x + 3 \left(x + 1\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-12*x + 3*(x + 1)**2) + 6*sqrt(-1 + 2/(x + 1))*(x + 1)/(-12*x + 3*(x + 1)**2) - 3*sqrt(-1 + 2/(x + 1))/(-12*x + 3*(x + 1)**2), 2/Abs(x + 1) > 1), (-2*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-12*x + 3*(x + 1)**2) + 6*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-12*x + 3*(x + 1)**2) - 3*I*sqrt(1 - 2/(x + 1))/(-12*x + 3*(x + 1)**2), True))","B",0
1123,1,282,0,16.833418," ","integrate(1/(1-x)**(7/2)/(1+x)**(3/2),x)","\begin{cases} \frac{2 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} - \frac{10 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} + \frac{15 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} - \frac{5 \sqrt{-1 + \frac{2}{x + 1}}}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{2 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} - \frac{10 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} + \frac{15 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} - \frac{5 i \sqrt{1 - \frac{2}{x + 1}}}{- 60 x - 5 \left(x + 1\right)^{3} + 30 \left(x + 1\right)^{2} - 20} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(-1 + 2/(x + 1))*(x + 1)**3/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20) - 10*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20) + 15*sqrt(-1 + 2/(x + 1))*(x + 1)/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20) - 5*sqrt(-1 + 2/(x + 1))/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20), 2/Abs(x + 1) > 1), (2*I*sqrt(1 - 2/(x + 1))*(x + 1)**3/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20) - 10*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20) + 15*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20) - 5*I*sqrt(1 - 2/(x + 1))/(-60*x - 5*(x + 1)**3 + 30*(x + 1)**2 - 20), True))","B",0
1124,1,423,0,44.936692," ","integrate(1/(1-x)**(9/2)/(1+x)**(3/2),x)","\begin{cases} - \frac{8 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} + \frac{56 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} - \frac{140 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} + \frac{140 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} - \frac{35 \sqrt{-1 + \frac{2}{x + 1}}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{8 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} + \frac{56 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} - \frac{140 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} + \frac{140 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} - \frac{35 i \sqrt{1 - \frac{2}{x + 1}}}{- 1120 x + 35 \left(x + 1\right)^{4} - 280 \left(x + 1\right)^{3} + 840 \left(x + 1\right)^{2} - 560} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*sqrt(-1 + 2/(x + 1))*(x + 1)**4/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) + 56*sqrt(-1 + 2/(x + 1))*(x + 1)**3/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) - 140*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) + 140*sqrt(-1 + 2/(x + 1))*(x + 1)/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) - 35*sqrt(-1 + 2/(x + 1))/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560), 2/Abs(x + 1) > 1), (-8*I*sqrt(1 - 2/(x + 1))*(x + 1)**4/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) + 56*I*sqrt(1 - 2/(x + 1))*(x + 1)**3/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) - 140*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) + 140*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560) - 35*I*sqrt(1 - 2/(x + 1))/(-1120*x + 35*(x + 1)**4 - 280*(x + 1)**3 + 840*(x + 1)**2 - 560), True))","B",0
1125,1,592,0,113.605381," ","integrate(1/(1-x)**(11/2)/(1+x)**(3/2),x)","\begin{cases} \frac{8 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{5}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} - \frac{72 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} + \frac{252 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} - \frac{420 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} + \frac{315 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} - \frac{63 \sqrt{-1 + \frac{2}{x + 1}}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{8 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{5}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} - \frac{72 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} + \frac{252 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} - \frac{420 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} + \frac{315 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} - \frac{63 i \sqrt{1 - \frac{2}{x + 1}}}{- 5040 x - 63 \left(x + 1\right)^{5} + 630 \left(x + 1\right)^{4} - 2520 \left(x + 1\right)^{3} + 5040 \left(x + 1\right)^{2} - 3024} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sqrt(-1 + 2/(x + 1))*(x + 1)**5/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) - 72*sqrt(-1 + 2/(x + 1))*(x + 1)**4/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) + 252*sqrt(-1 + 2/(x + 1))*(x + 1)**3/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) - 420*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) + 315*sqrt(-1 + 2/(x + 1))*(x + 1)/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) - 63*sqrt(-1 + 2/(x + 1))/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024), 2/Abs(x + 1) > 1), (8*I*sqrt(1 - 2/(x + 1))*(x + 1)**5/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) - 72*I*sqrt(1 - 2/(x + 1))*(x + 1)**4/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) + 252*I*sqrt(1 - 2/(x + 1))*(x + 1)**3/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) - 420*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) + 315*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024) - 63*I*sqrt(1 - 2/(x + 1))/(-5040*x - 63*(x + 1)**5 + 630*(x + 1)**4 - 2520*(x + 1)**3 + 5040*(x + 1)**2 - 3024), True))","B",0
1126,1,250,0,45.202114," ","integrate((1-x)**(9/2)/(1+x)**(5/2),x)","\begin{cases} - 105 i \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{i \left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{x - 1}} - \frac{29 i \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{x - 1}} + \frac{215 i \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{x - 1}} + \frac{43 i \sqrt{x + 1}}{3 \sqrt{x - 1}} - \frac{448 i}{3 \sqrt{x - 1} \sqrt{x + 1}} + \frac{64 i}{3 \sqrt{x - 1} \left(x + 1\right)^{\frac{3}{2}}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\105 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{\left(x + 1\right)^{\frac{7}{2}}}{3 \sqrt{1 - x}} + \frac{29 \left(x + 1\right)^{\frac{5}{2}}}{6 \sqrt{1 - x}} - \frac{215 \left(x + 1\right)^{\frac{3}{2}}}{6 \sqrt{1 - x}} - \frac{43 \sqrt{x + 1}}{3 \sqrt{1 - x}} + \frac{448}{3 \sqrt{1 - x} \sqrt{x + 1}} - \frac{64}{3 \sqrt{1 - x} \left(x + 1\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*I*acosh(sqrt(2)*sqrt(x + 1)/2) + I*(x + 1)**(7/2)/(3*sqrt(x - 1)) - 29*I*(x + 1)**(5/2)/(6*sqrt(x - 1)) + 215*I*(x + 1)**(3/2)/(6*sqrt(x - 1)) + 43*I*sqrt(x + 1)/(3*sqrt(x - 1)) - 448*I/(3*sqrt(x - 1)*sqrt(x + 1)) + 64*I/(3*sqrt(x - 1)*(x + 1)**(3/2)), Abs(x + 1)/2 > 1), (105*asin(sqrt(2)*sqrt(x + 1)/2) - (x + 1)**(7/2)/(3*sqrt(1 - x)) + 29*(x + 1)**(5/2)/(6*sqrt(1 - x)) - 215*(x + 1)**(3/2)/(6*sqrt(1 - x)) - 43*sqrt(x + 1)/(3*sqrt(1 - x)) + 448/(3*sqrt(1 - x)*sqrt(x + 1)) - 64/(3*sqrt(1 - x)*(x + 1)**(3/2)), True))","A",0
1127,1,207,0,17.501493," ","integrate((1-x)**(7/2)/(1+x)**(5/2),x)","\begin{cases} - \frac{\sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{2} + \frac{13 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{2} + \frac{80 \sqrt{-1 + \frac{2}{x + 1}}}{3} - \frac{16 \sqrt{-1 + \frac{2}{x + 1}}}{3 \left(x + 1\right)} + \frac{35 i \log{\left(\frac{1}{x + 1} \right)}}{2} + \frac{35 i \log{\left(x + 1 \right)}}{2} + 35 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{2} + \frac{13 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{2} + \frac{80 i \sqrt{1 - \frac{2}{x + 1}}}{3} - \frac{16 i \sqrt{1 - \frac{2}{x + 1}}}{3 \left(x + 1\right)} + \frac{35 i \log{\left(\frac{1}{x + 1} \right)}}{2} - 35 i \log{\left(\sqrt{1 - \frac{2}{x + 1}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(-1 + 2/(x + 1))*(x + 1)**2/2 + 13*sqrt(-1 + 2/(x + 1))*(x + 1)/2 + 80*sqrt(-1 + 2/(x + 1))/3 - 16*sqrt(-1 + 2/(x + 1))/(3*(x + 1)) + 35*I*log(1/(x + 1))/2 + 35*I*log(x + 1)/2 + 35*asin(sqrt(2)*sqrt(x + 1)/2), 2/Abs(x + 1) > 1), (-I*sqrt(1 - 2/(x + 1))*(x + 1)**2/2 + 13*I*sqrt(1 - 2/(x + 1))*(x + 1)/2 + 80*I*sqrt(1 - 2/(x + 1))/3 - 16*I*sqrt(1 - 2/(x + 1))/(3*(x + 1)) + 35*I*log(1/(x + 1))/2 - 35*I*log(sqrt(1 - 2/(x + 1)) + 1), True))","C",0
1128,1,160,0,6.460968," ","integrate((1-x)**(5/2)/(1+x)**(5/2),x)","\begin{cases} \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right) + \frac{28 \sqrt{-1 + \frac{2}{x + 1}}}{3} - \frac{8 \sqrt{-1 + \frac{2}{x + 1}}}{3 \left(x + 1\right)} + 5 i \log{\left(\frac{1}{x + 1} \right)} + 5 i \log{\left(x + 1 \right)} + 10 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right) + \frac{28 i \sqrt{1 - \frac{2}{x + 1}}}{3} - \frac{8 i \sqrt{1 - \frac{2}{x + 1}}}{3 \left(x + 1\right)} + 5 i \log{\left(\frac{1}{x + 1} \right)} - 10 i \log{\left(\sqrt{1 - \frac{2}{x + 1}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(-1 + 2/(x + 1))*(x + 1) + 28*sqrt(-1 + 2/(x + 1))/3 - 8*sqrt(-1 + 2/(x + 1))/(3*(x + 1)) + 5*I*log(1/(x + 1)) + 5*I*log(x + 1) + 10*asin(sqrt(2)*sqrt(x + 1)/2), 2/Abs(x + 1) > 1), (I*sqrt(1 - 2/(x + 1))*(x + 1) + 28*I*sqrt(1 - 2/(x + 1))/3 - 8*I*sqrt(1 - 2/(x + 1))/(3*(x + 1)) + 5*I*log(1/(x + 1)) - 10*I*log(sqrt(1 - 2/(x + 1)) + 1), True))","C",0
1129,1,126,0,3.284419," ","integrate((1-x)**(3/2)/(1+x)**(5/2),x)","\begin{cases} \frac{8 \sqrt{-1 + \frac{2}{x + 1}}}{3} - \frac{4 \sqrt{-1 + \frac{2}{x + 1}}}{3 \left(x + 1\right)} + i \log{\left(\frac{1}{x + 1} \right)} + i \log{\left(x + 1 \right)} + 2 \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{8 i \sqrt{1 - \frac{2}{x + 1}}}{3} - \frac{4 i \sqrt{1 - \frac{2}{x + 1}}}{3 \left(x + 1\right)} + i \log{\left(\frac{1}{x + 1} \right)} - 2 i \log{\left(\sqrt{1 - \frac{2}{x + 1}} + 1 \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sqrt(-1 + 2/(x + 1))/3 - 4*sqrt(-1 + 2/(x + 1))/(3*(x + 1)) + I*log(1/(x + 1)) + I*log(x + 1) + 2*asin(sqrt(2)*sqrt(x + 1)/2), 2/Abs(x + 1) > 1), (8*I*sqrt(1 - 2/(x + 1))/3 - 4*I*sqrt(1 - 2/(x + 1))/(3*(x + 1)) + I*log(1/(x + 1)) - 2*I*log(sqrt(1 - 2/(x + 1)) + 1), True))","C",0
1130,1,65,0,1.694221," ","integrate((1-x)**(1/2)/(1+x)**(5/2),x)","\begin{cases} \frac{\sqrt{-1 + \frac{2}{x + 1}}}{3} - \frac{2 \sqrt{-1 + \frac{2}{x + 1}}}{3 \left(x + 1\right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{i \sqrt{1 - \frac{2}{x + 1}}}{3} - \frac{2 i \sqrt{1 - \frac{2}{x + 1}}}{3 \left(x + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(-1 + 2/(x + 1))/3 - 2*sqrt(-1 + 2/(x + 1))/(3*(x + 1)), 2/Abs(x + 1) > 1), (I*sqrt(1 - 2/(x + 1))/3 - 2*I*sqrt(1 - 2/(x + 1))/(3*(x + 1)), True))","A",0
1131,1,65,0,2.346265," ","integrate(1/(1-x)**(1/2)/(1+x)**(5/2),x)","\begin{cases} - \frac{\sqrt{-1 + \frac{2}{x + 1}}}{3} - \frac{\sqrt{-1 + \frac{2}{x + 1}}}{3 \left(x + 1\right)} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{i \sqrt{1 - \frac{2}{x + 1}}}{3} - \frac{i \sqrt{1 - \frac{2}{x + 1}}}{3 \left(x + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(-1 + 2/(x + 1))/3 - sqrt(-1 + 2/(x + 1))/(3*(x + 1)), 2/Abs(x + 1) > 1), (-I*sqrt(1 - 2/(x + 1))/3 - I*sqrt(1 - 2/(x + 1))/(3*(x + 1)), True))","A",0
1132,1,165,0,5.396923," ","integrate(1/(1-x)**(3/2)/(1+x)**(5/2),x)","\begin{cases} - \frac{2 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 6 x + 3 \left(x + 1\right)^{2} - 6} + \frac{2 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 6 x + 3 \left(x + 1\right)^{2} - 6} + \frac{\sqrt{-1 + \frac{2}{x + 1}}}{- 6 x + 3 \left(x + 1\right)^{2} - 6} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{2 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 6 x + 3 \left(x + 1\right)^{2} - 6} + \frac{2 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 6 x + 3 \left(x + 1\right)^{2} - 6} + \frac{i \sqrt{1 - \frac{2}{x + 1}}}{- 6 x + 3 \left(x + 1\right)^{2} - 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-6*x + 3*(x + 1)**2 - 6) + 2*sqrt(-1 + 2/(x + 1))*(x + 1)/(-6*x + 3*(x + 1)**2 - 6) + sqrt(-1 + 2/(x + 1))/(-6*x + 3*(x + 1)**2 - 6), 2/Abs(x + 1) > 1), (-2*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-6*x + 3*(x + 1)**2 - 6) + 2*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-6*x + 3*(x + 1)**2 - 6) + I*sqrt(1 - 2/(x + 1))/(-6*x + 3*(x + 1)**2 - 6), True))","A",0
1133,1,279,0,9.607355," ","integrate(1/(1-x)**(5/2)/(1+x)**(5/2),x)","\begin{cases} - \frac{2 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3}}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} + \frac{6 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} - \frac{3 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} - \frac{\sqrt{-1 + \frac{2}{x + 1}}}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{2 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3}}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} + \frac{6 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} - \frac{3 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} - \frac{i \sqrt{1 - \frac{2}{x + 1}}}{12 x + 3 \left(x + 1\right)^{3} - 12 \left(x + 1\right)^{2} + 12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(-1 + 2/(x + 1))*(x + 1)**3/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12) + 6*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12) - 3*sqrt(-1 + 2/(x + 1))*(x + 1)/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12) - sqrt(-1 + 2/(x + 1))/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12), 2/Abs(x + 1) > 1), (-2*I*sqrt(1 - 2/(x + 1))*(x + 1)**3/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12) + 6*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12) - 3*I*sqrt(1 - 2/(x + 1))*(x + 1)/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12) - I*sqrt(1 - 2/(x + 1))/(12*x + 3*(x + 1)**3 - 12*(x + 1)**2 + 12), True))","B",0
1134,1,423,0,27.605489," ","integrate(1/(1-x)**(7/2)/(1+x)**(5/2),x)","\begin{cases} - \frac{8 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} + \frac{40 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} - \frac{60 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} + \frac{20 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} + \frac{5 \sqrt{-1 + \frac{2}{x + 1}}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{8 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} + \frac{40 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} - \frac{60 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} + \frac{20 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} + \frac{5 i \sqrt{1 - \frac{2}{x + 1}}}{- 120 x + 15 \left(x + 1\right)^{4} - 90 \left(x + 1\right)^{3} + 180 \left(x + 1\right)^{2} - 120} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*sqrt(-1 + 2/(x + 1))*(x + 1)**4/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) + 40*sqrt(-1 + 2/(x + 1))*(x + 1)**3/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) - 60*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) + 20*sqrt(-1 + 2/(x + 1))*(x + 1)/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) + 5*sqrt(-1 + 2/(x + 1))/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120), 2/Abs(x + 1) > 1), (-8*I*sqrt(1 - 2/(x + 1))*(x + 1)**4/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) + 40*I*sqrt(1 - 2/(x + 1))*(x + 1)**3/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) - 60*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) + 20*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120) + 5*I*sqrt(1 - 2/(x + 1))/(-120*x + 15*(x + 1)**4 - 90*(x + 1)**3 + 180*(x + 1)**2 - 120), True))","B",0
1135,1,592,0,71.007425," ","integrate(1/(1-x)**(9/2)/(1+x)**(5/2),x)","\begin{cases} \frac{8 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{5}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} - \frac{56 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} + \frac{140 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} - \frac{140 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} + \frac{35 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} + \frac{7 \sqrt{-1 + \frac{2}{x + 1}}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\\frac{8 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{5}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} - \frac{56 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{4}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} + \frac{140 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{3}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} - \frac{140 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{2}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} + \frac{35 i \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} + \frac{7 i \sqrt{1 - \frac{2}{x + 1}}}{- 336 x - 21 \left(x + 1\right)^{5} + 168 \left(x + 1\right)^{4} - 504 \left(x + 1\right)^{3} + 672 \left(x + 1\right)^{2} - 336} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sqrt(-1 + 2/(x + 1))*(x + 1)**5/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) - 56*sqrt(-1 + 2/(x + 1))*(x + 1)**4/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) + 140*sqrt(-1 + 2/(x + 1))*(x + 1)**3/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) - 140*sqrt(-1 + 2/(x + 1))*(x + 1)**2/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) + 35*sqrt(-1 + 2/(x + 1))*(x + 1)/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) + 7*sqrt(-1 + 2/(x + 1))/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336), 2/Abs(x + 1) > 1), (8*I*sqrt(1 - 2/(x + 1))*(x + 1)**5/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) - 56*I*sqrt(1 - 2/(x + 1))*(x + 1)**4/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) + 140*I*sqrt(1 - 2/(x + 1))*(x + 1)**3/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) - 140*I*sqrt(1 - 2/(x + 1))*(x + 1)**2/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) + 35*I*sqrt(1 - 2/(x + 1))*(x + 1)/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336) + 7*I*sqrt(1 - 2/(x + 1))/(-336*x - 21*(x + 1)**5 + 168*(x + 1)**4 - 504*(x + 1)**3 + 672*(x + 1)**2 - 336), True))","B",0
1136,-1,0,0,0.000000," ","integrate(1/(1-x)**(11/2)/(1+x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1137,0,0,0,0.000000," ","integrate((a*x+a)**(5/2)*(-c*x+c)**(5/2),x)","\int \left(a \left(x + 1\right)\right)^{\frac{5}{2}} \left(- c \left(x - 1\right)\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*(x + 1))**(5/2)*(-c*(x - 1))**(5/2), x)","F",0
1138,0,0,0,0.000000," ","integrate((a*x+a)**(3/2)*(-c*x+c)**(3/2),x)","\int \left(a \left(x + 1\right)\right)^{\frac{3}{2}} \left(- c \left(x - 1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*(x + 1))**(3/2)*(-c*(x - 1))**(3/2), x)","F",0
1139,0,0,0,0.000000," ","integrate((a*x+a)**(1/2)*(-c*x+c)**(1/2),x)","\int \sqrt{a \left(x + 1\right)} \sqrt{- c \left(x - 1\right)}\, dx"," ",0,"Integral(sqrt(a*(x + 1))*sqrt(-c*(x - 1)), x)","F",0
1140,1,85,0,3.953143," ","integrate(1/(a*x+a)**(1/2)/(-c*x+c)**(1/2),x)","- \frac{i {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{1}{x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} \sqrt{a} \sqrt{c}} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} \sqrt{a} \sqrt{c}}"," ",0,"-I*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), x**(-2))/(4*pi**(3/2)*sqrt(a)*sqrt(c)) + meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), exp_polar(-2*I*pi)/x**2)/(4*pi**(3/2)*sqrt(a)*sqrt(c))","C",0
1141,1,82,0,4.443649," ","integrate(1/(a*x+a)**(3/2)/(-c*x+c)**(3/2),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & \frac{1}{2}, \frac{3}{2}, 2 \\\frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 2 & 0 \end{matrix} \middle| {\frac{1}{x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} a^{\frac{3}{2}} c^{\frac{3}{2}}} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 &  \\\frac{1}{4}, \frac{3}{4} & - \frac{1}{2}, 0, 1, 0 \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} a^{\frac{3}{2}} c^{\frac{3}{2}}}"," ",0,"-I*meijerg(((3/4, 5/4, 1), (1/2, 3/2, 2)), ((3/4, 1, 5/4, 3/2, 2), (0,)), x**(-2))/(2*pi**(3/2)*a**(3/2)*c**(3/2)) + meijerg(((-1/2, 0, 1/4, 1/2, 3/4, 1), ()), ((1/4, 3/4), (-1/2, 0, 1, 0)), exp_polar(-2*I*pi)/x**2)/(2*pi**(3/2)*a**(3/2)*c**(3/2))","C",0
1142,1,82,0,13.690331," ","integrate(1/(a*x+a)**(5/2)/(-c*x+c)**(5/2),x)","\frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & \frac{1}{2}, \frac{5}{2}, 3 \\\frac{5}{4}, \frac{7}{4}, 2, \frac{5}{2}, 3 & 0 \end{matrix} \middle| {\frac{1}{x^{2}}} \right)}}{3 \pi^{\frac{3}{2}} a^{\frac{5}{2}} c^{\frac{5}{2}}} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, \frac{3}{4}, \frac{5}{4}, 1 &  \\\frac{3}{4}, \frac{5}{4} & - \frac{1}{2}, 0, 2, 0 \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{2}}} \right)}}{3 \pi^{\frac{3}{2}} a^{\frac{5}{2}} c^{\frac{5}{2}}}"," ",0,"I*meijerg(((5/4, 7/4, 1), (1/2, 5/2, 3)), ((5/4, 7/4, 2, 5/2, 3), (0,)), x**(-2))/(3*pi**(3/2)*a**(5/2)*c**(5/2)) + meijerg(((-1/2, 0, 1/2, 3/4, 5/4, 1), ()), ((3/4, 5/4), (-1/2, 0, 2, 0)), exp_polar(-2*I*pi)/x**2)/(3*pi**(3/2)*a**(5/2)*c**(5/2))","C",0
1143,1,85,0,55.150707," ","integrate(1/(a*x+a)**(7/2)/(-c*x+c)**(7/2),x)","- \frac{2 i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4}, 1 & \frac{1}{2}, \frac{7}{2}, 4 \\\frac{7}{4}, \frac{9}{4}, 3, \frac{7}{2}, 4 & 0 \end{matrix} \middle| {\frac{1}{x^{2}}} \right)}}{15 \pi^{\frac{3}{2}} a^{\frac{7}{2}} c^{\frac{7}{2}}} + \frac{2 {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, \frac{5}{4}, \frac{7}{4}, 1 &  \\\frac{5}{4}, \frac{7}{4} & - \frac{1}{2}, 0, 3, 0 \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{2}}} \right)}}{15 \pi^{\frac{3}{2}} a^{\frac{7}{2}} c^{\frac{7}{2}}}"," ",0,"-2*I*meijerg(((7/4, 9/4, 1), (1/2, 7/2, 4)), ((7/4, 9/4, 3, 7/2, 4), (0,)), x**(-2))/(15*pi**(3/2)*a**(7/2)*c**(7/2)) + 2*meijerg(((-1/2, 0, 1/2, 5/4, 7/4, 1), ()), ((5/4, 7/4), (-1/2, 0, 3, 0)), exp_polar(-2*I*pi)/x**2)/(15*pi**(3/2)*a**(7/2)*c**(7/2))","C",0
1144,-1,0,0,0.000000," ","integrate(1/(a*x+a)**(9/2)/(-c*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1145,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)*(-b*c*x+a*c)**(5/2),x)","\int \left(- c \left(- a + b x\right)\right)^{\frac{5}{2}} \left(a + b x\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((-c*(-a + b*x))**(5/2)*(a + b*x)**(5/2), x)","F",0
1146,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(-b*c*x+a*c)**(3/2),x)","\int \left(- c \left(- a + b x\right)\right)^{\frac{3}{2}} \left(a + b x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-c*(-a + b*x))**(3/2)*(a + b*x)**(3/2), x)","F",0
1147,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(-b*c*x+a*c)**(1/2),x)","\int \sqrt{- c \left(- a + b x\right)} \sqrt{a + b x}\, dx"," ",0,"Integral(sqrt(-c*(-a + b*x))*sqrt(a + b*x), x)","F",0
1148,1,90,0,4.688403," ","integrate(1/(b*x+a)**(1/2)/(-b*c*x+a*c)**(1/2),x)","- \frac{i {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{a^{2}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b \sqrt{c}} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{a^{2} e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b \sqrt{c}}"," ",0,"-I*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), a**2/(b**2*x**2))/(4*pi**(3/2)*b*sqrt(c)) + meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), a**2*exp_polar(-2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b*sqrt(c))","C",0
1149,1,94,0,5.179109," ","integrate(1/(b*x+a)**(3/2)/(-b*c*x+a*c)**(3/2),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & \frac{1}{2}, \frac{3}{2}, 2 \\\frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 2 & 0 \end{matrix} \middle| {\frac{a^{2}}{b^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} a^{2} b c^{\frac{3}{2}}} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 &  \\\frac{1}{4}, \frac{3}{4} & - \frac{1}{2}, 0, 1, 0 \end{matrix} \middle| {\frac{a^{2} e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{2 \pi^{\frac{3}{2}} a^{2} b c^{\frac{3}{2}}}"," ",0,"-I*meijerg(((3/4, 5/4, 1), (1/2, 3/2, 2)), ((3/4, 1, 5/4, 3/2, 2), (0,)), a**2/(b**2*x**2))/(2*pi**(3/2)*a**2*b*c**(3/2)) + meijerg(((-1/2, 0, 1/4, 1/2, 3/4, 1), ()), ((1/4, 3/4), (-1/2, 0, 1, 0)), a**2*exp_polar(-2*I*pi)/(b**2*x**2))/(2*pi**(3/2)*a**2*b*c**(3/2))","C",0
1150,1,94,0,15.849018," ","integrate(1/(b*x+a)**(5/2)/(-b*c*x+a*c)**(5/2),x)","\frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{4}, \frac{7}{4}, 1 & \frac{1}{2}, \frac{5}{2}, 3 \\\frac{5}{4}, \frac{7}{4}, 2, \frac{5}{2}, 3 & 0 \end{matrix} \middle| {\frac{a^{2}}{b^{2} x^{2}}} \right)}}{3 \pi^{\frac{3}{2}} a^{4} b c^{\frac{5}{2}}} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, \frac{3}{4}, \frac{5}{4}, 1 &  \\\frac{3}{4}, \frac{5}{4} & - \frac{1}{2}, 0, 2, 0 \end{matrix} \middle| {\frac{a^{2} e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{3 \pi^{\frac{3}{2}} a^{4} b c^{\frac{5}{2}}}"," ",0,"I*meijerg(((5/4, 7/4, 1), (1/2, 5/2, 3)), ((5/4, 7/4, 2, 5/2, 3), (0,)), a**2/(b**2*x**2))/(3*pi**(3/2)*a**4*b*c**(5/2)) + meijerg(((-1/2, 0, 1/2, 3/4, 5/4, 1), ()), ((3/4, 5/4), (-1/2, 0, 2, 0)), a**2*exp_polar(-2*I*pi)/(b**2*x**2))/(3*pi**(3/2)*a**4*b*c**(5/2))","C",0
1151,1,97,0,59.496141," ","integrate(1/(b*x+a)**(7/2)/(-b*c*x+a*c)**(7/2),x)","- \frac{2 i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{7}{4}, \frac{9}{4}, 1 & \frac{1}{2}, \frac{7}{2}, 4 \\\frac{7}{4}, \frac{9}{4}, 3, \frac{7}{2}, 4 & 0 \end{matrix} \middle| {\frac{a^{2}}{b^{2} x^{2}}} \right)}}{15 \pi^{\frac{3}{2}} a^{6} b c^{\frac{7}{2}}} + \frac{2 {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, \frac{5}{4}, \frac{7}{4}, 1 &  \\\frac{5}{4}, \frac{7}{4} & - \frac{1}{2}, 0, 3, 0 \end{matrix} \middle| {\frac{a^{2} e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{15 \pi^{\frac{3}{2}} a^{6} b c^{\frac{7}{2}}}"," ",0,"-2*I*meijerg(((7/4, 9/4, 1), (1/2, 7/2, 4)), ((7/4, 9/4, 3, 7/2, 4), (0,)), a**2/(b**2*x**2))/(15*pi**(3/2)*a**6*b*c**(7/2)) + 2*meijerg(((-1/2, 0, 1/2, 5/4, 7/4, 1), ()), ((5/4, 7/4), (-1/2, 0, 3, 0)), a**2*exp_polar(-2*I*pi)/(b**2*x**2))/(15*pi**(3/2)*a**6*b*c**(7/2))","C",0
1152,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(9/2)/(-b*c*x+a*c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1153,-1,0,0,0.000000," ","integrate((3-6*x)**(5/2)*(4*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate((3-6*x)**(3/2)*(4*x+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,1,187,0,4.741698," ","integrate((3-6*x)**(1/2)*(4*x+2)**(1/2),x)","\begin{cases} - \frac{\sqrt{6} i \operatorname{acosh}{\left(\sqrt{x + \frac{1}{2}} \right)}}{2} + \frac{\sqrt{6} i \left(x + \frac{1}{2}\right)^{\frac{5}{2}}}{\sqrt{x - \frac{1}{2}}} - \frac{3 \sqrt{6} i \left(x + \frac{1}{2}\right)^{\frac{3}{2}}}{2 \sqrt{x - \frac{1}{2}}} + \frac{\sqrt{6} i \sqrt{x + \frac{1}{2}}}{2 \sqrt{x - \frac{1}{2}}} & \text{for}\: \left|{x + \frac{1}{2}}\right| > 1 \\\frac{\sqrt{6} \operatorname{asin}{\left(\sqrt{x + \frac{1}{2}} \right)}}{2} - \frac{\sqrt{6} \left(x + \frac{1}{2}\right)^{\frac{5}{2}}}{\sqrt{\frac{1}{2} - x}} + \frac{3 \sqrt{6} \left(x + \frac{1}{2}\right)^{\frac{3}{2}}}{2 \sqrt{\frac{1}{2} - x}} - \frac{\sqrt{6} \sqrt{x + \frac{1}{2}}}{2 \sqrt{\frac{1}{2} - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(6)*I*acosh(sqrt(x + 1/2))/2 + sqrt(6)*I*(x + 1/2)**(5/2)/sqrt(x - 1/2) - 3*sqrt(6)*I*(x + 1/2)**(3/2)/(2*sqrt(x - 1/2)) + sqrt(6)*I*sqrt(x + 1/2)/(2*sqrt(x - 1/2)), Abs(x + 1/2) > 1), (sqrt(6)*asin(sqrt(x + 1/2))/2 - sqrt(6)*(x + 1/2)**(5/2)/sqrt(1/2 - x) + 3*sqrt(6)*(x + 1/2)**(3/2)/(2*sqrt(1/2 - x)) - sqrt(6)*sqrt(x + 1/2)/(2*sqrt(1/2 - x)), True))","B",0
1156,1,41,0,3.346846," ","integrate(1/(3-6*x)**(1/2)/(4*x+2)**(1/2),x)","\begin{cases} - \frac{\sqrt{6} i \operatorname{acosh}{\left(\sqrt{x + \frac{1}{2}} \right)}}{6} & \text{for}\: \left|{x + \frac{1}{2}}\right| > 1 \\\frac{\sqrt{6} \operatorname{asin}{\left(\sqrt{x + \frac{1}{2}} \right)}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(6)*I*acosh(sqrt(x + 1/2))/6, Abs(x + 1/2) > 1), (sqrt(6)*asin(sqrt(x + 1/2))/6, True))","A",0
1157,1,156,0,85.283366," ","integrate(1/(3-6*x)**(3/2)/(4*x+2)**(3/2),x)","\begin{cases} - \frac{2 \sqrt{6} i \sqrt{x - \frac{1}{2}} \left(x + \frac{1}{2}\right)}{144 \left(x + \frac{1}{2}\right)^{\frac{3}{2}} - 144 \sqrt{x + \frac{1}{2}}} + \frac{\sqrt{6} i \sqrt{x - \frac{1}{2}}}{144 \left(x + \frac{1}{2}\right)^{\frac{3}{2}} - 144 \sqrt{x + \frac{1}{2}}} & \text{for}\: \left|{x + \frac{1}{2}}\right| > 1 \\- \frac{2 \sqrt{6} \sqrt{\frac{1}{2} - x} \left(x + \frac{1}{2}\right)}{144 \left(x + \frac{1}{2}\right)^{\frac{3}{2}} - 144 \sqrt{x + \frac{1}{2}}} + \frac{\sqrt{6} \sqrt{\frac{1}{2} - x}}{144 \left(x + \frac{1}{2}\right)^{\frac{3}{2}} - 144 \sqrt{x + \frac{1}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(6)*I*sqrt(x - 1/2)*(x + 1/2)/(144*(x + 1/2)**(3/2) - 144*sqrt(x + 1/2)) + sqrt(6)*I*sqrt(x - 1/2)/(144*(x + 1/2)**(3/2) - 144*sqrt(x + 1/2)), Abs(x + 1/2) > 1), (-2*sqrt(6)*sqrt(1/2 - x)*(x + 1/2)/(144*(x + 1/2)**(3/2) - 144*sqrt(x + 1/2)) + sqrt(6)*sqrt(1/2 - x)/(144*(x + 1/2)**(3/2) - 144*sqrt(x + 1/2)), True))","B",0
1158,-1,0,0,0.000000," ","integrate(1/(3-6*x)**(5/2)/(4*x+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1159,-1,0,0,0.000000," ","integrate(1/(3-6*x)**(7/2)/(4*x+2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1160,1,199,0,7.481569," ","integrate((3-x)**(3/2)*(-2+x)**(3/2),x)","\begin{cases} - \frac{3 i \operatorname{acosh}{\left(\sqrt{x - 2} \right)}}{64} - \frac{i \left(x - 2\right)^{\frac{9}{2}}}{4 \sqrt{x - 3}} + \frac{5 i \left(x - 2\right)^{\frac{7}{2}}}{8 \sqrt{x - 3}} - \frac{13 i \left(x - 2\right)^{\frac{5}{2}}}{32 \sqrt{x - 3}} - \frac{i \left(x - 2\right)^{\frac{3}{2}}}{64 \sqrt{x - 3}} + \frac{3 i \sqrt{x - 2}}{64 \sqrt{x - 3}} & \text{for}\: \left|{x - 2}\right| > 1 \\\frac{3 \operatorname{asin}{\left(\sqrt{x - 2} \right)}}{64} + \frac{\left(x - 2\right)^{\frac{9}{2}}}{4 \sqrt{3 - x}} - \frac{5 \left(x - 2\right)^{\frac{7}{2}}}{8 \sqrt{3 - x}} + \frac{13 \left(x - 2\right)^{\frac{5}{2}}}{32 \sqrt{3 - x}} + \frac{\left(x - 2\right)^{\frac{3}{2}}}{64 \sqrt{3 - x}} - \frac{3 \sqrt{x - 2}}{64 \sqrt{3 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*I*acosh(sqrt(x - 2))/64 - I*(x - 2)**(9/2)/(4*sqrt(x - 3)) + 5*I*(x - 2)**(7/2)/(8*sqrt(x - 3)) - 13*I*(x - 2)**(5/2)/(32*sqrt(x - 3)) - I*(x - 2)**(3/2)/(64*sqrt(x - 3)) + 3*I*sqrt(x - 2)/(64*sqrt(x - 3)), Abs(x - 2) > 1), (3*asin(sqrt(x - 2))/64 + (x - 2)**(9/2)/(4*sqrt(3 - x)) - 5*(x - 2)**(7/2)/(8*sqrt(3 - x)) + 13*(x - 2)**(5/2)/(32*sqrt(3 - x)) + (x - 2)**(3/2)/(64*sqrt(3 - x)) - 3*sqrt(x - 2)/(64*sqrt(3 - x)), True))","A",0
1161,1,124,0,3.010446," ","integrate((3-x)**(1/2)*(-2+x)**(1/2),x)","\begin{cases} - \frac{i \operatorname{acosh}{\left(\sqrt{x - 2} \right)}}{4} + \frac{i \left(x - 2\right)^{\frac{5}{2}}}{2 \sqrt{x - 3}} - \frac{3 i \left(x - 2\right)^{\frac{3}{2}}}{4 \sqrt{x - 3}} + \frac{i \sqrt{x - 2}}{4 \sqrt{x - 3}} & \text{for}\: \left|{x - 2}\right| > 1 \\\frac{\operatorname{asin}{\left(\sqrt{x - 2} \right)}}{4} - \frac{\left(x - 2\right)^{\frac{5}{2}}}{2 \sqrt{3 - x}} + \frac{3 \left(x - 2\right)^{\frac{3}{2}}}{4 \sqrt{3 - x}} - \frac{\sqrt{x - 2}}{4 \sqrt{3 - x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*acosh(sqrt(x - 2))/4 + I*(x - 2)**(5/2)/(2*sqrt(x - 3)) - 3*I*(x - 2)**(3/2)/(4*sqrt(x - 3)) + I*sqrt(x - 2)/(4*sqrt(x - 3)), Abs(x - 2) > 1), (asin(sqrt(x - 2))/4 - (x - 2)**(5/2)/(2*sqrt(3 - x)) + 3*(x - 2)**(3/2)/(4*sqrt(3 - x)) - sqrt(x - 2)/(4*sqrt(3 - x)), True))","A",0
1162,1,26,0,1.607404," ","integrate(1/(3-x)**(1/2)/(-2+x)**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\sqrt{x - 2} \right)} & \text{for}\: \left|{x - 2}\right| > 1 \\2 \operatorname{asin}{\left(\sqrt{x - 2} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(x - 2)), Abs(x - 2) > 1), (2*asin(sqrt(x - 2)), True))","A",0
1163,1,100,0,2.301531," ","integrate(1/(3-x)**(3/2)/(-2+x)**(3/2),x)","\begin{cases} - \frac{4 i \sqrt{x - 3} \left(x - 2\right)}{\left(x - 2\right)^{\frac{3}{2}} - \sqrt{x - 2}} + \frac{2 i \sqrt{x - 3}}{\left(x - 2\right)^{\frac{3}{2}} - \sqrt{x - 2}} & \text{for}\: \left|{x - 2}\right| > 1 \\- \frac{4 \sqrt{3 - x} \left(x - 2\right)}{\left(x - 2\right)^{\frac{3}{2}} - \sqrt{x - 2}} + \frac{2 \sqrt{3 - x}}{\left(x - 2\right)^{\frac{3}{2}} - \sqrt{x - 2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*I*sqrt(x - 3)*(x - 2)/((x - 2)**(3/2) - sqrt(x - 2)) + 2*I*sqrt(x - 3)/((x - 2)**(3/2) - sqrt(x - 2)), Abs(x - 2) > 1), (-4*sqrt(3 - x)*(x - 2)/((x - 2)**(3/2) - sqrt(x - 2)) + 2*sqrt(3 - x)/((x - 2)**(3/2) - sqrt(x - 2)), True))","A",0
1164,1,282,0,9.848595," ","integrate(1/(3-x)**(5/2)/(-2+x)**(5/2),x)","\begin{cases} - \frac{32 \sqrt{-1 + \frac{1}{x - 2}} \left(x - 2\right)^{3}}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} + \frac{48 \sqrt{-1 + \frac{1}{x - 2}} \left(x - 2\right)^{2}}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} - \frac{12 \sqrt{-1 + \frac{1}{x - 2}} \left(x - 2\right)}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} - \frac{2 \sqrt{-1 + \frac{1}{x - 2}}}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} & \text{for}\: \frac{1}{\left|{x - 2}\right|} > 1 \\- \frac{32 i \sqrt{1 - \frac{1}{x - 2}} \left(x - 2\right)^{3}}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} + \frac{48 i \sqrt{1 - \frac{1}{x - 2}} \left(x - 2\right)^{2}}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} - \frac{12 i \sqrt{1 - \frac{1}{x - 2}} \left(x - 2\right)}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} - \frac{2 i \sqrt{1 - \frac{1}{x - 2}}}{3 x + 3 \left(x - 2\right)^{3} - 6 \left(x - 2\right)^{2} - 6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*sqrt(-1 + 1/(x - 2))*(x - 2)**3/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6) + 48*sqrt(-1 + 1/(x - 2))*(x - 2)**2/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6) - 12*sqrt(-1 + 1/(x - 2))*(x - 2)/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6) - 2*sqrt(-1 + 1/(x - 2))/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6), 1/Abs(x - 2) > 1), (-32*I*sqrt(1 - 1/(x - 2))*(x - 2)**3/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6) + 48*I*sqrt(1 - 1/(x - 2))*(x - 2)**2/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6) - 12*I*sqrt(1 - 1/(x - 2))*(x - 2)/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6) - 2*I*sqrt(1 - 1/(x - 2))/(3*x + 3*(x - 2)**3 - 6*(x - 2)**2 - 6), True))","B",0
1165,1,73,0,1.800457," ","integrate(1/(3-x)**(3/2)/(3+x)**(3/2),x)","\begin{cases} \frac{1}{9 \sqrt{-1 + \frac{6}{x + 3}}} - \frac{1}{3 \sqrt{-1 + \frac{6}{x + 3}} \left(x + 3\right)} & \text{for}\: \frac{6}{\left|{x + 3}\right|} > 1 \\\frac{i \sqrt{1 - \frac{6}{x + 3}} \left(x + 3\right)}{27 - 9 x} - \frac{3 i \sqrt{1 - \frac{6}{x + 3}}}{27 - 9 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/(9*sqrt(-1 + 6/(x + 3))) - 1/(3*sqrt(-1 + 6/(x + 3))*(x + 3)), 6/Abs(x + 3) > 1), (I*sqrt(1 - 6/(x + 3))*(x + 3)/(27 - 9*x) - 3*I*sqrt(1 - 6/(x + 3))/(27 - 9*x), True))","A",0
1166,1,73,0,5.162366," ","integrate(1/(-b*x+3)**(3/2)/(b*x+3)**(3/2),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & \frac{1}{2}, \frac{3}{2}, 2 \\\frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 2 & 0 \end{matrix} \middle| {\frac{9}{b^{2} x^{2}}} \right)}}{18 \pi^{\frac{3}{2}} b} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 &  \\\frac{1}{4}, \frac{3}{4} & - \frac{1}{2}, 0, 1, 0 \end{matrix} \middle| {\frac{9 e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{18 \pi^{\frac{3}{2}} b}"," ",0,"-I*meijerg(((3/4, 5/4, 1), (1/2, 3/2, 2)), ((3/4, 1, 5/4, 3/2, 2), (0,)), 9/(b**2*x**2))/(18*pi**(3/2)*b) + meijerg(((-1/2, 0, 1/4, 1/2, 3/4, 1), ()), ((1/4, 3/4), (-1/2, 0, 1, 0)), 9*exp_polar(-2*I*pi)/(b**2*x**2))/(18*pi**(3/2)*b)","C",0
1167,1,90,0,20.445621," ","integrate(1/(6-2*x)**(3/2)/(3+x)**(3/2),x)","\begin{cases} \frac{\sqrt{2}}{36 \sqrt{-1 + \frac{6}{x + 3}}} - \frac{\sqrt{2}}{12 \sqrt{-1 + \frac{6}{x + 3}} \left(x + 3\right)} & \text{for}\: \frac{6}{\left|{x + 3}\right|} > 1 \\\frac{\sqrt{2} i \sqrt{1 - \frac{6}{x + 3}} \left(x + 3\right)}{108 - 36 x} - \frac{3 \sqrt{2} i \sqrt{1 - \frac{6}{x + 3}}}{108 - 36 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(2)/(36*sqrt(-1 + 6/(x + 3))) - sqrt(2)/(12*sqrt(-1 + 6/(x + 3))*(x + 3)), 6/Abs(x + 3) > 1), (sqrt(2)*I*sqrt(1 - 6/(x + 3))*(x + 3)/(108 - 36*x) - 3*sqrt(2)*I*sqrt(1 - 6/(x + 3))/(108 - 36*x), True))","A",0
1168,1,83,0,31.495539," ","integrate(1/(-2*b*x+6)**(3/2)/(b*x+3)**(3/2),x)","- \frac{\sqrt{2} i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4}, 1 & \frac{1}{2}, \frac{3}{2}, 2 \\\frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, 2 & 0 \end{matrix} \middle| {\frac{9}{b^{2} x^{2}}} \right)}}{72 \pi^{\frac{3}{2}} b} + \frac{\sqrt{2} {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1 &  \\\frac{1}{4}, \frac{3}{4} & - \frac{1}{2}, 0, 1, 0 \end{matrix} \middle| {\frac{9 e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{72 \pi^{\frac{3}{2}} b}"," ",0,"-sqrt(2)*I*meijerg(((3/4, 5/4, 1), (1/2, 3/2, 2)), ((3/4, 1, 5/4, 3/2, 2), (0,)), 9/(b**2*x**2))/(72*pi**(3/2)*b) + sqrt(2)*meijerg(((-1/2, 0, 1/4, 1/2, 3/4, 1), ()), ((1/4, 3/4), (-1/2, 0, 1, 0)), 9*exp_polar(-2*I*pi)/(b**2*x**2))/(72*pi**(3/2)*b)","C",0
1169,1,88,0,4.766245," ","integrate(1/(b*x+a)**(1/2)/(b*d*x-a*d)**(1/2),x)","\frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{a^{2}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b \sqrt{d}} - \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{a^{2} e^{2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b \sqrt{d}}"," ",0,"meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), a**2/(b**2*x**2))/(4*pi**(3/2)*b*sqrt(d)) - I*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), a**2*exp_polar(2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b*sqrt(d))","C",0
1170,0,0,0,0.000000," ","integrate(1/(-3*e*x+6)**(1/4)/(e*x+2)**(3/4),x)","\frac{3^{\frac{3}{4}} \int \frac{1}{\sqrt[4]{- e x + 2} \left(e x + 2\right)^{\frac{3}{4}}}\, dx}{3}"," ",0,"3**(3/4)*Integral(1/((-e*x + 2)**(1/4)*(e*x + 2)**(3/4)), x)/3","F",0
1171,0,0,0,0.000000," ","integrate((a-I*a*x)**(7/4)/(a+I*a*x)**(1/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}{\sqrt[4]{i a \left(x - i\right)}}\, dx"," ",0,"Integral((-I*a*(x + I))**(7/4)/(I*a*(x - I))**(1/4), x)","F",0
1172,0,0,0,0.000000," ","integrate((a-I*a*x)**(3/4)/(a+I*a*x)**(1/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}{\sqrt[4]{i a \left(x - i\right)}}\, dx"," ",0,"Integral((-I*a*(x + I))**(3/4)/(I*a*(x - I))**(1/4), x)","F",0
1173,1,102,0,3.792624," ","integrate(1/(a-I*a*x)**(1/4)/(a+I*a*x)**(1/4),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{8}, \frac{5}{8}, 1 & \frac{1}{4}, \frac{1}{2}, \frac{3}{4} \\- \frac{1}{4}, \frac{1}{8}, \frac{1}{4}, \frac{5}{8}, \frac{3}{4} & 0 \end{matrix} \middle| {\frac{e^{- 3 i \pi}}{x^{2}}} \right)} e^{\frac{i \pi}{4}}}{4 \pi \sqrt{a} \Gamma\left(\frac{1}{4}\right)} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{3}{8}, 0, \frac{1}{8}, \frac{1}{2}, 1 &  \\- \frac{3}{8}, \frac{1}{8} & - \frac{1}{2}, - \frac{1}{4}, 0, 0 \end{matrix} \middle| {\frac{e^{- i \pi}}{x^{2}}} \right)}}{4 \pi \sqrt{a} \Gamma\left(\frac{1}{4}\right)}"," ",0,"-I*meijerg(((1/8, 5/8, 1), (1/4, 1/2, 3/4)), ((-1/4, 1/8, 1/4, 5/8, 3/4), (0,)), exp_polar(-3*I*pi)/x**2)*exp(I*pi/4)/(4*pi*sqrt(a)*gamma(1/4)) + I*meijerg(((-1/2, -3/8, 0, 1/8, 1/2, 1), ()), ((-3/8, 1/8), (-1/2, -1/4, 0, 0)), exp_polar(-I*pi)/x**2)/(4*pi*sqrt(a)*gamma(1/4))","A",0
1174,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(5/4)/(a+I*a*x)**(1/4),x)","\int \frac{1}{\sqrt[4]{i a \left(x - i\right)} \left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(1/4)*(-I*a*(x + I))**(5/4)), x)","F",0
1175,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(9/4)/(a+I*a*x)**(1/4),x)","\int \frac{1}{\sqrt[4]{i a \left(x - i\right)} \left(- i a \left(x + i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(1/4)*(-I*a*(x + I))**(9/4)), x)","F",0
1176,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(13/4)/(a+I*a*x)**(1/4),x)","\int \frac{1}{\sqrt[4]{i a \left(x - i\right)} \left(- i a \left(x + i\right)\right)^{\frac{13}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(1/4)*(-I*a*(x + I))**(13/4)), x)","F",0
1177,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(17/4)/(a+I*a*x)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1178,0,0,0,0.000000," ","integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(1/4),x)","\int \frac{\sqrt[4]{- i a \left(x + i\right)}}{\sqrt[4]{i a \left(x - i\right)}}\, dx"," ",0,"Integral((-I*a*(x + I))**(1/4)/(I*a*(x - I))**(1/4), x)","F",0
1179,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(3/4)/(a+I*a*x)**(1/4),x)","\int \frac{1}{\sqrt[4]{i a \left(x - i\right)} \left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(1/4)*(-I*a*(x + I))**(3/4)), x)","F",0
1180,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(1/4),x)","\int \frac{1}{\sqrt[4]{i a \left(x - i\right)} \left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(1/4)*(-I*a*(x + I))**(7/4)), x)","F",0
1181,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(11/4)/(a+I*a*x)**(1/4),x)","\int \frac{1}{\sqrt[4]{i a \left(x - i\right)} \left(- i a \left(x + i\right)\right)^{\frac{11}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(1/4)*(-I*a*(x + I))**(11/4)), x)","F",0
1182,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(15/4)/(a+I*a*x)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1183,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(19/4)/(a+I*a*x)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1184,0,0,0,0.000000," ","integrate((a-I*a*x)**(3/4)/(a+I*a*x)**(3/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(3/4)/(I*a*(x - I))**(3/4), x)","F",0
1185,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(1/4)/(a+I*a*x)**(3/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}} \sqrt[4]{- i a \left(x + i\right)}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(3/4)*(-I*a*(x + I))**(1/4)), x)","F",0
1186,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(5/4)/(a+I*a*x)**(3/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}} \left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(3/4)*(-I*a*(x + I))**(5/4)), x)","F",0
1187,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(9/4)/(a+I*a*x)**(3/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}} \left(- i a \left(x + i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(3/4)*(-I*a*(x + I))**(9/4)), x)","F",0
1188,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(13/4)/(a+I*a*x)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1189,0,0,0,0.000000," ","integrate((a-I*a*x)**(5/4)/(a+I*a*x)**(3/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(5/4)/(I*a*(x - I))**(3/4), x)","F",0
1190,0,0,0,0.000000," ","integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(3/4),x)","\int \frac{\sqrt[4]{- i a \left(x + i\right)}}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(1/4)/(I*a*(x - I))**(3/4), x)","F",0
1191,1,100,0,5.337528," ","integrate(1/(a-I*a*x)**(3/4)/(a+I*a*x)**(3/4),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{3}{8}, \frac{7}{8}, 1 & \frac{1}{2}, \frac{3}{4}, \frac{5}{4} \\\frac{1}{4}, \frac{3}{8}, \frac{3}{4}, \frac{7}{8}, \frac{5}{4} & 0 \end{matrix} \middle| {\frac{e^{- 3 i \pi}}{x^{2}}} \right)} e^{\frac{3 i \pi}{4}}}{4 \pi a^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{8}, 0, \frac{3}{8}, \frac{1}{2}, 1 &  \\- \frac{1}{8}, \frac{3}{8} & - \frac{1}{2}, 0, \frac{1}{4}, 0 \end{matrix} \middle| {\frac{e^{- i \pi}}{x^{2}}} \right)}}{4 \pi a^{\frac{3}{2}} \Gamma\left(\frac{3}{4}\right)}"," ",0,"-I*meijerg(((3/8, 7/8, 1), (1/2, 3/4, 5/4)), ((1/4, 3/8, 3/4, 7/8, 5/4), (0,)), exp_polar(-3*I*pi)/x**2)*exp(3*I*pi/4)/(4*pi*a**(3/2)*gamma(3/4)) + I*meijerg(((-1/2, -1/8, 0, 3/8, 1/2, 1), ()), ((-1/8, 3/8), (-1/2, 0, 1/4, 0)), exp_polar(-I*pi)/x**2)/(4*pi*a**(3/2)*gamma(3/4))","A",0
1192,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(3/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}} \left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(3/4)*(-I*a*(x + I))**(7/4)), x)","F",0
1193,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(11/4)/(a+I*a*x)**(3/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{3}{4}} \left(- i a \left(x + i\right)\right)^{\frac{11}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(3/4)*(-I*a*(x + I))**(11/4)), x)","F",0
1194,0,0,0,0.000000," ","integrate((a-I*a*x)**(7/4)/(a+I*a*x)**(7/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(7/4)/(I*a*(x - I))**(7/4), x)","F",0
1195,0,0,0,0.000000," ","integrate((a-I*a*x)**(3/4)/(a+I*a*x)**(7/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(3/4)/(I*a*(x - I))**(7/4), x)","F",0
1196,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(1/4)/(a+I*a*x)**(7/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}} \sqrt[4]{- i a \left(x + i\right)}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(7/4)*(-I*a*(x + I))**(1/4)), x)","F",0
1197,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(5/4)/(a+I*a*x)**(7/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}} \left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(7/4)*(-I*a*(x + I))**(5/4)), x)","F",0
1198,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(9/4)/(a+I*a*x)**(7/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}} \left(- i a \left(x + i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(7/4)*(-I*a*(x + I))**(9/4)), x)","F",0
1199,0,0,0,0.000000," ","integrate((a-I*a*x)**(9/4)/(a+I*a*x)**(7/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{9}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(9/4)/(I*a*(x - I))**(7/4), x)","F",0
1200,0,0,0,0.000000," ","integrate((a-I*a*x)**(5/4)/(a+I*a*x)**(7/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(5/4)/(I*a*(x - I))**(7/4), x)","F",0
1201,0,0,0,0.000000," ","integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(7/4),x)","\int \frac{\sqrt[4]{- i a \left(x + i\right)}}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(1/4)/(I*a*(x - I))**(7/4), x)","F",0
1202,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(3/4)/(a+I*a*x)**(7/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{7}{4}} \left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(7/4)*(-I*a*(x + I))**(3/4)), x)","F",0
1203,1,95,0,36.699056," ","integrate(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(7/4),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{7}{8}, \frac{11}{8}, 1 & \frac{1}{2}, \frac{7}{4}, \frac{9}{4} \\\frac{7}{8}, \frac{5}{4}, \frac{11}{8}, \frac{7}{4}, \frac{9}{4} & 0 \end{matrix} \middle| {\frac{e^{- 3 i \pi}}{x^{2}}} \right)} e^{- \frac{i \pi}{4}}}{4 \pi a^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{3}{8}, \frac{1}{2}, \frac{7}{8}, 1 &  \\\frac{3}{8}, \frac{7}{8} & - \frac{1}{2}, 0, \frac{5}{4}, 0 \end{matrix} \middle| {\frac{e^{- i \pi}}{x^{2}}} \right)}}{4 \pi a^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right)}"," ",0,"-I*meijerg(((7/8, 11/8, 1), (1/2, 7/4, 9/4)), ((7/8, 5/4, 11/8, 7/4, 9/4), (0,)), exp_polar(-3*I*pi)/x**2)*exp(-I*pi/4)/(4*pi*a**(7/2)*gamma(7/4)) + I*meijerg(((-1/2, 0, 3/8, 1/2, 7/8, 1), ()), ((3/8, 7/8), (-1/2, 0, 5/4, 0)), exp_polar(-I*pi)/x**2)/(4*pi*a**(7/2)*gamma(7/4))","A",0
1204,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(11/4)/(a+I*a*x)**(7/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1205,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(15/4)/(a+I*a*x)**(7/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1206,0,0,0,0.000000," ","integrate((a-I*a*x)**(7/4)/(a+I*a*x)**(5/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(7/4)/(I*a*(x - I))**(5/4), x)","F",0
1207,0,0,0,0.000000," ","integrate((a-I*a*x)**(3/4)/(a+I*a*x)**(5/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(3/4)/(I*a*(x - I))**(5/4), x)","F",0
1208,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(1/4)/(a+I*a*x)**(5/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}} \sqrt[4]{- i a \left(x + i\right)}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(5/4)*(-I*a*(x + I))**(1/4)), x)","F",0
1209,1,97,0,11.909551," ","integrate(1/(a-I*a*x)**(5/4)/(a+I*a*x)**(5/4),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{5}{8}, \frac{9}{8}, 1 & \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \\\frac{5}{8}, \frac{3}{4}, \frac{9}{8}, \frac{5}{4}, \frac{7}{4} & 0 \end{matrix} \middle| {\frac{e^{- 3 i \pi}}{x^{2}}} \right)} e^{- \frac{3 i \pi}{4}}}{4 \pi a^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{8}, \frac{1}{2}, \frac{5}{8}, 1 &  \\\frac{1}{8}, \frac{5}{8} & - \frac{1}{2}, 0, \frac{3}{4}, 0 \end{matrix} \middle| {\frac{e^{- i \pi}}{x^{2}}} \right)}}{4 \pi a^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right)}"," ",0,"-I*meijerg(((5/8, 9/8, 1), (1/2, 5/4, 7/4)), ((5/8, 3/4, 9/8, 5/4, 7/4), (0,)), exp_polar(-3*I*pi)/x**2)*exp(-3*I*pi/4)/(4*pi*a**(5/2)*gamma(5/4)) + I*meijerg(((-1/2, 0, 1/8, 1/2, 5/8, 1), ()), ((1/8, 5/8), (-1/2, 0, 3/4, 0)), exp_polar(-I*pi)/x**2)/(4*pi*a**(5/2)*gamma(5/4))","A",0
1210,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(9/4)/(a+I*a*x)**(5/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}} \left(- i a \left(x + i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(5/4)*(-I*a*(x + I))**(9/4)), x)","F",0
1211,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(13/4)/(a+I*a*x)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1212,0,0,0,0.000000," ","integrate((a-I*a*x)**(5/4)/(a+I*a*x)**(5/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(5/4)/(I*a*(x - I))**(5/4), x)","F",0
1213,0,0,0,0.000000," ","integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(5/4),x)","\int \frac{\sqrt[4]{- i a \left(x + i\right)}}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(1/4)/(I*a*(x - I))**(5/4), x)","F",0
1214,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(3/4)/(a+I*a*x)**(5/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}} \left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(5/4)*(-I*a*(x + I))**(3/4)), x)","F",0
1215,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(5/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}} \left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(5/4)*(-I*a*(x + I))**(7/4)), x)","F",0
1216,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(11/4)/(a+I*a*x)**(5/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{5}{4}} \left(- i a \left(x + i\right)\right)^{\frac{11}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(5/4)*(-I*a*(x + I))**(11/4)), x)","F",0
1217,0,0,0,0.000000," ","integrate((a-I*a*x)**(7/4)/(a+I*a*x)**(9/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(7/4)/(I*a*(x - I))**(9/4), x)","F",0
1218,0,0,0,0.000000," ","integrate((a-I*a*x)**(3/4)/(a+I*a*x)**(9/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(3/4)/(I*a*(x - I))**(9/4), x)","F",0
1219,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(1/4)/(a+I*a*x)**(9/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}} \sqrt[4]{- i a \left(x + i\right)}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(9/4)*(-I*a*(x + I))**(1/4)), x)","F",0
1220,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(5/4)/(a+I*a*x)**(9/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}} \left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(9/4)*(-I*a*(x + I))**(5/4)), x)","F",0
1221,1,95,0,132.493384," ","integrate(1/(a-I*a*x)**(9/4)/(a+I*a*x)**(9/4),x)","- \frac{i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{9}{8}, \frac{13}{8}, 1 & \frac{1}{2}, \frac{9}{4}, \frac{11}{4} \\\frac{9}{8}, \frac{13}{8}, \frac{7}{4}, \frac{9}{4}, \frac{11}{4} & 0 \end{matrix} \middle| {\frac{e^{- 3 i \pi}}{x^{2}}} \right)} e^{\frac{i \pi}{4}}}{4 \pi a^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right)} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, \frac{5}{8}, \frac{9}{8}, 1 &  \\\frac{5}{8}, \frac{9}{8} & - \frac{1}{2}, 0, \frac{7}{4}, 0 \end{matrix} \middle| {\frac{e^{- i \pi}}{x^{2}}} \right)}}{4 \pi a^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right)}"," ",0,"-I*meijerg(((9/8, 13/8, 1), (1/2, 9/4, 11/4)), ((9/8, 13/8, 7/4, 9/4, 11/4), (0,)), exp_polar(-3*I*pi)/x**2)*exp(I*pi/4)/(4*pi*a**(9/2)*gamma(9/4)) + I*meijerg(((-1/2, 0, 1/2, 5/8, 9/8, 1), ()), ((5/8, 9/8), (-1/2, 0, 7/4, 0)), exp_polar(-I*pi)/x**2)/(4*pi*a**(9/2)*gamma(9/4))","A",0
1222,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(13/4)/(a+I*a*x)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1223,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(17/4)/(a+I*a*x)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1224,0,0,0,0.000000," ","integrate((a-I*a*x)**(5/4)/(a+I*a*x)**(9/4),x)","\int \frac{\left(- i a \left(x + i\right)\right)^{\frac{5}{4}}}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(5/4)/(I*a*(x - I))**(9/4), x)","F",0
1225,0,0,0,0.000000," ","integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(9/4),x)","\int \frac{\sqrt[4]{- i a \left(x + i\right)}}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((-I*a*(x + I))**(1/4)/(I*a*(x - I))**(9/4), x)","F",0
1226,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(3/4)/(a+I*a*x)**(9/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}} \left(- i a \left(x + i\right)\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(9/4)*(-I*a*(x + I))**(3/4)), x)","F",0
1227,0,0,0,0.000000," ","integrate(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(9/4),x)","\int \frac{1}{\left(i a \left(x - i\right)\right)^{\frac{9}{4}} \left(- i a \left(x + i\right)\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/((I*a*(x - I))**(9/4)*(-I*a*(x + I))**(7/4)), x)","F",0
1228,-1,0,0,0.000000," ","integrate(1/(a-I*a*x)**(11/4)/(a+I*a*x)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1229,1,819,0,1.295141," ","integrate((b*x+a)**2*(-b*c*x+a*c)**n,x)","\begin{cases} a^{2} x \left(a c\right)^{n} & \text{for}\: b = 0 \\- \frac{a^{2} \log{\left(- \frac{a}{b} + x \right)}}{a^{2} b c^{3} - 2 a b^{2} c^{3} x + b^{3} c^{3} x^{2}} - \frac{2 a^{2}}{a^{2} b c^{3} - 2 a b^{2} c^{3} x + b^{3} c^{3} x^{2}} + \frac{2 a b x \log{\left(- \frac{a}{b} + x \right)}}{a^{2} b c^{3} - 2 a b^{2} c^{3} x + b^{3} c^{3} x^{2}} + \frac{4 a b x}{a^{2} b c^{3} - 2 a b^{2} c^{3} x + b^{3} c^{3} x^{2}} - \frac{b^{2} x^{2} \log{\left(- \frac{a}{b} + x \right)}}{a^{2} b c^{3} - 2 a b^{2} c^{3} x + b^{3} c^{3} x^{2}} & \text{for}\: n = -3 \\- \frac{4 a^{2} \log{\left(- \frac{a}{b} + x \right)}}{- a b c^{2} + b^{2} c^{2} x} - \frac{5 a^{2}}{- a b c^{2} + b^{2} c^{2} x} + \frac{4 a b x \log{\left(- \frac{a}{b} + x \right)}}{- a b c^{2} + b^{2} c^{2} x} + \frac{b^{2} x^{2}}{- a b c^{2} + b^{2} c^{2} x} & \text{for}\: n = -2 \\- \frac{4 a^{2} \log{\left(- \frac{a}{b} + x \right)}}{b c} - \frac{3 a x}{c} - \frac{b x^{2}}{2 c} & \text{for}\: n = -1 \\- \frac{a^{3} n^{2} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} - \frac{7 a^{3} n \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} - \frac{14 a^{3} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} - \frac{a^{2} b n^{2} x \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} - \frac{3 a^{2} b n x \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{6 a^{2} b x \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{a b^{2} n^{2} x^{2} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{7 a b^{2} n x^{2} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{6 a b^{2} x^{2} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{b^{3} n^{2} x^{3} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{3 b^{3} n x^{3} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} + \frac{2 b^{3} x^{3} \left(a c - b c x\right)^{n}}{b n^{3} + 6 b n^{2} + 11 b n + 6 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*(a*c)**n, Eq(b, 0)), (-a**2*log(-a/b + x)/(a**2*b*c**3 - 2*a*b**2*c**3*x + b**3*c**3*x**2) - 2*a**2/(a**2*b*c**3 - 2*a*b**2*c**3*x + b**3*c**3*x**2) + 2*a*b*x*log(-a/b + x)/(a**2*b*c**3 - 2*a*b**2*c**3*x + b**3*c**3*x**2) + 4*a*b*x/(a**2*b*c**3 - 2*a*b**2*c**3*x + b**3*c**3*x**2) - b**2*x**2*log(-a/b + x)/(a**2*b*c**3 - 2*a*b**2*c**3*x + b**3*c**3*x**2), Eq(n, -3)), (-4*a**2*log(-a/b + x)/(-a*b*c**2 + b**2*c**2*x) - 5*a**2/(-a*b*c**2 + b**2*c**2*x) + 4*a*b*x*log(-a/b + x)/(-a*b*c**2 + b**2*c**2*x) + b**2*x**2/(-a*b*c**2 + b**2*c**2*x), Eq(n, -2)), (-4*a**2*log(-a/b + x)/(b*c) - 3*a*x/c - b*x**2/(2*c), Eq(n, -1)), (-a**3*n**2*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) - 7*a**3*n*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) - 14*a**3*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) - a**2*b*n**2*x*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) - 3*a**2*b*n*x*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + 6*a**2*b*x*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + a*b**2*n**2*x**2*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + 7*a*b**2*n*x**2*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + 6*a*b**2*x**2*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + b**3*n**2*x**3*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + 3*b**3*n*x**3*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b) + 2*b**3*x**3*(a*c - b*c*x)**n/(b*n**3 + 6*b*n**2 + 11*b*n + 6*b), True))","A",0
1230,1,245,0,0.699383," ","integrate((b*x+a)*(-b*c*x+a*c)**n,x)","\begin{cases} a x \left(a c\right)^{n} & \text{for}\: b = 0 \\- \frac{a \log{\left(- \frac{a}{b} + x \right)}}{- a b c^{2} + b^{2} c^{2} x} - \frac{2 a}{- a b c^{2} + b^{2} c^{2} x} + \frac{b x \log{\left(- \frac{a}{b} + x \right)}}{- a b c^{2} + b^{2} c^{2} x} & \text{for}\: n = -2 \\- \frac{2 a \log{\left(- \frac{a}{b} + x \right)}}{b c} - \frac{x}{c} & \text{for}\: n = -1 \\- \frac{a^{2} n \left(a c - b c x\right)^{n}}{b n^{2} + 3 b n + 2 b} - \frac{3 a^{2} \left(a c - b c x\right)^{n}}{b n^{2} + 3 b n + 2 b} + \frac{2 a b x \left(a c - b c x\right)^{n}}{b n^{2} + 3 b n + 2 b} + \frac{b^{2} n x^{2} \left(a c - b c x\right)^{n}}{b n^{2} + 3 b n + 2 b} + \frac{b^{2} x^{2} \left(a c - b c x\right)^{n}}{b n^{2} + 3 b n + 2 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*(a*c)**n, Eq(b, 0)), (-a*log(-a/b + x)/(-a*b*c**2 + b**2*c**2*x) - 2*a/(-a*b*c**2 + b**2*c**2*x) + b*x*log(-a/b + x)/(-a*b*c**2 + b**2*c**2*x), Eq(n, -2)), (-2*a*log(-a/b + x)/(b*c) - x/c, Eq(n, -1)), (-a**2*n*(a*c - b*c*x)**n/(b*n**2 + 3*b*n + 2*b) - 3*a**2*(a*c - b*c*x)**n/(b*n**2 + 3*b*n + 2*b) + 2*a*b*x*(a*c - b*c*x)**n/(b*n**2 + 3*b*n + 2*b) + b**2*n*x**2*(a*c - b*c*x)**n/(b*n**2 + 3*b*n + 2*b) + b**2*x**2*(a*c - b*c*x)**n/(b*n**2 + 3*b*n + 2*b), True))","A",0
1231,0,0,0,0.000000," ","integrate((-b*c*x+a*c)**n/(b*x+a),x)","\int \frac{\left(- c \left(- a + b x\right)\right)^{n}}{a + b x}\, dx"," ",0,"Integral((-c*(-a + b*x))**n/(a + b*x), x)","F",0
1232,0,0,0,0.000000," ","integrate((-b*c*x+a*c)**n/(b*x+a)**2,x)","\int \frac{\left(- c \left(- a + b x\right)\right)^{n}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((-c*(-a + b*x))**n/(a + b*x)**2, x)","F",0
1233,1,124,0,4.377980," ","integrate((a*x+a)**m*(-c*x+c)**m,x)","\frac{a^{m} c^{m} {G_{6, 6}^{5, 3}\left(\begin{matrix} - \frac{m}{2}, \frac{1}{2} - \frac{m}{2}, 1 & \frac{1}{2}, - m, \frac{1}{2} - m \\- m - \frac{1}{2}, - m, - \frac{m}{2}, \frac{1}{2} - m, \frac{1}{2} - \frac{m}{2} & 0 \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{2}}} \right)} e^{- i \pi m}}{4 \pi \Gamma\left(- m\right)} - \frac{a^{m} c^{m} {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, - \frac{m}{2} - \frac{1}{2}, - \frac{m}{2}, 1 &  \\- \frac{m}{2} - \frac{1}{2}, - \frac{m}{2} & - \frac{1}{2}, 0, - m - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{1}{x^{2}}} \right)}}{4 \pi \Gamma\left(- m\right)}"," ",0,"a**m*c**m*meijerg(((-m/2, 1/2 - m/2, 1), (1/2, -m, 1/2 - m)), ((-m - 1/2, -m, -m/2, 1/2 - m, 1/2 - m/2), (0,)), exp_polar(-2*I*pi)/x**2)*exp(-I*pi*m)/(4*pi*gamma(-m)) - a**m*c**m*meijerg(((-1/2, 0, 1/2, -m/2 - 1/2, -m/2, 1), ()), ((-m/2 - 1/2, -m/2), (-1/2, 0, -m - 1/2, 0)), x**(-2))/(4*pi*gamma(-m))","C",0
1234,1,146,0,5.864703," ","integrate((b*x+a)**m*(-b*c*x+a*c)**m,x)","\frac{a a^{2 m} c^{m} {G_{6, 6}^{5, 3}\left(\begin{matrix} - \frac{m}{2}, \frac{1}{2} - \frac{m}{2}, 1 & \frac{1}{2}, - m, \frac{1}{2} - m \\- m - \frac{1}{2}, - m, - \frac{m}{2}, \frac{1}{2} - m, \frac{1}{2} - \frac{m}{2} & 0 \end{matrix} \middle| {\frac{a^{2} e^{- 2 i \pi}}{b^{2} x^{2}}} \right)} e^{- i \pi m}}{4 \pi b \Gamma\left(- m\right)} - \frac{a a^{2 m} c^{m} {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, 0, \frac{1}{2}, - \frac{m}{2} - \frac{1}{2}, - \frac{m}{2}, 1 &  \\- \frac{m}{2} - \frac{1}{2}, - \frac{m}{2} & - \frac{1}{2}, 0, - m - \frac{1}{2}, 0 \end{matrix} \middle| {\frac{a^{2}}{b^{2} x^{2}}} \right)}}{4 \pi b \Gamma\left(- m\right)}"," ",0,"a*a**(2*m)*c**m*meijerg(((-m/2, 1/2 - m/2, 1), (1/2, -m, 1/2 - m)), ((-m - 1/2, -m, -m/2, 1/2 - m, 1/2 - m/2), (0,)), a**2*exp_polar(-2*I*pi)/(b**2*x**2))*exp(-I*pi*m)/(4*pi*b*gamma(-m)) - a*a**(2*m)*c**m*meijerg(((-1/2, 0, 1/2, -m/2 - 1/2, -m/2, 1), ()), ((-m/2 - 1/2, -m/2), (-1/2, 0, -m - 1/2, 0)), a**2/(b**2*x**2))/(4*pi*b*gamma(-m))","C",0
1235,1,42,0,4.341878," ","integrate((3-6*x)**m*(4*x+2)**m,x)","\frac{24^{m} \left(x + \frac{1}{2}\right) \left(x + \frac{1}{2}\right)^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - m, m + 1 \\ m + 2 \end{matrix}\middle| {\left(x + \frac{1}{2}\right) e^{2 i \pi}} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"24**m*(x + 1/2)*(x + 1/2)**m*gamma(m + 1)*hyper((-m, m + 1), (m + 2,), (x + 1/2)*exp_polar(2*I*pi))/gamma(m + 2)","C",0
1236,1,100,0,0.082753," ","integrate((b*x+a)**4*(d*x+c),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
1237,1,73,0,0.078179," ","integrate((b*x+a)**3*(d*x+c),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
1238,1,49,0,0.071398," ","integrate((b*x+a)**2*(d*x+c),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
1239,1,26,0,0.060132," ","integrate((b*x+a)*(d*x+c),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
1240,1,8,0,0.055127," ","integrate(d*x+c,x)","c x + \frac{d x^{2}}{2}"," ",0,"c*x + d*x**2/2","A",0
1241,1,20,0,0.149554," ","integrate((d*x+c)/(b*x+a),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
1242,1,27,0,0.186933," ","integrate((d*x+c)/(b*x+a)**2,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
1243,1,39,0,0.259557," ","integrate((d*x+c)/(b*x+a)**3,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
1244,1,53,0,0.338310," ","integrate((d*x+c)/(b*x+a)**4,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
1245,1,65,0,0.427746," ","integrate((d*x+c)/(b*x+a)**5,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
1246,1,168,0,0.096592," ","integrate((b*x+a)**4*(d*x+c)**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
1247,1,133,0,0.090567," ","integrate((b*x+a)**3*(d*x+c)**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
1248,1,87,0,0.079920," ","integrate((b*x+a)**2*(d*x+c)**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
1249,1,49,0,0.070620," ","integrate((b*x+a)*(d*x+c)**2,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
1250,1,19,0,0.061003," ","integrate((d*x+c)**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
1251,1,44,0,0.224093," ","integrate((d*x+c)**2/(b*x+a),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
1252,1,60,0,0.337116," ","integrate((d*x+c)**2/(b*x+a)**2,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
1253,1,80,0,0.453552," ","integrate((d*x+c)**2/(b*x+a)**3,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
1254,1,88,0,0.597450," ","integrate((d*x+c)**2/(b*x+a)**4,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
1255,1,104,0,0.763722," ","integrate((d*x+c)**2/(b*x+a)**5,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
1256,1,116,0,0.955920," ","integrate((d*x+c)**2/(b*x+a)**6,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
1257,1,128,0,1.158661," ","integrate((d*x+c)**2/(b*x+a)**7,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
1258,1,308,0,0.116407," ","integrate((b*x+a)**5*(d*x+c)**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
1259,1,243,0,0.106173," ","integrate((b*x+a)**4*(d*x+c)**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
1260,1,190,0,0.096768," ","integrate((b*x+a)**3*(d*x+c)**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
1261,1,133,0,0.087314," ","integrate((b*x+a)**2*(d*x+c)**3,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
1262,1,73,0,0.077194," ","integrate((b*x+a)*(d*x+c)**3,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
1263,1,32,0,0.064818," ","integrate((d*x+c)**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
1264,1,83,0,0.303479," ","integrate((d*x+c)**3/(b*x+a),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
1265,1,102,0,0.502914," ","integrate((d*x+c)**3/(b*x+a)**2,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
1266,1,128,0,0.820971," ","integrate((d*x+c)**3/(b*x+a)**3,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
1267,1,148,0,1.126215," ","integrate((d*x+c)**3/(b*x+a)**4,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
1268,1,155,0,1.496882," ","integrate((d*x+c)**3/(b*x+a)**5,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
1269,1,172,0,1.961057," ","integrate((d*x+c)**3/(b*x+a)**6,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
1270,1,184,0,2.536243," ","integrate((d*x+c)**3/(b*x+a)**7,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
1271,1,196,0,3.122750," ","integrate((d*x+c)**3/(b*x+a)**8,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
1272,1,207,0,3.953721," ","integrate((d*x+c)**3/(b*x+a)**9,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
1273,1,1163,0,0.231741," ","integrate((b*x+a)**9*(d*x+c)**7,x)","a^{9} c^{7} x + \frac{b^{9} d^{7} x^{17}}{17} + x^{16} \left(\frac{9 a b^{8} d^{7}}{16} + \frac{7 b^{9} c d^{6}}{16}\right) + x^{15} \left(\frac{12 a^{2} b^{7} d^{7}}{5} + \frac{21 a b^{8} c d^{6}}{5} + \frac{7 b^{9} c^{2} d^{5}}{5}\right) + x^{14} \left(6 a^{3} b^{6} d^{7} + 18 a^{2} b^{7} c d^{6} + \frac{27 a b^{8} c^{2} d^{5}}{2} + \frac{5 b^{9} c^{3} d^{4}}{2}\right) + x^{13} \left(\frac{126 a^{4} b^{5} d^{7}}{13} + \frac{588 a^{3} b^{6} c d^{6}}{13} + \frac{756 a^{2} b^{7} c^{2} d^{5}}{13} + \frac{315 a b^{8} c^{3} d^{4}}{13} + \frac{35 b^{9} c^{4} d^{3}}{13}\right) + x^{12} \left(\frac{21 a^{5} b^{4} d^{7}}{2} + \frac{147 a^{4} b^{5} c d^{6}}{2} + 147 a^{3} b^{6} c^{2} d^{5} + 105 a^{2} b^{7} c^{3} d^{4} + \frac{105 a b^{8} c^{4} d^{3}}{4} + \frac{7 b^{9} c^{5} d^{2}}{4}\right) + x^{11} \left(\frac{84 a^{6} b^{3} d^{7}}{11} + \frac{882 a^{5} b^{4} c d^{6}}{11} + \frac{2646 a^{4} b^{5} c^{2} d^{5}}{11} + \frac{2940 a^{3} b^{6} c^{3} d^{4}}{11} + \frac{1260 a^{2} b^{7} c^{4} d^{3}}{11} + \frac{189 a b^{8} c^{5} d^{2}}{11} + \frac{7 b^{9} c^{6} d}{11}\right) + x^{10} \left(\frac{18 a^{7} b^{2} d^{7}}{5} + \frac{294 a^{6} b^{3} c d^{6}}{5} + \frac{1323 a^{5} b^{4} c^{2} d^{5}}{5} + 441 a^{4} b^{5} c^{3} d^{4} + 294 a^{3} b^{6} c^{4} d^{3} + \frac{378 a^{2} b^{7} c^{5} d^{2}}{5} + \frac{63 a b^{8} c^{6} d}{10} + \frac{b^{9} c^{7}}{10}\right) + x^{9} \left(a^{8} b d^{7} + 28 a^{7} b^{2} c d^{6} + 196 a^{6} b^{3} c^{2} d^{5} + 490 a^{5} b^{4} c^{3} d^{4} + 490 a^{4} b^{5} c^{4} d^{3} + 196 a^{3} b^{6} c^{5} d^{2} + 28 a^{2} b^{7} c^{6} d + a b^{8} c^{7}\right) + x^{8} \left(\frac{a^{9} d^{7}}{8} + \frac{63 a^{8} b c d^{6}}{8} + \frac{189 a^{7} b^{2} c^{2} d^{5}}{2} + \frac{735 a^{6} b^{3} c^{3} d^{4}}{2} + \frac{2205 a^{5} b^{4} c^{4} d^{3}}{4} + \frac{1323 a^{4} b^{5} c^{5} d^{2}}{4} + \frac{147 a^{3} b^{6} c^{6} d}{2} + \frac{9 a^{2} b^{7} c^{7}}{2}\right) + x^{7} \left(a^{9} c d^{6} + 27 a^{8} b c^{2} d^{5} + 180 a^{7} b^{2} c^{3} d^{4} + 420 a^{6} b^{3} c^{4} d^{3} + 378 a^{5} b^{4} c^{5} d^{2} + 126 a^{4} b^{5} c^{6} d + 12 a^{3} b^{6} c^{7}\right) + x^{6} \left(\frac{7 a^{9} c^{2} d^{5}}{2} + \frac{105 a^{8} b c^{3} d^{4}}{2} + 210 a^{7} b^{2} c^{4} d^{3} + 294 a^{6} b^{3} c^{5} d^{2} + 147 a^{5} b^{4} c^{6} d + 21 a^{4} b^{5} c^{7}\right) + x^{5} \left(7 a^{9} c^{3} d^{4} + 63 a^{8} b c^{4} d^{3} + \frac{756 a^{7} b^{2} c^{5} d^{2}}{5} + \frac{588 a^{6} b^{3} c^{6} d}{5} + \frac{126 a^{5} b^{4} c^{7}}{5}\right) + x^{4} \left(\frac{35 a^{9} c^{4} d^{3}}{4} + \frac{189 a^{8} b c^{5} d^{2}}{4} + 63 a^{7} b^{2} c^{6} d + 21 a^{6} b^{3} c^{7}\right) + x^{3} \left(7 a^{9} c^{5} d^{2} + 21 a^{8} b c^{6} d + 12 a^{7} b^{2} c^{7}\right) + x^{2} \left(\frac{7 a^{9} c^{6} d}{2} + \frac{9 a^{8} b c^{7}}{2}\right)"," ",0,"a**9*c**7*x + b**9*d**7*x**17/17 + x**16*(9*a*b**8*d**7/16 + 7*b**9*c*d**6/16) + x**15*(12*a**2*b**7*d**7/5 + 21*a*b**8*c*d**6/5 + 7*b**9*c**2*d**5/5) + x**14*(6*a**3*b**6*d**7 + 18*a**2*b**7*c*d**6 + 27*a*b**8*c**2*d**5/2 + 5*b**9*c**3*d**4/2) + x**13*(126*a**4*b**5*d**7/13 + 588*a**3*b**6*c*d**6/13 + 756*a**2*b**7*c**2*d**5/13 + 315*a*b**8*c**3*d**4/13 + 35*b**9*c**4*d**3/13) + x**12*(21*a**5*b**4*d**7/2 + 147*a**4*b**5*c*d**6/2 + 147*a**3*b**6*c**2*d**5 + 105*a**2*b**7*c**3*d**4 + 105*a*b**8*c**4*d**3/4 + 7*b**9*c**5*d**2/4) + x**11*(84*a**6*b**3*d**7/11 + 882*a**5*b**4*c*d**6/11 + 2646*a**4*b**5*c**2*d**5/11 + 2940*a**3*b**6*c**3*d**4/11 + 1260*a**2*b**7*c**4*d**3/11 + 189*a*b**8*c**5*d**2/11 + 7*b**9*c**6*d/11) + x**10*(18*a**7*b**2*d**7/5 + 294*a**6*b**3*c*d**6/5 + 1323*a**5*b**4*c**2*d**5/5 + 441*a**4*b**5*c**3*d**4 + 294*a**3*b**6*c**4*d**3 + 378*a**2*b**7*c**5*d**2/5 + 63*a*b**8*c**6*d/10 + b**9*c**7/10) + x**9*(a**8*b*d**7 + 28*a**7*b**2*c*d**6 + 196*a**6*b**3*c**2*d**5 + 490*a**5*b**4*c**3*d**4 + 490*a**4*b**5*c**4*d**3 + 196*a**3*b**6*c**5*d**2 + 28*a**2*b**7*c**6*d + a*b**8*c**7) + x**8*(a**9*d**7/8 + 63*a**8*b*c*d**6/8 + 189*a**7*b**2*c**2*d**5/2 + 735*a**6*b**3*c**3*d**4/2 + 2205*a**5*b**4*c**4*d**3/4 + 1323*a**4*b**5*c**5*d**2/4 + 147*a**3*b**6*c**6*d/2 + 9*a**2*b**7*c**7/2) + x**7*(a**9*c*d**6 + 27*a**8*b*c**2*d**5 + 180*a**7*b**2*c**3*d**4 + 420*a**6*b**3*c**4*d**3 + 378*a**5*b**4*c**5*d**2 + 126*a**4*b**5*c**6*d + 12*a**3*b**6*c**7) + x**6*(7*a**9*c**2*d**5/2 + 105*a**8*b*c**3*d**4/2 + 210*a**7*b**2*c**4*d**3 + 294*a**6*b**3*c**5*d**2 + 147*a**5*b**4*c**6*d + 21*a**4*b**5*c**7) + x**5*(7*a**9*c**3*d**4 + 63*a**8*b*c**4*d**3 + 756*a**7*b**2*c**5*d**2/5 + 588*a**6*b**3*c**6*d/5 + 126*a**5*b**4*c**7/5) + x**4*(35*a**9*c**4*d**3/4 + 189*a**8*b*c**5*d**2/4 + 63*a**7*b**2*c**6*d + 21*a**6*b**3*c**7) + x**3*(7*a**9*c**5*d**2 + 21*a**8*b*c**6*d + 12*a**7*b**2*c**7) + x**2*(7*a**9*c**6*d/2 + 9*a**8*b*c**7/2)","B",0
1274,1,1046,0,0.213872," ","integrate((b*x+a)**8*(d*x+c)**7,x)","a^{8} c^{7} x + \frac{b^{8} d^{7} x^{16}}{16} + x^{15} \left(\frac{8 a b^{7} d^{7}}{15} + \frac{7 b^{8} c d^{6}}{15}\right) + x^{14} \left(2 a^{2} b^{6} d^{7} + 4 a b^{7} c d^{6} + \frac{3 b^{8} c^{2} d^{5}}{2}\right) + x^{13} \left(\frac{56 a^{3} b^{5} d^{7}}{13} + \frac{196 a^{2} b^{6} c d^{6}}{13} + \frac{168 a b^{7} c^{2} d^{5}}{13} + \frac{35 b^{8} c^{3} d^{4}}{13}\right) + x^{12} \left(\frac{35 a^{4} b^{4} d^{7}}{6} + \frac{98 a^{3} b^{5} c d^{6}}{3} + 49 a^{2} b^{6} c^{2} d^{5} + \frac{70 a b^{7} c^{3} d^{4}}{3} + \frac{35 b^{8} c^{4} d^{3}}{12}\right) + x^{11} \left(\frac{56 a^{5} b^{3} d^{7}}{11} + \frac{490 a^{4} b^{4} c d^{6}}{11} + \frac{1176 a^{3} b^{5} c^{2} d^{5}}{11} + \frac{980 a^{2} b^{6} c^{3} d^{4}}{11} + \frac{280 a b^{7} c^{4} d^{3}}{11} + \frac{21 b^{8} c^{5} d^{2}}{11}\right) + x^{10} \left(\frac{14 a^{6} b^{2} d^{7}}{5} + \frac{196 a^{5} b^{3} c d^{6}}{5} + 147 a^{4} b^{4} c^{2} d^{5} + 196 a^{3} b^{5} c^{3} d^{4} + 98 a^{2} b^{6} c^{4} d^{3} + \frac{84 a b^{7} c^{5} d^{2}}{5} + \frac{7 b^{8} c^{6} d}{10}\right) + x^{9} \left(\frac{8 a^{7} b d^{7}}{9} + \frac{196 a^{6} b^{2} c d^{6}}{9} + \frac{392 a^{5} b^{3} c^{2} d^{5}}{3} + \frac{2450 a^{4} b^{4} c^{3} d^{4}}{9} + \frac{1960 a^{3} b^{5} c^{4} d^{3}}{9} + \frac{196 a^{2} b^{6} c^{5} d^{2}}{3} + \frac{56 a b^{7} c^{6} d}{9} + \frac{b^{8} c^{7}}{9}\right) + x^{8} \left(\frac{a^{8} d^{7}}{8} + 7 a^{7} b c d^{6} + \frac{147 a^{6} b^{2} c^{2} d^{5}}{2} + 245 a^{5} b^{3} c^{3} d^{4} + \frac{1225 a^{4} b^{4} c^{4} d^{3}}{4} + 147 a^{3} b^{5} c^{5} d^{2} + \frac{49 a^{2} b^{6} c^{6} d}{2} + a b^{7} c^{7}\right) + x^{7} \left(a^{8} c d^{6} + 24 a^{7} b c^{2} d^{5} + 140 a^{6} b^{2} c^{3} d^{4} + 280 a^{5} b^{3} c^{4} d^{3} + 210 a^{4} b^{4} c^{5} d^{2} + 56 a^{3} b^{5} c^{6} d + 4 a^{2} b^{6} c^{7}\right) + x^{6} \left(\frac{7 a^{8} c^{2} d^{5}}{2} + \frac{140 a^{7} b c^{3} d^{4}}{3} + \frac{490 a^{6} b^{2} c^{4} d^{3}}{3} + 196 a^{5} b^{3} c^{5} d^{2} + \frac{245 a^{4} b^{4} c^{6} d}{3} + \frac{28 a^{3} b^{5} c^{7}}{3}\right) + x^{5} \left(7 a^{8} c^{3} d^{4} + 56 a^{7} b c^{4} d^{3} + \frac{588 a^{6} b^{2} c^{5} d^{2}}{5} + \frac{392 a^{5} b^{3} c^{6} d}{5} + 14 a^{4} b^{4} c^{7}\right) + x^{4} \left(\frac{35 a^{8} c^{4} d^{3}}{4} + 42 a^{7} b c^{5} d^{2} + 49 a^{6} b^{2} c^{6} d + 14 a^{5} b^{3} c^{7}\right) + x^{3} \left(7 a^{8} c^{5} d^{2} + \frac{56 a^{7} b c^{6} d}{3} + \frac{28 a^{6} b^{2} c^{7}}{3}\right) + x^{2} \left(\frac{7 a^{8} c^{6} d}{2} + 4 a^{7} b c^{7}\right)"," ",0,"a**8*c**7*x + b**8*d**7*x**16/16 + x**15*(8*a*b**7*d**7/15 + 7*b**8*c*d**6/15) + x**14*(2*a**2*b**6*d**7 + 4*a*b**7*c*d**6 + 3*b**8*c**2*d**5/2) + x**13*(56*a**3*b**5*d**7/13 + 196*a**2*b**6*c*d**6/13 + 168*a*b**7*c**2*d**5/13 + 35*b**8*c**3*d**4/13) + x**12*(35*a**4*b**4*d**7/6 + 98*a**3*b**5*c*d**6/3 + 49*a**2*b**6*c**2*d**5 + 70*a*b**7*c**3*d**4/3 + 35*b**8*c**4*d**3/12) + x**11*(56*a**5*b**3*d**7/11 + 490*a**4*b**4*c*d**6/11 + 1176*a**3*b**5*c**2*d**5/11 + 980*a**2*b**6*c**3*d**4/11 + 280*a*b**7*c**4*d**3/11 + 21*b**8*c**5*d**2/11) + x**10*(14*a**6*b**2*d**7/5 + 196*a**5*b**3*c*d**6/5 + 147*a**4*b**4*c**2*d**5 + 196*a**3*b**5*c**3*d**4 + 98*a**2*b**6*c**4*d**3 + 84*a*b**7*c**5*d**2/5 + 7*b**8*c**6*d/10) + x**9*(8*a**7*b*d**7/9 + 196*a**6*b**2*c*d**6/9 + 392*a**5*b**3*c**2*d**5/3 + 2450*a**4*b**4*c**3*d**4/9 + 1960*a**3*b**5*c**4*d**3/9 + 196*a**2*b**6*c**5*d**2/3 + 56*a*b**7*c**6*d/9 + b**8*c**7/9) + x**8*(a**8*d**7/8 + 7*a**7*b*c*d**6 + 147*a**6*b**2*c**2*d**5/2 + 245*a**5*b**3*c**3*d**4 + 1225*a**4*b**4*c**4*d**3/4 + 147*a**3*b**5*c**5*d**2 + 49*a**2*b**6*c**6*d/2 + a*b**7*c**7) + x**7*(a**8*c*d**6 + 24*a**7*b*c**2*d**5 + 140*a**6*b**2*c**3*d**4 + 280*a**5*b**3*c**4*d**3 + 210*a**4*b**4*c**5*d**2 + 56*a**3*b**5*c**6*d + 4*a**2*b**6*c**7) + x**6*(7*a**8*c**2*d**5/2 + 140*a**7*b*c**3*d**4/3 + 490*a**6*b**2*c**4*d**3/3 + 196*a**5*b**3*c**5*d**2 + 245*a**4*b**4*c**6*d/3 + 28*a**3*b**5*c**7/3) + x**5*(7*a**8*c**3*d**4 + 56*a**7*b*c**4*d**3 + 588*a**6*b**2*c**5*d**2/5 + 392*a**5*b**3*c**6*d/5 + 14*a**4*b**4*c**7) + x**4*(35*a**8*c**4*d**3/4 + 42*a**7*b*c**5*d**2 + 49*a**6*b**2*c**6*d + 14*a**5*b**3*c**7) + x**3*(7*a**8*c**5*d**2 + 56*a**7*b*c**6*d/3 + 28*a**6*b**2*c**7/3) + x**2*(7*a**8*c**6*d/2 + 4*a**7*b*c**7)","B",0
1275,1,935,0,0.194147," ","integrate((b*x+a)**7*(d*x+c)**7,x)","a^{7} c^{7} x + \frac{b^{7} d^{7} x^{15}}{15} + x^{14} \left(\frac{a b^{6} d^{7}}{2} + \frac{b^{7} c d^{6}}{2}\right) + x^{13} \left(\frac{21 a^{2} b^{5} d^{7}}{13} + \frac{49 a b^{6} c d^{6}}{13} + \frac{21 b^{7} c^{2} d^{5}}{13}\right) + x^{12} \left(\frac{35 a^{3} b^{4} d^{7}}{12} + \frac{49 a^{2} b^{5} c d^{6}}{4} + \frac{49 a b^{6} c^{2} d^{5}}{4} + \frac{35 b^{7} c^{3} d^{4}}{12}\right) + x^{11} \left(\frac{35 a^{4} b^{3} d^{7}}{11} + \frac{245 a^{3} b^{4} c d^{6}}{11} + \frac{441 a^{2} b^{5} c^{2} d^{5}}{11} + \frac{245 a b^{6} c^{3} d^{4}}{11} + \frac{35 b^{7} c^{4} d^{3}}{11}\right) + x^{10} \left(\frac{21 a^{5} b^{2} d^{7}}{10} + \frac{49 a^{4} b^{3} c d^{6}}{2} + \frac{147 a^{3} b^{4} c^{2} d^{5}}{2} + \frac{147 a^{2} b^{5} c^{3} d^{4}}{2} + \frac{49 a b^{6} c^{4} d^{3}}{2} + \frac{21 b^{7} c^{5} d^{2}}{10}\right) + x^{9} \left(\frac{7 a^{6} b d^{7}}{9} + \frac{49 a^{5} b^{2} c d^{6}}{3} + \frac{245 a^{4} b^{3} c^{2} d^{5}}{3} + \frac{1225 a^{3} b^{4} c^{3} d^{4}}{9} + \frac{245 a^{2} b^{5} c^{4} d^{3}}{3} + \frac{49 a b^{6} c^{5} d^{2}}{3} + \frac{7 b^{7} c^{6} d}{9}\right) + x^{8} \left(\frac{a^{7} d^{7}}{8} + \frac{49 a^{6} b c d^{6}}{8} + \frac{441 a^{5} b^{2} c^{2} d^{5}}{8} + \frac{1225 a^{4} b^{3} c^{3} d^{4}}{8} + \frac{1225 a^{3} b^{4} c^{4} d^{3}}{8} + \frac{441 a^{2} b^{5} c^{5} d^{2}}{8} + \frac{49 a b^{6} c^{6} d}{8} + \frac{b^{7} c^{7}}{8}\right) + x^{7} \left(a^{7} c d^{6} + 21 a^{6} b c^{2} d^{5} + 105 a^{5} b^{2} c^{3} d^{4} + 175 a^{4} b^{3} c^{4} d^{3} + 105 a^{3} b^{4} c^{5} d^{2} + 21 a^{2} b^{5} c^{6} d + a b^{6} c^{7}\right) + x^{6} \left(\frac{7 a^{7} c^{2} d^{5}}{2} + \frac{245 a^{6} b c^{3} d^{4}}{6} + \frac{245 a^{5} b^{2} c^{4} d^{3}}{2} + \frac{245 a^{4} b^{3} c^{5} d^{2}}{2} + \frac{245 a^{3} b^{4} c^{6} d}{6} + \frac{7 a^{2} b^{5} c^{7}}{2}\right) + x^{5} \left(7 a^{7} c^{3} d^{4} + 49 a^{6} b c^{4} d^{3} + \frac{441 a^{5} b^{2} c^{5} d^{2}}{5} + 49 a^{4} b^{3} c^{6} d + 7 a^{3} b^{4} c^{7}\right) + x^{4} \left(\frac{35 a^{7} c^{4} d^{3}}{4} + \frac{147 a^{6} b c^{5} d^{2}}{4} + \frac{147 a^{5} b^{2} c^{6} d}{4} + \frac{35 a^{4} b^{3} c^{7}}{4}\right) + x^{3} \left(7 a^{7} c^{5} d^{2} + \frac{49 a^{6} b c^{6} d}{3} + 7 a^{5} b^{2} c^{7}\right) + x^{2} \left(\frac{7 a^{7} c^{6} d}{2} + \frac{7 a^{6} b c^{7}}{2}\right)"," ",0,"a**7*c**7*x + b**7*d**7*x**15/15 + x**14*(a*b**6*d**7/2 + b**7*c*d**6/2) + x**13*(21*a**2*b**5*d**7/13 + 49*a*b**6*c*d**6/13 + 21*b**7*c**2*d**5/13) + x**12*(35*a**3*b**4*d**7/12 + 49*a**2*b**5*c*d**6/4 + 49*a*b**6*c**2*d**5/4 + 35*b**7*c**3*d**4/12) + x**11*(35*a**4*b**3*d**7/11 + 245*a**3*b**4*c*d**6/11 + 441*a**2*b**5*c**2*d**5/11 + 245*a*b**6*c**3*d**4/11 + 35*b**7*c**4*d**3/11) + x**10*(21*a**5*b**2*d**7/10 + 49*a**4*b**3*c*d**6/2 + 147*a**3*b**4*c**2*d**5/2 + 147*a**2*b**5*c**3*d**4/2 + 49*a*b**6*c**4*d**3/2 + 21*b**7*c**5*d**2/10) + x**9*(7*a**6*b*d**7/9 + 49*a**5*b**2*c*d**6/3 + 245*a**4*b**3*c**2*d**5/3 + 1225*a**3*b**4*c**3*d**4/9 + 245*a**2*b**5*c**4*d**3/3 + 49*a*b**6*c**5*d**2/3 + 7*b**7*c**6*d/9) + x**8*(a**7*d**7/8 + 49*a**6*b*c*d**6/8 + 441*a**5*b**2*c**2*d**5/8 + 1225*a**4*b**3*c**3*d**4/8 + 1225*a**3*b**4*c**4*d**3/8 + 441*a**2*b**5*c**5*d**2/8 + 49*a*b**6*c**6*d/8 + b**7*c**7/8) + x**7*(a**7*c*d**6 + 21*a**6*b*c**2*d**5 + 105*a**5*b**2*c**3*d**4 + 175*a**4*b**3*c**4*d**3 + 105*a**3*b**4*c**5*d**2 + 21*a**2*b**5*c**6*d + a*b**6*c**7) + x**6*(7*a**7*c**2*d**5/2 + 245*a**6*b*c**3*d**4/6 + 245*a**5*b**2*c**4*d**3/2 + 245*a**4*b**3*c**5*d**2/2 + 245*a**3*b**4*c**6*d/6 + 7*a**2*b**5*c**7/2) + x**5*(7*a**7*c**3*d**4 + 49*a**6*b*c**4*d**3 + 441*a**5*b**2*c**5*d**2/5 + 49*a**4*b**3*c**6*d + 7*a**3*b**4*c**7) + x**4*(35*a**7*c**4*d**3/4 + 147*a**6*b*c**5*d**2/4 + 147*a**5*b**2*c**6*d/4 + 35*a**4*b**3*c**7/4) + x**3*(7*a**7*c**5*d**2 + 49*a**6*b*c**6*d/3 + 7*a**5*b**2*c**7) + x**2*(7*a**7*c**6*d/2 + 7*a**6*b*c**7/2)","B",0
1276,1,796,0,0.178054," ","integrate((b*x+a)**6*(d*x+c)**7,x)","a^{6} c^{7} x + \frac{b^{6} d^{7} x^{14}}{14} + x^{13} \left(\frac{6 a b^{5} d^{7}}{13} + \frac{7 b^{6} c d^{6}}{13}\right) + x^{12} \left(\frac{5 a^{2} b^{4} d^{7}}{4} + \frac{7 a b^{5} c d^{6}}{2} + \frac{7 b^{6} c^{2} d^{5}}{4}\right) + x^{11} \left(\frac{20 a^{3} b^{3} d^{7}}{11} + \frac{105 a^{2} b^{4} c d^{6}}{11} + \frac{126 a b^{5} c^{2} d^{5}}{11} + \frac{35 b^{6} c^{3} d^{4}}{11}\right) + x^{10} \left(\frac{3 a^{4} b^{2} d^{7}}{2} + 14 a^{3} b^{3} c d^{6} + \frac{63 a^{2} b^{4} c^{2} d^{5}}{2} + 21 a b^{5} c^{3} d^{4} + \frac{7 b^{6} c^{4} d^{3}}{2}\right) + x^{9} \left(\frac{2 a^{5} b d^{7}}{3} + \frac{35 a^{4} b^{2} c d^{6}}{3} + \frac{140 a^{3} b^{3} c^{2} d^{5}}{3} + \frac{175 a^{2} b^{4} c^{3} d^{4}}{3} + \frac{70 a b^{5} c^{4} d^{3}}{3} + \frac{7 b^{6} c^{5} d^{2}}{3}\right) + x^{8} \left(\frac{a^{6} d^{7}}{8} + \frac{21 a^{5} b c d^{6}}{4} + \frac{315 a^{4} b^{2} c^{2} d^{5}}{8} + \frac{175 a^{3} b^{3} c^{3} d^{4}}{2} + \frac{525 a^{2} b^{4} c^{4} d^{3}}{8} + \frac{63 a b^{5} c^{5} d^{2}}{4} + \frac{7 b^{6} c^{6} d}{8}\right) + x^{7} \left(a^{6} c d^{6} + 18 a^{5} b c^{2} d^{5} + 75 a^{4} b^{2} c^{3} d^{4} + 100 a^{3} b^{3} c^{4} d^{3} + 45 a^{2} b^{4} c^{5} d^{2} + 6 a b^{5} c^{6} d + \frac{b^{6} c^{7}}{7}\right) + x^{6} \left(\frac{7 a^{6} c^{2} d^{5}}{2} + 35 a^{5} b c^{3} d^{4} + \frac{175 a^{4} b^{2} c^{4} d^{3}}{2} + 70 a^{3} b^{3} c^{5} d^{2} + \frac{35 a^{2} b^{4} c^{6} d}{2} + a b^{5} c^{7}\right) + x^{5} \left(7 a^{6} c^{3} d^{4} + 42 a^{5} b c^{4} d^{3} + 63 a^{4} b^{2} c^{5} d^{2} + 28 a^{3} b^{3} c^{6} d + 3 a^{2} b^{4} c^{7}\right) + x^{4} \left(\frac{35 a^{6} c^{4} d^{3}}{4} + \frac{63 a^{5} b c^{5} d^{2}}{2} + \frac{105 a^{4} b^{2} c^{6} d}{4} + 5 a^{3} b^{3} c^{7}\right) + x^{3} \left(7 a^{6} c^{5} d^{2} + 14 a^{5} b c^{6} d + 5 a^{4} b^{2} c^{7}\right) + x^{2} \left(\frac{7 a^{6} c^{6} d}{2} + 3 a^{5} b c^{7}\right)"," ",0,"a**6*c**7*x + b**6*d**7*x**14/14 + x**13*(6*a*b**5*d**7/13 + 7*b**6*c*d**6/13) + x**12*(5*a**2*b**4*d**7/4 + 7*a*b**5*c*d**6/2 + 7*b**6*c**2*d**5/4) + x**11*(20*a**3*b**3*d**7/11 + 105*a**2*b**4*c*d**6/11 + 126*a*b**5*c**2*d**5/11 + 35*b**6*c**3*d**4/11) + x**10*(3*a**4*b**2*d**7/2 + 14*a**3*b**3*c*d**6 + 63*a**2*b**4*c**2*d**5/2 + 21*a*b**5*c**3*d**4 + 7*b**6*c**4*d**3/2) + x**9*(2*a**5*b*d**7/3 + 35*a**4*b**2*c*d**6/3 + 140*a**3*b**3*c**2*d**5/3 + 175*a**2*b**4*c**3*d**4/3 + 70*a*b**5*c**4*d**3/3 + 7*b**6*c**5*d**2/3) + x**8*(a**6*d**7/8 + 21*a**5*b*c*d**6/4 + 315*a**4*b**2*c**2*d**5/8 + 175*a**3*b**3*c**3*d**4/2 + 525*a**2*b**4*c**4*d**3/8 + 63*a*b**5*c**5*d**2/4 + 7*b**6*c**6*d/8) + x**7*(a**6*c*d**6 + 18*a**5*b*c**2*d**5 + 75*a**4*b**2*c**3*d**4 + 100*a**3*b**3*c**4*d**3 + 45*a**2*b**4*c**5*d**2 + 6*a*b**5*c**6*d + b**6*c**7/7) + x**6*(7*a**6*c**2*d**5/2 + 35*a**5*b*c**3*d**4 + 175*a**4*b**2*c**4*d**3/2 + 70*a**3*b**3*c**5*d**2 + 35*a**2*b**4*c**6*d/2 + a*b**5*c**7) + x**5*(7*a**6*c**3*d**4 + 42*a**5*b*c**4*d**3 + 63*a**4*b**2*c**5*d**2 + 28*a**3*b**3*c**6*d + 3*a**2*b**4*c**7) + x**4*(35*a**6*c**4*d**3/4 + 63*a**5*b*c**5*d**2/2 + 105*a**4*b**2*c**6*d/4 + 5*a**3*b**3*c**7) + x**3*(7*a**6*c**5*d**2 + 14*a**5*b*c**6*d + 5*a**4*b**2*c**7) + x**2*(7*a**6*c**6*d/2 + 3*a**5*b*c**7)","B",0
1277,1,673,0,0.164296," ","integrate((b*x+a)**5*(d*x+c)**7,x)","a^{5} c^{7} x + \frac{b^{5} d^{7} x^{13}}{13} + x^{12} \left(\frac{5 a b^{4} d^{7}}{12} + \frac{7 b^{5} c d^{6}}{12}\right) + x^{11} \left(\frac{10 a^{2} b^{3} d^{7}}{11} + \frac{35 a b^{4} c d^{6}}{11} + \frac{21 b^{5} c^{2} d^{5}}{11}\right) + x^{10} \left(a^{3} b^{2} d^{7} + 7 a^{2} b^{3} c d^{6} + \frac{21 a b^{4} c^{2} d^{5}}{2} + \frac{7 b^{5} c^{3} d^{4}}{2}\right) + x^{9} \left(\frac{5 a^{4} b d^{7}}{9} + \frac{70 a^{3} b^{2} c d^{6}}{9} + \frac{70 a^{2} b^{3} c^{2} d^{5}}{3} + \frac{175 a b^{4} c^{3} d^{4}}{9} + \frac{35 b^{5} c^{4} d^{3}}{9}\right) + x^{8} \left(\frac{a^{5} d^{7}}{8} + \frac{35 a^{4} b c d^{6}}{8} + \frac{105 a^{3} b^{2} c^{2} d^{5}}{4} + \frac{175 a^{2} b^{3} c^{3} d^{4}}{4} + \frac{175 a b^{4} c^{4} d^{3}}{8} + \frac{21 b^{5} c^{5} d^{2}}{8}\right) + x^{7} \left(a^{5} c d^{6} + 15 a^{4} b c^{2} d^{5} + 50 a^{3} b^{2} c^{3} d^{4} + 50 a^{2} b^{3} c^{4} d^{3} + 15 a b^{4} c^{5} d^{2} + b^{5} c^{6} d\right) + x^{6} \left(\frac{7 a^{5} c^{2} d^{5}}{2} + \frac{175 a^{4} b c^{3} d^{4}}{6} + \frac{175 a^{3} b^{2} c^{4} d^{3}}{3} + 35 a^{2} b^{3} c^{5} d^{2} + \frac{35 a b^{4} c^{6} d}{6} + \frac{b^{5} c^{7}}{6}\right) + x^{5} \left(7 a^{5} c^{3} d^{4} + 35 a^{4} b c^{4} d^{3} + 42 a^{3} b^{2} c^{5} d^{2} + 14 a^{2} b^{3} c^{6} d + a b^{4} c^{7}\right) + x^{4} \left(\frac{35 a^{5} c^{4} d^{3}}{4} + \frac{105 a^{4} b c^{5} d^{2}}{4} + \frac{35 a^{3} b^{2} c^{6} d}{2} + \frac{5 a^{2} b^{3} c^{7}}{2}\right) + x^{3} \left(7 a^{5} c^{5} d^{2} + \frac{35 a^{4} b c^{6} d}{3} + \frac{10 a^{3} b^{2} c^{7}}{3}\right) + x^{2} \left(\frac{7 a^{5} c^{6} d}{2} + \frac{5 a^{4} b c^{7}}{2}\right)"," ",0,"a**5*c**7*x + b**5*d**7*x**13/13 + x**12*(5*a*b**4*d**7/12 + 7*b**5*c*d**6/12) + x**11*(10*a**2*b**3*d**7/11 + 35*a*b**4*c*d**6/11 + 21*b**5*c**2*d**5/11) + x**10*(a**3*b**2*d**7 + 7*a**2*b**3*c*d**6 + 21*a*b**4*c**2*d**5/2 + 7*b**5*c**3*d**4/2) + x**9*(5*a**4*b*d**7/9 + 70*a**3*b**2*c*d**6/9 + 70*a**2*b**3*c**2*d**5/3 + 175*a*b**4*c**3*d**4/9 + 35*b**5*c**4*d**3/9) + x**8*(a**5*d**7/8 + 35*a**4*b*c*d**6/8 + 105*a**3*b**2*c**2*d**5/4 + 175*a**2*b**3*c**3*d**4/4 + 175*a*b**4*c**4*d**3/8 + 21*b**5*c**5*d**2/8) + x**7*(a**5*c*d**6 + 15*a**4*b*c**2*d**5 + 50*a**3*b**2*c**3*d**4 + 50*a**2*b**3*c**4*d**3 + 15*a*b**4*c**5*d**2 + b**5*c**6*d) + x**6*(7*a**5*c**2*d**5/2 + 175*a**4*b*c**3*d**4/6 + 175*a**3*b**2*c**4*d**3/3 + 35*a**2*b**3*c**5*d**2 + 35*a*b**4*c**6*d/6 + b**5*c**7/6) + x**5*(7*a**5*c**3*d**4 + 35*a**4*b*c**4*d**3 + 42*a**3*b**2*c**5*d**2 + 14*a**2*b**3*c**6*d + a*b**4*c**7) + x**4*(35*a**5*c**4*d**3/4 + 105*a**4*b*c**5*d**2/4 + 35*a**3*b**2*c**6*d/2 + 5*a**2*b**3*c**7/2) + x**3*(7*a**5*c**5*d**2 + 35*a**4*b*c**6*d/3 + 10*a**3*b**2*c**7/3) + x**2*(7*a**5*c**6*d/2 + 5*a**4*b*c**7/2)","B",0
1278,1,549,0,0.146497," ","integrate((b*x+a)**4*(d*x+c)**7,x)","a^{4} c^{7} x + \frac{b^{4} d^{7} x^{12}}{12} + x^{11} \left(\frac{4 a b^{3} d^{7}}{11} + \frac{7 b^{4} c d^{6}}{11}\right) + x^{10} \left(\frac{3 a^{2} b^{2} d^{7}}{5} + \frac{14 a b^{3} c d^{6}}{5} + \frac{21 b^{4} c^{2} d^{5}}{10}\right) + x^{9} \left(\frac{4 a^{3} b d^{7}}{9} + \frac{14 a^{2} b^{2} c d^{6}}{3} + \frac{28 a b^{3} c^{2} d^{5}}{3} + \frac{35 b^{4} c^{3} d^{4}}{9}\right) + x^{8} \left(\frac{a^{4} d^{7}}{8} + \frac{7 a^{3} b c d^{6}}{2} + \frac{63 a^{2} b^{2} c^{2} d^{5}}{4} + \frac{35 a b^{3} c^{3} d^{4}}{2} + \frac{35 b^{4} c^{4} d^{3}}{8}\right) + x^{7} \left(a^{4} c d^{6} + 12 a^{3} b c^{2} d^{5} + 30 a^{2} b^{2} c^{3} d^{4} + 20 a b^{3} c^{4} d^{3} + 3 b^{4} c^{5} d^{2}\right) + x^{6} \left(\frac{7 a^{4} c^{2} d^{5}}{2} + \frac{70 a^{3} b c^{3} d^{4}}{3} + 35 a^{2} b^{2} c^{4} d^{3} + 14 a b^{3} c^{5} d^{2} + \frac{7 b^{4} c^{6} d}{6}\right) + x^{5} \left(7 a^{4} c^{3} d^{4} + 28 a^{3} b c^{4} d^{3} + \frac{126 a^{2} b^{2} c^{5} d^{2}}{5} + \frac{28 a b^{3} c^{6} d}{5} + \frac{b^{4} c^{7}}{5}\right) + x^{4} \left(\frac{35 a^{4} c^{4} d^{3}}{4} + 21 a^{3} b c^{5} d^{2} + \frac{21 a^{2} b^{2} c^{6} d}{2} + a b^{3} c^{7}\right) + x^{3} \left(7 a^{4} c^{5} d^{2} + \frac{28 a^{3} b c^{6} d}{3} + 2 a^{2} b^{2} c^{7}\right) + x^{2} \left(\frac{7 a^{4} c^{6} d}{2} + 2 a^{3} b c^{7}\right)"," ",0,"a**4*c**7*x + b**4*d**7*x**12/12 + x**11*(4*a*b**3*d**7/11 + 7*b**4*c*d**6/11) + x**10*(3*a**2*b**2*d**7/5 + 14*a*b**3*c*d**6/5 + 21*b**4*c**2*d**5/10) + x**9*(4*a**3*b*d**7/9 + 14*a**2*b**2*c*d**6/3 + 28*a*b**3*c**2*d**5/3 + 35*b**4*c**3*d**4/9) + x**8*(a**4*d**7/8 + 7*a**3*b*c*d**6/2 + 63*a**2*b**2*c**2*d**5/4 + 35*a*b**3*c**3*d**4/2 + 35*b**4*c**4*d**3/8) + x**7*(a**4*c*d**6 + 12*a**3*b*c**2*d**5 + 30*a**2*b**2*c**3*d**4 + 20*a*b**3*c**4*d**3 + 3*b**4*c**5*d**2) + x**6*(7*a**4*c**2*d**5/2 + 70*a**3*b*c**3*d**4/3 + 35*a**2*b**2*c**4*d**3 + 14*a*b**3*c**5*d**2 + 7*b**4*c**6*d/6) + x**5*(7*a**4*c**3*d**4 + 28*a**3*b*c**4*d**3 + 126*a**2*b**2*c**5*d**2/5 + 28*a*b**3*c**6*d/5 + b**4*c**7/5) + x**4*(35*a**4*c**4*d**3/4 + 21*a**3*b*c**5*d**2 + 21*a**2*b**2*c**6*d/2 + a*b**3*c**7) + x**3*(7*a**4*c**5*d**2 + 28*a**3*b*c**6*d/3 + 2*a**2*b**2*c**7) + x**2*(7*a**4*c**6*d/2 + 2*a**3*b*c**7)","B",0
1279,1,427,0,0.130882," ","integrate((b*x+a)**3*(d*x+c)**7,x)","a^{3} c^{7} x + \frac{b^{3} d^{7} x^{11}}{11} + x^{10} \left(\frac{3 a b^{2} d^{7}}{10} + \frac{7 b^{3} c d^{6}}{10}\right) + x^{9} \left(\frac{a^{2} b d^{7}}{3} + \frac{7 a b^{2} c d^{6}}{3} + \frac{7 b^{3} c^{2} d^{5}}{3}\right) + x^{8} \left(\frac{a^{3} d^{7}}{8} + \frac{21 a^{2} b c d^{6}}{8} + \frac{63 a b^{2} c^{2} d^{5}}{8} + \frac{35 b^{3} c^{3} d^{4}}{8}\right) + x^{7} \left(a^{3} c d^{6} + 9 a^{2} b c^{2} d^{5} + 15 a b^{2} c^{3} d^{4} + 5 b^{3} c^{4} d^{3}\right) + x^{6} \left(\frac{7 a^{3} c^{2} d^{5}}{2} + \frac{35 a^{2} b c^{3} d^{4}}{2} + \frac{35 a b^{2} c^{4} d^{3}}{2} + \frac{7 b^{3} c^{5} d^{2}}{2}\right) + x^{5} \left(7 a^{3} c^{3} d^{4} + 21 a^{2} b c^{4} d^{3} + \frac{63 a b^{2} c^{5} d^{2}}{5} + \frac{7 b^{3} c^{6} d}{5}\right) + x^{4} \left(\frac{35 a^{3} c^{4} d^{3}}{4} + \frac{63 a^{2} b c^{5} d^{2}}{4} + \frac{21 a b^{2} c^{6} d}{4} + \frac{b^{3} c^{7}}{4}\right) + x^{3} \left(7 a^{3} c^{5} d^{2} + 7 a^{2} b c^{6} d + a b^{2} c^{7}\right) + x^{2} \left(\frac{7 a^{3} c^{6} d}{2} + \frac{3 a^{2} b c^{7}}{2}\right)"," ",0,"a**3*c**7*x + b**3*d**7*x**11/11 + x**10*(3*a*b**2*d**7/10 + 7*b**3*c*d**6/10) + x**9*(a**2*b*d**7/3 + 7*a*b**2*c*d**6/3 + 7*b**3*c**2*d**5/3) + x**8*(a**3*d**7/8 + 21*a**2*b*c*d**6/8 + 63*a*b**2*c**2*d**5/8 + 35*b**3*c**3*d**4/8) + x**7*(a**3*c*d**6 + 9*a**2*b*c**2*d**5 + 15*a*b**2*c**3*d**4 + 5*b**3*c**4*d**3) + x**6*(7*a**3*c**2*d**5/2 + 35*a**2*b*c**3*d**4/2 + 35*a*b**2*c**4*d**3/2 + 7*b**3*c**5*d**2/2) + x**5*(7*a**3*c**3*d**4 + 21*a**2*b*c**4*d**3 + 63*a*b**2*c**5*d**2/5 + 7*b**3*c**6*d/5) + x**4*(35*a**3*c**4*d**3/4 + 63*a**2*b*c**5*d**2/4 + 21*a*b**2*c**6*d/4 + b**3*c**7/4) + x**3*(7*a**3*c**5*d**2 + 7*a**2*b*c**6*d + a*b**2*c**7) + x**2*(7*a**3*c**6*d/2 + 3*a**2*b*c**7/2)","B",0
1280,1,303,0,0.116116," ","integrate((b*x+a)**2*(d*x+c)**7,x)","a^{2} c^{7} x + \frac{b^{2} d^{7} x^{10}}{10} + x^{9} \left(\frac{2 a b d^{7}}{9} + \frac{7 b^{2} c d^{6}}{9}\right) + x^{8} \left(\frac{a^{2} d^{7}}{8} + \frac{7 a b c d^{6}}{4} + \frac{21 b^{2} c^{2} d^{5}}{8}\right) + x^{7} \left(a^{2} c d^{6} + 6 a b c^{2} d^{5} + 5 b^{2} c^{3} d^{4}\right) + x^{6} \left(\frac{7 a^{2} c^{2} d^{5}}{2} + \frac{35 a b c^{3} d^{4}}{3} + \frac{35 b^{2} c^{4} d^{3}}{6}\right) + x^{5} \left(7 a^{2} c^{3} d^{4} + 14 a b c^{4} d^{3} + \frac{21 b^{2} c^{5} d^{2}}{5}\right) + x^{4} \left(\frac{35 a^{2} c^{4} d^{3}}{4} + \frac{21 a b c^{5} d^{2}}{2} + \frac{7 b^{2} c^{6} d}{4}\right) + x^{3} \left(7 a^{2} c^{5} d^{2} + \frac{14 a b c^{6} d}{3} + \frac{b^{2} c^{7}}{3}\right) + x^{2} \left(\frac{7 a^{2} c^{6} d}{2} + a b c^{7}\right)"," ",0,"a**2*c**7*x + b**2*d**7*x**10/10 + x**9*(2*a*b*d**7/9 + 7*b**2*c*d**6/9) + x**8*(a**2*d**7/8 + 7*a*b*c*d**6/4 + 21*b**2*c**2*d**5/8) + x**7*(a**2*c*d**6 + 6*a*b*c**2*d**5 + 5*b**2*c**3*d**4) + x**6*(7*a**2*c**2*d**5/2 + 35*a*b*c**3*d**4/3 + 35*b**2*c**4*d**3/6) + x**5*(7*a**2*c**3*d**4 + 14*a*b*c**4*d**3 + 21*b**2*c**5*d**2/5) + x**4*(35*a**2*c**4*d**3/4 + 21*a*b*c**5*d**2/2 + 7*b**2*c**6*d/4) + x**3*(7*a**2*c**5*d**2 + 14*a*b*c**6*d/3 + b**2*c**7/3) + x**2*(7*a**2*c**6*d/2 + a*b*c**7)","B",0
1281,1,178,0,0.100009," ","integrate((b*x+a)*(d*x+c)**7,x)","a c^{7} x + \frac{b d^{7} x^{9}}{9} + x^{8} \left(\frac{a d^{7}}{8} + \frac{7 b c d^{6}}{8}\right) + x^{7} \left(a c d^{6} + 3 b c^{2} d^{5}\right) + x^{6} \left(\frac{7 a c^{2} d^{5}}{2} + \frac{35 b c^{3} d^{4}}{6}\right) + x^{5} \left(7 a c^{3} d^{4} + 7 b c^{4} d^{3}\right) + x^{4} \left(\frac{35 a c^{4} d^{3}}{4} + \frac{21 b c^{5} d^{2}}{4}\right) + x^{3} \left(7 a c^{5} d^{2} + \frac{7 b c^{6} d}{3}\right) + x^{2} \left(\frac{7 a c^{6} d}{2} + \frac{b c^{7}}{2}\right)"," ",0,"a*c**7*x + b*d**7*x**9/9 + x**8*(a*d**7/8 + 7*b*c*d**6/8) + x**7*(a*c*d**6 + 3*b*c**2*d**5) + x**6*(7*a*c**2*d**5/2 + 35*b*c**3*d**4/6) + x**5*(7*a*c**3*d**4 + 7*b*c**4*d**3) + x**4*(35*a*c**4*d**3/4 + 21*b*c**5*d**2/4) + x**3*(7*a*c**5*d**2 + 7*b*c**6*d/3) + x**2*(7*a*c**6*d/2 + b*c**7/2)","B",0
1282,1,83,0,0.076494," ","integrate((d*x+c)**7,x)","c^{7} x + \frac{7 c^{6} d x^{2}}{2} + 7 c^{5} d^{2} x^{3} + \frac{35 c^{4} d^{3} x^{4}}{4} + 7 c^{3} d^{4} x^{5} + \frac{7 c^{2} d^{5} x^{6}}{2} + c d^{6} x^{7} + \frac{d^{7} x^{8}}{8}"," ",0,"c**7*x + 7*c**6*d*x**2/2 + 7*c**5*d**2*x**3 + 35*c**4*d**3*x**4/4 + 7*c**3*d**4*x**5 + 7*c**2*d**5*x**6/2 + c*d**6*x**7 + d**7*x**8/8","B",0
1283,1,408,0,0.802021," ","integrate((d*x+c)**7/(b*x+a),x)","x^{6} \left(- \frac{a d^{7}}{6 b^{2}} + \frac{7 c d^{6}}{6 b}\right) + x^{5} \left(\frac{a^{2} d^{7}}{5 b^{3}} - \frac{7 a c d^{6}}{5 b^{2}} + \frac{21 c^{2} d^{5}}{5 b}\right) + x^{4} \left(- \frac{a^{3} d^{7}}{4 b^{4}} + \frac{7 a^{2} c d^{6}}{4 b^{3}} - \frac{21 a c^{2} d^{5}}{4 b^{2}} + \frac{35 c^{3} d^{4}}{4 b}\right) + x^{3} \left(\frac{a^{4} d^{7}}{3 b^{5}} - \frac{7 a^{3} c d^{6}}{3 b^{4}} + \frac{7 a^{2} c^{2} d^{5}}{b^{3}} - \frac{35 a c^{3} d^{4}}{3 b^{2}} + \frac{35 c^{4} d^{3}}{3 b}\right) + x^{2} \left(- \frac{a^{5} d^{7}}{2 b^{6}} + \frac{7 a^{4} c d^{6}}{2 b^{5}} - \frac{21 a^{3} c^{2} d^{5}}{2 b^{4}} + \frac{35 a^{2} c^{3} d^{4}}{2 b^{3}} - \frac{35 a c^{4} d^{3}}{2 b^{2}} + \frac{21 c^{5} d^{2}}{2 b}\right) + x \left(\frac{a^{6} d^{7}}{b^{7}} - \frac{7 a^{5} c d^{6}}{b^{6}} + \frac{21 a^{4} c^{2} d^{5}}{b^{5}} - \frac{35 a^{3} c^{3} d^{4}}{b^{4}} + \frac{35 a^{2} c^{4} d^{3}}{b^{3}} - \frac{21 a c^{5} d^{2}}{b^{2}} + \frac{7 c^{6} d}{b}\right) + \frac{d^{7} x^{7}}{7 b} - \frac{\left(a d - b c\right)^{7} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x**6*(-a*d**7/(6*b**2) + 7*c*d**6/(6*b)) + x**5*(a**2*d**7/(5*b**3) - 7*a*c*d**6/(5*b**2) + 21*c**2*d**5/(5*b)) + x**4*(-a**3*d**7/(4*b**4) + 7*a**2*c*d**6/(4*b**3) - 21*a*c**2*d**5/(4*b**2) + 35*c**3*d**4/(4*b)) + x**3*(a**4*d**7/(3*b**5) - 7*a**3*c*d**6/(3*b**4) + 7*a**2*c**2*d**5/b**3 - 35*a*c**3*d**4/(3*b**2) + 35*c**4*d**3/(3*b)) + x**2*(-a**5*d**7/(2*b**6) + 7*a**4*c*d**6/(2*b**5) - 21*a**3*c**2*d**5/(2*b**4) + 35*a**2*c**3*d**4/(2*b**3) - 35*a*c**4*d**3/(2*b**2) + 21*c**5*d**2/(2*b)) + x*(a**6*d**7/b**7 - 7*a**5*c*d**6/b**6 + 21*a**4*c**2*d**5/b**5 - 35*a**3*c**3*d**4/b**4 + 35*a**2*c**4*d**3/b**3 - 21*a*c**5*d**2/b**2 + 7*c**6*d/b) + d**7*x**7/(7*b) - (a*d - b*c)**7*log(a + b*x)/b**8","B",0
1284,1,428,0,1.444560," ","integrate((d*x+c)**7/(b*x+a)**2,x)","x^{5} \left(- \frac{2 a d^{7}}{5 b^{3}} + \frac{7 c d^{6}}{5 b^{2}}\right) + x^{4} \left(\frac{3 a^{2} d^{7}}{4 b^{4}} - \frac{7 a c d^{6}}{2 b^{3}} + \frac{21 c^{2} d^{5}}{4 b^{2}}\right) + x^{3} \left(- \frac{4 a^{3} d^{7}}{3 b^{5}} + \frac{7 a^{2} c d^{6}}{b^{4}} - \frac{14 a c^{2} d^{5}}{b^{3}} + \frac{35 c^{3} d^{4}}{3 b^{2}}\right) + x^{2} \left(\frac{5 a^{4} d^{7}}{2 b^{6}} - \frac{14 a^{3} c d^{6}}{b^{5}} + \frac{63 a^{2} c^{2} d^{5}}{2 b^{4}} - \frac{35 a c^{3} d^{4}}{b^{3}} + \frac{35 c^{4} d^{3}}{2 b^{2}}\right) + x \left(- \frac{6 a^{5} d^{7}}{b^{7}} + \frac{35 a^{4} c d^{6}}{b^{6}} - \frac{84 a^{3} c^{2} d^{5}}{b^{5}} + \frac{105 a^{2} c^{3} d^{4}}{b^{4}} - \frac{70 a c^{4} d^{3}}{b^{3}} + \frac{21 c^{5} d^{2}}{b^{2}}\right) + \frac{a^{7} d^{7} - 7 a^{6} b c d^{6} + 21 a^{5} b^{2} c^{2} d^{5} - 35 a^{4} b^{3} c^{3} d^{4} + 35 a^{3} b^{4} c^{4} d^{3} - 21 a^{2} b^{5} c^{5} d^{2} + 7 a b^{6} c^{6} d - b^{7} c^{7}}{a b^{8} + b^{9} x} + \frac{d^{7} x^{6}}{6 b^{2}} + \frac{7 d \left(a d - b c\right)^{6} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x**5*(-2*a*d**7/(5*b**3) + 7*c*d**6/(5*b**2)) + x**4*(3*a**2*d**7/(4*b**4) - 7*a*c*d**6/(2*b**3) + 21*c**2*d**5/(4*b**2)) + x**3*(-4*a**3*d**7/(3*b**5) + 7*a**2*c*d**6/b**4 - 14*a*c**2*d**5/b**3 + 35*c**3*d**4/(3*b**2)) + x**2*(5*a**4*d**7/(2*b**6) - 14*a**3*c*d**6/b**5 + 63*a**2*c**2*d**5/(2*b**4) - 35*a*c**3*d**4/b**3 + 35*c**4*d**3/(2*b**2)) + x*(-6*a**5*d**7/b**7 + 35*a**4*c*d**6/b**6 - 84*a**3*c**2*d**5/b**5 + 105*a**2*c**3*d**4/b**4 - 70*a*c**4*d**3/b**3 + 21*c**5*d**2/b**2) + (a**7*d**7 - 7*a**6*b*c*d**6 + 21*a**5*b**2*c**2*d**5 - 35*a**4*b**3*c**3*d**4 + 35*a**3*b**4*c**4*d**3 - 21*a**2*b**5*c**5*d**2 + 7*a*b**6*c**6*d - b**7*c**7)/(a*b**8 + b**9*x) + d**7*x**6/(6*b**2) + 7*d*(a*d - b*c)**6*log(a + b*x)/b**8","B",0
1285,1,447,0,2.948936," ","integrate((d*x+c)**7/(b*x+a)**3,x)","x^{4} \left(- \frac{3 a d^{7}}{4 b^{4}} + \frac{7 c d^{6}}{4 b^{3}}\right) + x^{3} \left(\frac{2 a^{2} d^{7}}{b^{5}} - \frac{7 a c d^{6}}{b^{4}} + \frac{7 c^{2} d^{5}}{b^{3}}\right) + x^{2} \left(- \frac{5 a^{3} d^{7}}{b^{6}} + \frac{21 a^{2} c d^{6}}{b^{5}} - \frac{63 a c^{2} d^{5}}{2 b^{4}} + \frac{35 c^{3} d^{4}}{2 b^{3}}\right) + x \left(\frac{15 a^{4} d^{7}}{b^{7}} - \frac{70 a^{3} c d^{6}}{b^{6}} + \frac{126 a^{2} c^{2} d^{5}}{b^{5}} - \frac{105 a c^{3} d^{4}}{b^{4}} + \frac{35 c^{4} d^{3}}{b^{3}}\right) + \frac{- 13 a^{7} d^{7} + 77 a^{6} b c d^{6} - 189 a^{5} b^{2} c^{2} d^{5} + 245 a^{4} b^{3} c^{3} d^{4} - 175 a^{3} b^{4} c^{4} d^{3} + 63 a^{2} b^{5} c^{5} d^{2} - 7 a b^{6} c^{6} d - b^{7} c^{7} + x \left(- 14 a^{6} b d^{7} + 84 a^{5} b^{2} c d^{6} - 210 a^{4} b^{3} c^{2} d^{5} + 280 a^{3} b^{4} c^{3} d^{4} - 210 a^{2} b^{5} c^{4} d^{3} + 84 a b^{6} c^{5} d^{2} - 14 b^{7} c^{6} d\right)}{2 a^{2} b^{8} + 4 a b^{9} x + 2 b^{10} x^{2}} + \frac{d^{7} x^{5}}{5 b^{3}} - \frac{21 d^{2} \left(a d - b c\right)^{5} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x**4*(-3*a*d**7/(4*b**4) + 7*c*d**6/(4*b**3)) + x**3*(2*a**2*d**7/b**5 - 7*a*c*d**6/b**4 + 7*c**2*d**5/b**3) + x**2*(-5*a**3*d**7/b**6 + 21*a**2*c*d**6/b**5 - 63*a*c**2*d**5/(2*b**4) + 35*c**3*d**4/(2*b**3)) + x*(15*a**4*d**7/b**7 - 70*a**3*c*d**6/b**6 + 126*a**2*c**2*d**5/b**5 - 105*a*c**3*d**4/b**4 + 35*c**4*d**3/b**3) + (-13*a**7*d**7 + 77*a**6*b*c*d**6 - 189*a**5*b**2*c**2*d**5 + 245*a**4*b**3*c**3*d**4 - 175*a**3*b**4*c**4*d**3 + 63*a**2*b**5*c**5*d**2 - 7*a*b**6*c**6*d - b**7*c**7 + x*(-14*a**6*b*d**7 + 84*a**5*b**2*c*d**6 - 210*a**4*b**3*c**2*d**5 + 280*a**3*b**4*c**3*d**4 - 210*a**2*b**5*c**4*d**3 + 84*a*b**6*c**5*d**2 - 14*b**7*c**6*d))/(2*a**2*b**8 + 4*a*b**9*x + 2*b**10*x**2) + d**7*x**5/(5*b**3) - 21*d**2*(a*d - b*c)**5*log(a + b*x)/b**8","B",0
1286,1,474,0,6.123747," ","integrate((d*x+c)**7/(b*x+a)**4,x)","x^{3} \left(- \frac{4 a d^{7}}{3 b^{5}} + \frac{7 c d^{6}}{3 b^{4}}\right) + x^{2} \left(\frac{5 a^{2} d^{7}}{b^{6}} - \frac{14 a c d^{6}}{b^{5}} + \frac{21 c^{2} d^{5}}{2 b^{4}}\right) + x \left(- \frac{20 a^{3} d^{7}}{b^{7}} + \frac{70 a^{2} c d^{6}}{b^{6}} - \frac{84 a c^{2} d^{5}}{b^{5}} + \frac{35 c^{3} d^{4}}{b^{4}}\right) + \frac{107 a^{7} d^{7} - 518 a^{6} b c d^{6} + 987 a^{5} b^{2} c^{2} d^{5} - 910 a^{4} b^{3} c^{3} d^{4} + 385 a^{3} b^{4} c^{4} d^{3} - 42 a^{2} b^{5} c^{5} d^{2} - 7 a b^{6} c^{6} d - 2 b^{7} c^{7} + x^{2} \left(126 a^{5} b^{2} d^{7} - 630 a^{4} b^{3} c d^{6} + 1260 a^{3} b^{4} c^{2} d^{5} - 1260 a^{2} b^{5} c^{3} d^{4} + 630 a b^{6} c^{4} d^{3} - 126 b^{7} c^{5} d^{2}\right) + x \left(231 a^{6} b d^{7} - 1134 a^{5} b^{2} c d^{6} + 2205 a^{4} b^{3} c^{2} d^{5} - 2100 a^{3} b^{4} c^{3} d^{4} + 945 a^{2} b^{5} c^{4} d^{3} - 126 a b^{6} c^{5} d^{2} - 21 b^{7} c^{6} d\right)}{6 a^{3} b^{8} + 18 a^{2} b^{9} x + 18 a b^{10} x^{2} + 6 b^{11} x^{3}} + \frac{d^{7} x^{4}}{4 b^{4}} + \frac{35 d^{3} \left(a d - b c\right)^{4} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x**3*(-4*a*d**7/(3*b**5) + 7*c*d**6/(3*b**4)) + x**2*(5*a**2*d**7/b**6 - 14*a*c*d**6/b**5 + 21*c**2*d**5/(2*b**4)) + x*(-20*a**3*d**7/b**7 + 70*a**2*c*d**6/b**6 - 84*a*c**2*d**5/b**5 + 35*c**3*d**4/b**4) + (107*a**7*d**7 - 518*a**6*b*c*d**6 + 987*a**5*b**2*c**2*d**5 - 910*a**4*b**3*c**3*d**4 + 385*a**3*b**4*c**4*d**3 - 42*a**2*b**5*c**5*d**2 - 7*a*b**6*c**6*d - 2*b**7*c**7 + x**2*(126*a**5*b**2*d**7 - 630*a**4*b**3*c*d**6 + 1260*a**3*b**4*c**2*d**5 - 1260*a**2*b**5*c**3*d**4 + 630*a*b**6*c**4*d**3 - 126*b**7*c**5*d**2) + x*(231*a**6*b*d**7 - 1134*a**5*b**2*c*d**6 + 2205*a**4*b**3*c**2*d**5 - 2100*a**3*b**4*c**3*d**4 + 945*a**2*b**5*c**4*d**3 - 126*a*b**6*c**5*d**2 - 21*b**7*c**6*d))/(6*a**3*b**8 + 18*a**2*b**9*x + 18*a*b**10*x**2 + 6*b**11*x**3) + d**7*x**4/(4*b**4) + 35*d**3*(a*d - b*c)**4*log(a + b*x)/b**8","B",0
1287,1,500,0,22.438257," ","integrate((d*x+c)**7/(b*x+a)**5,x)","x^{2} \left(- \frac{5 a d^{7}}{2 b^{6}} + \frac{7 c d^{6}}{2 b^{5}}\right) + x \left(\frac{15 a^{2} d^{7}}{b^{7}} - \frac{35 a c d^{6}}{b^{6}} + \frac{21 c^{2} d^{5}}{b^{5}}\right) + \frac{- 319 a^{7} d^{7} + 1197 a^{6} b c d^{6} - 1617 a^{5} b^{2} c^{2} d^{5} + 875 a^{4} b^{3} c^{3} d^{4} - 105 a^{3} b^{4} c^{4} d^{3} - 21 a^{2} b^{5} c^{5} d^{2} - 7 a b^{6} c^{6} d - 3 b^{7} c^{7} + x^{3} \left(- 420 a^{4} b^{3} d^{7} + 1680 a^{3} b^{4} c d^{6} - 2520 a^{2} b^{5} c^{2} d^{5} + 1680 a b^{6} c^{3} d^{4} - 420 b^{7} c^{4} d^{3}\right) + x^{2} \left(- 1134 a^{5} b^{2} d^{7} + 4410 a^{4} b^{3} c d^{6} - 6300 a^{3} b^{4} c^{2} d^{5} + 3780 a^{2} b^{5} c^{3} d^{4} - 630 a b^{6} c^{4} d^{3} - 126 b^{7} c^{5} d^{2}\right) + x \left(- 1036 a^{6} b d^{7} + 3948 a^{5} b^{2} c d^{6} - 5460 a^{4} b^{3} c^{2} d^{5} + 3080 a^{3} b^{4} c^{3} d^{4} - 420 a^{2} b^{5} c^{4} d^{3} - 84 a b^{6} c^{5} d^{2} - 28 b^{7} c^{6} d\right)}{12 a^{4} b^{8} + 48 a^{3} b^{9} x + 72 a^{2} b^{10} x^{2} + 48 a b^{11} x^{3} + 12 b^{12} x^{4}} + \frac{d^{7} x^{3}}{3 b^{5}} - \frac{35 d^{4} \left(a d - b c\right)^{3} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x**2*(-5*a*d**7/(2*b**6) + 7*c*d**6/(2*b**5)) + x*(15*a**2*d**7/b**7 - 35*a*c*d**6/b**6 + 21*c**2*d**5/b**5) + (-319*a**7*d**7 + 1197*a**6*b*c*d**6 - 1617*a**5*b**2*c**2*d**5 + 875*a**4*b**3*c**3*d**4 - 105*a**3*b**4*c**4*d**3 - 21*a**2*b**5*c**5*d**2 - 7*a*b**6*c**6*d - 3*b**7*c**7 + x**3*(-420*a**4*b**3*d**7 + 1680*a**3*b**4*c*d**6 - 2520*a**2*b**5*c**2*d**5 + 1680*a*b**6*c**3*d**4 - 420*b**7*c**4*d**3) + x**2*(-1134*a**5*b**2*d**7 + 4410*a**4*b**3*c*d**6 - 6300*a**3*b**4*c**2*d**5 + 3780*a**2*b**5*c**3*d**4 - 630*a*b**6*c**4*d**3 - 126*b**7*c**5*d**2) + x*(-1036*a**6*b*d**7 + 3948*a**5*b**2*c*d**6 - 5460*a**4*b**3*c**2*d**5 + 3080*a**3*b**4*c**3*d**4 - 420*a**2*b**5*c**4*d**3 - 84*a*b**6*c**5*d**2 - 28*b**7*c**6*d))/(12*a**4*b**8 + 48*a**3*b**9*x + 72*a**2*b**10*x**2 + 48*a*b**11*x**3 + 12*b**12*x**4) + d**7*x**3/(3*b**5) - 35*d**4*(a*d - b*c)**3*log(a + b*x)/b**8","B",0
1288,1,524,0,97.193407," ","integrate((d*x+c)**7/(b*x+a)**6,x)","x \left(- \frac{6 a d^{7}}{b^{7}} + \frac{7 c d^{6}}{b^{6}}\right) + \frac{459 a^{7} d^{7} - 1218 a^{6} b c d^{6} + 959 a^{5} b^{2} c^{2} d^{5} - 140 a^{4} b^{3} c^{3} d^{4} - 35 a^{3} b^{4} c^{4} d^{3} - 14 a^{2} b^{5} c^{5} d^{2} - 7 a b^{6} c^{6} d - 4 b^{7} c^{7} + x^{4} \left(700 a^{3} b^{4} d^{7} - 2100 a^{2} b^{5} c d^{6} + 2100 a b^{6} c^{2} d^{5} - 700 b^{7} c^{3} d^{4}\right) + x^{3} \left(2450 a^{4} b^{3} d^{7} - 7000 a^{3} b^{4} c d^{6} + 6300 a^{2} b^{5} c^{2} d^{5} - 1400 a b^{6} c^{3} d^{4} - 350 b^{7} c^{4} d^{3}\right) + x^{2} \left(3290 a^{5} b^{2} d^{7} - 9100 a^{4} b^{3} c d^{6} + 7700 a^{3} b^{4} c^{2} d^{5} - 1400 a^{2} b^{5} c^{3} d^{4} - 350 a b^{6} c^{4} d^{3} - 140 b^{7} c^{5} d^{2}\right) + x \left(1995 a^{6} b d^{7} - 5390 a^{5} b^{2} c d^{6} + 4375 a^{4} b^{3} c^{2} d^{5} - 700 a^{3} b^{4} c^{3} d^{4} - 175 a^{2} b^{5} c^{4} d^{3} - 70 a b^{6} c^{5} d^{2} - 35 b^{7} c^{6} d\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{d^{7} x^{2}}{2 b^{6}} + \frac{21 d^{5} \left(a d - b c\right)^{2} \log{\left(a + b x \right)}}{b^{8}}"," ",0,"x*(-6*a*d**7/b**7 + 7*c*d**6/b**6) + (459*a**7*d**7 - 1218*a**6*b*c*d**6 + 959*a**5*b**2*c**2*d**5 - 140*a**4*b**3*c**3*d**4 - 35*a**3*b**4*c**4*d**3 - 14*a**2*b**5*c**5*d**2 - 7*a*b**6*c**6*d - 4*b**7*c**7 + x**4*(700*a**3*b**4*d**7 - 2100*a**2*b**5*c*d**6 + 2100*a*b**6*c**2*d**5 - 700*b**7*c**3*d**4) + x**3*(2450*a**4*b**3*d**7 - 7000*a**3*b**4*c*d**6 + 6300*a**2*b**5*c**2*d**5 - 1400*a*b**6*c**3*d**4 - 350*b**7*c**4*d**3) + x**2*(3290*a**5*b**2*d**7 - 9100*a**4*b**3*c*d**6 + 7700*a**3*b**4*c**2*d**5 - 1400*a**2*b**5*c**3*d**4 - 350*a*b**6*c**4*d**3 - 140*b**7*c**5*d**2) + x*(1995*a**6*b*d**7 - 5390*a**5*b**2*c*d**6 + 4375*a**4*b**3*c**2*d**5 - 700*a**3*b**4*c**3*d**4 - 175*a**2*b**5*c**4*d**3 - 70*a*b**6*c**5*d**2 - 35*b**7*c**6*d))/(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) + d**7*x**2/(2*b**6) + 21*d**5*(a*d - b*c)**2*log(a + b*x)/b**8","B",0
1289,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1290,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1291,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1292,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1293,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1294,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**12,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1295,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**13,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1296,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**14,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**15,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((d*x+c)**7/(b*x+a)**16,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,1,2088,0,0.371998," ","integrate((b*x+a)**12*(d*x+c)**10,x)","a^{12} c^{10} x + \frac{b^{12} d^{10} x^{23}}{23} + x^{22} \left(\frac{6 a b^{11} d^{10}}{11} + \frac{5 b^{12} c d^{9}}{11}\right) + x^{21} \left(\frac{22 a^{2} b^{10} d^{10}}{7} + \frac{40 a b^{11} c d^{9}}{7} + \frac{15 b^{12} c^{2} d^{8}}{7}\right) + x^{20} \left(11 a^{3} b^{9} d^{10} + 33 a^{2} b^{10} c d^{9} + 27 a b^{11} c^{2} d^{8} + 6 b^{12} c^{3} d^{7}\right) + x^{19} \left(\frac{495 a^{4} b^{8} d^{10}}{19} + \frac{2200 a^{3} b^{9} c d^{9}}{19} + \frac{2970 a^{2} b^{10} c^{2} d^{8}}{19} + \frac{1440 a b^{11} c^{3} d^{7}}{19} + \frac{210 b^{12} c^{4} d^{6}}{19}\right) + x^{18} \left(44 a^{5} b^{7} d^{10} + 275 a^{4} b^{8} c d^{9} + 550 a^{3} b^{9} c^{2} d^{8} + 440 a^{2} b^{10} c^{3} d^{7} + 140 a b^{11} c^{4} d^{6} + 14 b^{12} c^{5} d^{5}\right) + x^{17} \left(\frac{924 a^{6} b^{6} d^{10}}{17} + \frac{7920 a^{5} b^{7} c d^{9}}{17} + \frac{22275 a^{4} b^{8} c^{2} d^{8}}{17} + \frac{26400 a^{3} b^{9} c^{3} d^{7}}{17} + \frac{13860 a^{2} b^{10} c^{4} d^{6}}{17} + \frac{3024 a b^{11} c^{5} d^{5}}{17} + \frac{210 b^{12} c^{6} d^{4}}{17}\right) + x^{16} \left(\frac{99 a^{7} b^{5} d^{10}}{2} + \frac{1155 a^{6} b^{6} c d^{9}}{2} + \frac{4455 a^{5} b^{7} c^{2} d^{8}}{2} + \frac{7425 a^{4} b^{8} c^{3} d^{7}}{2} + \frac{5775 a^{3} b^{9} c^{4} d^{6}}{2} + \frac{2079 a^{2} b^{10} c^{5} d^{5}}{2} + \frac{315 a b^{11} c^{6} d^{4}}{2} + \frac{15 b^{12} c^{7} d^{3}}{2}\right) + x^{15} \left(33 a^{8} b^{4} d^{10} + 528 a^{7} b^{5} c d^{9} + 2772 a^{6} b^{6} c^{2} d^{8} + 6336 a^{5} b^{7} c^{3} d^{7} + 6930 a^{4} b^{8} c^{4} d^{6} + 3696 a^{3} b^{9} c^{5} d^{5} + 924 a^{2} b^{10} c^{6} d^{4} + 96 a b^{11} c^{7} d^{3} + 3 b^{12} c^{8} d^{2}\right) + x^{14} \left(\frac{110 a^{9} b^{3} d^{10}}{7} + \frac{2475 a^{8} b^{4} c d^{9}}{7} + \frac{17820 a^{7} b^{5} c^{2} d^{8}}{7} + 7920 a^{6} b^{6} c^{3} d^{7} + 11880 a^{5} b^{7} c^{4} d^{6} + 8910 a^{4} b^{8} c^{5} d^{5} + 3300 a^{3} b^{9} c^{6} d^{4} + \frac{3960 a^{2} b^{10} c^{7} d^{3}}{7} + \frac{270 a b^{11} c^{8} d^{2}}{7} + \frac{5 b^{12} c^{9} d}{7}\right) + x^{13} \left(\frac{66 a^{10} b^{2} d^{10}}{13} + \frac{2200 a^{9} b^{3} c d^{9}}{13} + \frac{22275 a^{8} b^{4} c^{2} d^{8}}{13} + \frac{95040 a^{7} b^{5} c^{3} d^{7}}{13} + \frac{194040 a^{6} b^{6} c^{4} d^{6}}{13} + \frac{199584 a^{5} b^{7} c^{5} d^{5}}{13} + \frac{103950 a^{4} b^{8} c^{6} d^{4}}{13} + \frac{26400 a^{3} b^{9} c^{7} d^{3}}{13} + \frac{2970 a^{2} b^{10} c^{8} d^{2}}{13} + \frac{120 a b^{11} c^{9} d}{13} + \frac{b^{12} c^{10}}{13}\right) + x^{12} \left(a^{11} b d^{10} + 55 a^{10} b^{2} c d^{9} + 825 a^{9} b^{3} c^{2} d^{8} + 4950 a^{8} b^{4} c^{3} d^{7} + 13860 a^{7} b^{5} c^{4} d^{6} + 19404 a^{6} b^{6} c^{5} d^{5} + 13860 a^{5} b^{7} c^{6} d^{4} + 4950 a^{4} b^{8} c^{7} d^{3} + 825 a^{3} b^{9} c^{8} d^{2} + 55 a^{2} b^{10} c^{9} d + a b^{11} c^{10}\right) + x^{11} \left(\frac{a^{12} d^{10}}{11} + \frac{120 a^{11} b c d^{9}}{11} + 270 a^{10} b^{2} c^{2} d^{8} + 2400 a^{9} b^{3} c^{3} d^{7} + 9450 a^{8} b^{4} c^{4} d^{6} + 18144 a^{7} b^{5} c^{5} d^{5} + 17640 a^{6} b^{6} c^{6} d^{4} + 8640 a^{5} b^{7} c^{7} d^{3} + 2025 a^{4} b^{8} c^{8} d^{2} + 200 a^{3} b^{9} c^{9} d + 6 a^{2} b^{10} c^{10}\right) + x^{10} \left(a^{12} c d^{9} + 54 a^{11} b c^{2} d^{8} + 792 a^{10} b^{2} c^{3} d^{7} + 4620 a^{9} b^{3} c^{4} d^{6} + 12474 a^{8} b^{4} c^{5} d^{5} + 16632 a^{7} b^{5} c^{6} d^{4} + 11088 a^{6} b^{6} c^{7} d^{3} + 3564 a^{5} b^{7} c^{8} d^{2} + 495 a^{4} b^{8} c^{9} d + 22 a^{3} b^{9} c^{10}\right) + x^{9} \left(5 a^{12} c^{2} d^{8} + 160 a^{11} b c^{3} d^{7} + 1540 a^{10} b^{2} c^{4} d^{6} + 6160 a^{9} b^{3} c^{5} d^{5} + 11550 a^{8} b^{4} c^{6} d^{4} + 10560 a^{7} b^{5} c^{7} d^{3} + 4620 a^{6} b^{6} c^{8} d^{2} + 880 a^{5} b^{7} c^{9} d + 55 a^{4} b^{8} c^{10}\right) + x^{8} \left(15 a^{12} c^{3} d^{7} + 315 a^{11} b c^{4} d^{6} + 2079 a^{10} b^{2} c^{5} d^{5} + 5775 a^{9} b^{3} c^{6} d^{4} + 7425 a^{8} b^{4} c^{7} d^{3} + 4455 a^{7} b^{5} c^{8} d^{2} + 1155 a^{6} b^{6} c^{9} d + 99 a^{5} b^{7} c^{10}\right) + x^{7} \left(30 a^{12} c^{4} d^{6} + 432 a^{11} b c^{5} d^{5} + 1980 a^{10} b^{2} c^{6} d^{4} + \frac{26400 a^{9} b^{3} c^{7} d^{3}}{7} + \frac{22275 a^{8} b^{4} c^{8} d^{2}}{7} + \frac{7920 a^{7} b^{5} c^{9} d}{7} + 132 a^{6} b^{6} c^{10}\right) + x^{6} \left(42 a^{12} c^{5} d^{5} + 420 a^{11} b c^{6} d^{4} + 1320 a^{10} b^{2} c^{7} d^{3} + 1650 a^{9} b^{3} c^{8} d^{2} + 825 a^{8} b^{4} c^{9} d + 132 a^{7} b^{5} c^{10}\right) + x^{5} \left(42 a^{12} c^{6} d^{4} + 288 a^{11} b c^{7} d^{3} + 594 a^{10} b^{2} c^{8} d^{2} + 440 a^{9} b^{3} c^{9} d + 99 a^{8} b^{4} c^{10}\right) + x^{4} \left(30 a^{12} c^{7} d^{3} + 135 a^{11} b c^{8} d^{2} + 165 a^{10} b^{2} c^{9} d + 55 a^{9} b^{3} c^{10}\right) + x^{3} \left(15 a^{12} c^{8} d^{2} + 40 a^{11} b c^{9} d + 22 a^{10} b^{2} c^{10}\right) + x^{2} \left(5 a^{12} c^{9} d + 6 a^{11} b c^{10}\right)"," ",0,"a**12*c**10*x + b**12*d**10*x**23/23 + x**22*(6*a*b**11*d**10/11 + 5*b**12*c*d**9/11) + x**21*(22*a**2*b**10*d**10/7 + 40*a*b**11*c*d**9/7 + 15*b**12*c**2*d**8/7) + x**20*(11*a**3*b**9*d**10 + 33*a**2*b**10*c*d**9 + 27*a*b**11*c**2*d**8 + 6*b**12*c**3*d**7) + x**19*(495*a**4*b**8*d**10/19 + 2200*a**3*b**9*c*d**9/19 + 2970*a**2*b**10*c**2*d**8/19 + 1440*a*b**11*c**3*d**7/19 + 210*b**12*c**4*d**6/19) + x**18*(44*a**5*b**7*d**10 + 275*a**4*b**8*c*d**9 + 550*a**3*b**9*c**2*d**8 + 440*a**2*b**10*c**3*d**7 + 140*a*b**11*c**4*d**6 + 14*b**12*c**5*d**5) + x**17*(924*a**6*b**6*d**10/17 + 7920*a**5*b**7*c*d**9/17 + 22275*a**4*b**8*c**2*d**8/17 + 26400*a**3*b**9*c**3*d**7/17 + 13860*a**2*b**10*c**4*d**6/17 + 3024*a*b**11*c**5*d**5/17 + 210*b**12*c**6*d**4/17) + x**16*(99*a**7*b**5*d**10/2 + 1155*a**6*b**6*c*d**9/2 + 4455*a**5*b**7*c**2*d**8/2 + 7425*a**4*b**8*c**3*d**7/2 + 5775*a**3*b**9*c**4*d**6/2 + 2079*a**2*b**10*c**5*d**5/2 + 315*a*b**11*c**6*d**4/2 + 15*b**12*c**7*d**3/2) + x**15*(33*a**8*b**4*d**10 + 528*a**7*b**5*c*d**9 + 2772*a**6*b**6*c**2*d**8 + 6336*a**5*b**7*c**3*d**7 + 6930*a**4*b**8*c**4*d**6 + 3696*a**3*b**9*c**5*d**5 + 924*a**2*b**10*c**6*d**4 + 96*a*b**11*c**7*d**3 + 3*b**12*c**8*d**2) + x**14*(110*a**9*b**3*d**10/7 + 2475*a**8*b**4*c*d**9/7 + 17820*a**7*b**5*c**2*d**8/7 + 7920*a**6*b**6*c**3*d**7 + 11880*a**5*b**7*c**4*d**6 + 8910*a**4*b**8*c**5*d**5 + 3300*a**3*b**9*c**6*d**4 + 3960*a**2*b**10*c**7*d**3/7 + 270*a*b**11*c**8*d**2/7 + 5*b**12*c**9*d/7) + x**13*(66*a**10*b**2*d**10/13 + 2200*a**9*b**3*c*d**9/13 + 22275*a**8*b**4*c**2*d**8/13 + 95040*a**7*b**5*c**3*d**7/13 + 194040*a**6*b**6*c**4*d**6/13 + 199584*a**5*b**7*c**5*d**5/13 + 103950*a**4*b**8*c**6*d**4/13 + 26400*a**3*b**9*c**7*d**3/13 + 2970*a**2*b**10*c**8*d**2/13 + 120*a*b**11*c**9*d/13 + b**12*c**10/13) + x**12*(a**11*b*d**10 + 55*a**10*b**2*c*d**9 + 825*a**9*b**3*c**2*d**8 + 4950*a**8*b**4*c**3*d**7 + 13860*a**7*b**5*c**4*d**6 + 19404*a**6*b**6*c**5*d**5 + 13860*a**5*b**7*c**6*d**4 + 4950*a**4*b**8*c**7*d**3 + 825*a**3*b**9*c**8*d**2 + 55*a**2*b**10*c**9*d + a*b**11*c**10) + x**11*(a**12*d**10/11 + 120*a**11*b*c*d**9/11 + 270*a**10*b**2*c**2*d**8 + 2400*a**9*b**3*c**3*d**7 + 9450*a**8*b**4*c**4*d**6 + 18144*a**7*b**5*c**5*d**5 + 17640*a**6*b**6*c**6*d**4 + 8640*a**5*b**7*c**7*d**3 + 2025*a**4*b**8*c**8*d**2 + 200*a**3*b**9*c**9*d + 6*a**2*b**10*c**10) + x**10*(a**12*c*d**9 + 54*a**11*b*c**2*d**8 + 792*a**10*b**2*c**3*d**7 + 4620*a**9*b**3*c**4*d**6 + 12474*a**8*b**4*c**5*d**5 + 16632*a**7*b**5*c**6*d**4 + 11088*a**6*b**6*c**7*d**3 + 3564*a**5*b**7*c**8*d**2 + 495*a**4*b**8*c**9*d + 22*a**3*b**9*c**10) + x**9*(5*a**12*c**2*d**8 + 160*a**11*b*c**3*d**7 + 1540*a**10*b**2*c**4*d**6 + 6160*a**9*b**3*c**5*d**5 + 11550*a**8*b**4*c**6*d**4 + 10560*a**7*b**5*c**7*d**3 + 4620*a**6*b**6*c**8*d**2 + 880*a**5*b**7*c**9*d + 55*a**4*b**8*c**10) + x**8*(15*a**12*c**3*d**7 + 315*a**11*b*c**4*d**6 + 2079*a**10*b**2*c**5*d**5 + 5775*a**9*b**3*c**6*d**4 + 7425*a**8*b**4*c**7*d**3 + 4455*a**7*b**5*c**8*d**2 + 1155*a**6*b**6*c**9*d + 99*a**5*b**7*c**10) + x**7*(30*a**12*c**4*d**6 + 432*a**11*b*c**5*d**5 + 1980*a**10*b**2*c**6*d**4 + 26400*a**9*b**3*c**7*d**3/7 + 22275*a**8*b**4*c**8*d**2/7 + 7920*a**7*b**5*c**9*d/7 + 132*a**6*b**6*c**10) + x**6*(42*a**12*c**5*d**5 + 420*a**11*b*c**6*d**4 + 1320*a**10*b**2*c**7*d**3 + 1650*a**9*b**3*c**8*d**2 + 825*a**8*b**4*c**9*d + 132*a**7*b**5*c**10) + x**5*(42*a**12*c**6*d**4 + 288*a**11*b*c**7*d**3 + 594*a**10*b**2*c**8*d**2 + 440*a**9*b**3*c**9*d + 99*a**8*b**4*c**10) + x**4*(30*a**12*c**7*d**3 + 135*a**11*b*c**8*d**2 + 165*a**10*b**2*c**9*d + 55*a**9*b**3*c**10) + x**3*(15*a**12*c**8*d**2 + 40*a**11*b*c**9*d + 22*a**10*b**2*c**10) + x**2*(5*a**12*c**9*d + 6*a**11*b*c**10)","B",0
1300,1,1965,0,0.343579," ","integrate((b*x+a)**11*(d*x+c)**10,x)","a^{11} c^{10} x + \frac{b^{11} d^{10} x^{22}}{22} + x^{21} \left(\frac{11 a b^{10} d^{10}}{21} + \frac{10 b^{11} c d^{9}}{21}\right) + x^{20} \left(\frac{11 a^{2} b^{9} d^{10}}{4} + \frac{11 a b^{10} c d^{9}}{2} + \frac{9 b^{11} c^{2} d^{8}}{4}\right) + x^{19} \left(\frac{165 a^{3} b^{8} d^{10}}{19} + \frac{550 a^{2} b^{9} c d^{9}}{19} + \frac{495 a b^{10} c^{2} d^{8}}{19} + \frac{120 b^{11} c^{3} d^{7}}{19}\right) + x^{18} \left(\frac{55 a^{4} b^{7} d^{10}}{3} + \frac{275 a^{3} b^{8} c d^{9}}{3} + \frac{275 a^{2} b^{9} c^{2} d^{8}}{2} + \frac{220 a b^{10} c^{3} d^{7}}{3} + \frac{35 b^{11} c^{4} d^{6}}{3}\right) + x^{17} \left(\frac{462 a^{5} b^{6} d^{10}}{17} + \frac{3300 a^{4} b^{7} c d^{9}}{17} + \frac{7425 a^{3} b^{8} c^{2} d^{8}}{17} + \frac{6600 a^{2} b^{9} c^{3} d^{7}}{17} + \frac{2310 a b^{10} c^{4} d^{6}}{17} + \frac{252 b^{11} c^{5} d^{5}}{17}\right) + x^{16} \left(\frac{231 a^{6} b^{5} d^{10}}{8} + \frac{1155 a^{5} b^{6} c d^{9}}{4} + \frac{7425 a^{4} b^{7} c^{2} d^{8}}{8} + \frac{2475 a^{3} b^{8} c^{3} d^{7}}{2} + \frac{5775 a^{2} b^{9} c^{4} d^{6}}{8} + \frac{693 a b^{10} c^{5} d^{5}}{4} + \frac{105 b^{11} c^{6} d^{4}}{8}\right) + x^{15} \left(22 a^{7} b^{4} d^{10} + 308 a^{6} b^{5} c d^{9} + 1386 a^{5} b^{6} c^{2} d^{8} + 2640 a^{4} b^{7} c^{3} d^{7} + 2310 a^{3} b^{8} c^{4} d^{6} + 924 a^{2} b^{9} c^{5} d^{5} + 154 a b^{10} c^{6} d^{4} + 8 b^{11} c^{7} d^{3}\right) + x^{14} \left(\frac{165 a^{8} b^{3} d^{10}}{14} + \frac{1650 a^{7} b^{4} c d^{9}}{7} + 1485 a^{6} b^{5} c^{2} d^{8} + 3960 a^{5} b^{6} c^{3} d^{7} + 4950 a^{4} b^{7} c^{4} d^{6} + 2970 a^{3} b^{8} c^{5} d^{5} + 825 a^{2} b^{9} c^{6} d^{4} + \frac{660 a b^{10} c^{7} d^{3}}{7} + \frac{45 b^{11} c^{8} d^{2}}{14}\right) + x^{13} \left(\frac{55 a^{9} b^{2} d^{10}}{13} + \frac{1650 a^{8} b^{3} c d^{9}}{13} + \frac{14850 a^{7} b^{4} c^{2} d^{8}}{13} + \frac{55440 a^{6} b^{5} c^{3} d^{7}}{13} + \frac{97020 a^{5} b^{6} c^{4} d^{6}}{13} + \frac{83160 a^{4} b^{7} c^{5} d^{5}}{13} + \frac{34650 a^{3} b^{8} c^{6} d^{4}}{13} + \frac{6600 a^{2} b^{9} c^{7} d^{3}}{13} + \frac{495 a b^{10} c^{8} d^{2}}{13} + \frac{10 b^{11} c^{9} d}{13}\right) + x^{12} \left(\frac{11 a^{10} b d^{10}}{12} + \frac{275 a^{9} b^{2} c d^{9}}{6} + \frac{2475 a^{8} b^{3} c^{2} d^{8}}{4} + 3300 a^{7} b^{4} c^{3} d^{7} + 8085 a^{6} b^{5} c^{4} d^{6} + 9702 a^{5} b^{6} c^{5} d^{5} + 5775 a^{4} b^{7} c^{6} d^{4} + 1650 a^{3} b^{8} c^{7} d^{3} + \frac{825 a^{2} b^{9} c^{8} d^{2}}{4} + \frac{55 a b^{10} c^{9} d}{6} + \frac{b^{11} c^{10}}{12}\right) + x^{11} \left(\frac{a^{11} d^{10}}{11} + 10 a^{10} b c d^{9} + 225 a^{9} b^{2} c^{2} d^{8} + 1800 a^{8} b^{3} c^{3} d^{7} + 6300 a^{7} b^{4} c^{4} d^{6} + 10584 a^{6} b^{5} c^{5} d^{5} + 8820 a^{5} b^{6} c^{6} d^{4} + 3600 a^{4} b^{7} c^{7} d^{3} + 675 a^{3} b^{8} c^{8} d^{2} + 50 a^{2} b^{9} c^{9} d + a b^{10} c^{10}\right) + x^{10} \left(a^{11} c d^{9} + \frac{99 a^{10} b c^{2} d^{8}}{2} + 660 a^{9} b^{2} c^{3} d^{7} + 3465 a^{8} b^{3} c^{4} d^{6} + 8316 a^{7} b^{4} c^{5} d^{5} + 9702 a^{6} b^{5} c^{6} d^{4} + 5544 a^{5} b^{6} c^{7} d^{3} + 1485 a^{4} b^{7} c^{8} d^{2} + 165 a^{3} b^{8} c^{9} d + \frac{11 a^{2} b^{9} c^{10}}{2}\right) + x^{9} \left(5 a^{11} c^{2} d^{8} + \frac{440 a^{10} b c^{3} d^{7}}{3} + \frac{3850 a^{9} b^{2} c^{4} d^{6}}{3} + 4620 a^{8} b^{3} c^{5} d^{5} + 7700 a^{7} b^{4} c^{6} d^{4} + 6160 a^{6} b^{5} c^{7} d^{3} + 2310 a^{5} b^{6} c^{8} d^{2} + \frac{1100 a^{4} b^{7} c^{9} d}{3} + \frac{55 a^{3} b^{8} c^{10}}{3}\right) + x^{8} \left(15 a^{11} c^{3} d^{7} + \frac{1155 a^{10} b c^{4} d^{6}}{4} + \frac{3465 a^{9} b^{2} c^{5} d^{5}}{2} + \frac{17325 a^{8} b^{3} c^{6} d^{4}}{4} + 4950 a^{7} b^{4} c^{7} d^{3} + \frac{10395 a^{6} b^{5} c^{8} d^{2}}{4} + \frac{1155 a^{5} b^{6} c^{9} d}{2} + \frac{165 a^{4} b^{7} c^{10}}{4}\right) + x^{7} \left(30 a^{11} c^{4} d^{6} + 396 a^{10} b c^{5} d^{5} + 1650 a^{9} b^{2} c^{6} d^{4} + \frac{19800 a^{8} b^{3} c^{7} d^{3}}{7} + \frac{14850 a^{7} b^{4} c^{8} d^{2}}{7} + 660 a^{6} b^{5} c^{9} d + 66 a^{5} b^{6} c^{10}\right) + x^{6} \left(42 a^{11} c^{5} d^{5} + 385 a^{10} b c^{6} d^{4} + 1100 a^{9} b^{2} c^{7} d^{3} + \frac{2475 a^{8} b^{3} c^{8} d^{2}}{2} + 550 a^{7} b^{4} c^{9} d + 77 a^{6} b^{5} c^{10}\right) + x^{5} \left(42 a^{11} c^{6} d^{4} + 264 a^{10} b c^{7} d^{3} + 495 a^{9} b^{2} c^{8} d^{2} + 330 a^{8} b^{3} c^{9} d + 66 a^{7} b^{4} c^{10}\right) + x^{4} \left(30 a^{11} c^{7} d^{3} + \frac{495 a^{10} b c^{8} d^{2}}{4} + \frac{275 a^{9} b^{2} c^{9} d}{2} + \frac{165 a^{8} b^{3} c^{10}}{4}\right) + x^{3} \left(15 a^{11} c^{8} d^{2} + \frac{110 a^{10} b c^{9} d}{3} + \frac{55 a^{9} b^{2} c^{10}}{3}\right) + x^{2} \left(5 a^{11} c^{9} d + \frac{11 a^{10} b c^{10}}{2}\right)"," ",0,"a**11*c**10*x + b**11*d**10*x**22/22 + x**21*(11*a*b**10*d**10/21 + 10*b**11*c*d**9/21) + x**20*(11*a**2*b**9*d**10/4 + 11*a*b**10*c*d**9/2 + 9*b**11*c**2*d**8/4) + x**19*(165*a**3*b**8*d**10/19 + 550*a**2*b**9*c*d**9/19 + 495*a*b**10*c**2*d**8/19 + 120*b**11*c**3*d**7/19) + x**18*(55*a**4*b**7*d**10/3 + 275*a**3*b**8*c*d**9/3 + 275*a**2*b**9*c**2*d**8/2 + 220*a*b**10*c**3*d**7/3 + 35*b**11*c**4*d**6/3) + x**17*(462*a**5*b**6*d**10/17 + 3300*a**4*b**7*c*d**9/17 + 7425*a**3*b**8*c**2*d**8/17 + 6600*a**2*b**9*c**3*d**7/17 + 2310*a*b**10*c**4*d**6/17 + 252*b**11*c**5*d**5/17) + x**16*(231*a**6*b**5*d**10/8 + 1155*a**5*b**6*c*d**9/4 + 7425*a**4*b**7*c**2*d**8/8 + 2475*a**3*b**8*c**3*d**7/2 + 5775*a**2*b**9*c**4*d**6/8 + 693*a*b**10*c**5*d**5/4 + 105*b**11*c**6*d**4/8) + x**15*(22*a**7*b**4*d**10 + 308*a**6*b**5*c*d**9 + 1386*a**5*b**6*c**2*d**8 + 2640*a**4*b**7*c**3*d**7 + 2310*a**3*b**8*c**4*d**6 + 924*a**2*b**9*c**5*d**5 + 154*a*b**10*c**6*d**4 + 8*b**11*c**7*d**3) + x**14*(165*a**8*b**3*d**10/14 + 1650*a**7*b**4*c*d**9/7 + 1485*a**6*b**5*c**2*d**8 + 3960*a**5*b**6*c**3*d**7 + 4950*a**4*b**7*c**4*d**6 + 2970*a**3*b**8*c**5*d**5 + 825*a**2*b**9*c**6*d**4 + 660*a*b**10*c**7*d**3/7 + 45*b**11*c**8*d**2/14) + x**13*(55*a**9*b**2*d**10/13 + 1650*a**8*b**3*c*d**9/13 + 14850*a**7*b**4*c**2*d**8/13 + 55440*a**6*b**5*c**3*d**7/13 + 97020*a**5*b**6*c**4*d**6/13 + 83160*a**4*b**7*c**5*d**5/13 + 34650*a**3*b**8*c**6*d**4/13 + 6600*a**2*b**9*c**7*d**3/13 + 495*a*b**10*c**8*d**2/13 + 10*b**11*c**9*d/13) + x**12*(11*a**10*b*d**10/12 + 275*a**9*b**2*c*d**9/6 + 2475*a**8*b**3*c**2*d**8/4 + 3300*a**7*b**4*c**3*d**7 + 8085*a**6*b**5*c**4*d**6 + 9702*a**5*b**6*c**5*d**5 + 5775*a**4*b**7*c**6*d**4 + 1650*a**3*b**8*c**7*d**3 + 825*a**2*b**9*c**8*d**2/4 + 55*a*b**10*c**9*d/6 + b**11*c**10/12) + x**11*(a**11*d**10/11 + 10*a**10*b*c*d**9 + 225*a**9*b**2*c**2*d**8 + 1800*a**8*b**3*c**3*d**7 + 6300*a**7*b**4*c**4*d**6 + 10584*a**6*b**5*c**5*d**5 + 8820*a**5*b**6*c**6*d**4 + 3600*a**4*b**7*c**7*d**3 + 675*a**3*b**8*c**8*d**2 + 50*a**2*b**9*c**9*d + a*b**10*c**10) + x**10*(a**11*c*d**9 + 99*a**10*b*c**2*d**8/2 + 660*a**9*b**2*c**3*d**7 + 3465*a**8*b**3*c**4*d**6 + 8316*a**7*b**4*c**5*d**5 + 9702*a**6*b**5*c**6*d**4 + 5544*a**5*b**6*c**7*d**3 + 1485*a**4*b**7*c**8*d**2 + 165*a**3*b**8*c**9*d + 11*a**2*b**9*c**10/2) + x**9*(5*a**11*c**2*d**8 + 440*a**10*b*c**3*d**7/3 + 3850*a**9*b**2*c**4*d**6/3 + 4620*a**8*b**3*c**5*d**5 + 7700*a**7*b**4*c**6*d**4 + 6160*a**6*b**5*c**7*d**3 + 2310*a**5*b**6*c**8*d**2 + 1100*a**4*b**7*c**9*d/3 + 55*a**3*b**8*c**10/3) + x**8*(15*a**11*c**3*d**7 + 1155*a**10*b*c**4*d**6/4 + 3465*a**9*b**2*c**5*d**5/2 + 17325*a**8*b**3*c**6*d**4/4 + 4950*a**7*b**4*c**7*d**3 + 10395*a**6*b**5*c**8*d**2/4 + 1155*a**5*b**6*c**9*d/2 + 165*a**4*b**7*c**10/4) + x**7*(30*a**11*c**4*d**6 + 396*a**10*b*c**5*d**5 + 1650*a**9*b**2*c**6*d**4 + 19800*a**8*b**3*c**7*d**3/7 + 14850*a**7*b**4*c**8*d**2/7 + 660*a**6*b**5*c**9*d + 66*a**5*b**6*c**10) + x**6*(42*a**11*c**5*d**5 + 385*a**10*b*c**6*d**4 + 1100*a**9*b**2*c**7*d**3 + 2475*a**8*b**3*c**8*d**2/2 + 550*a**7*b**4*c**9*d + 77*a**6*b**5*c**10) + x**5*(42*a**11*c**6*d**4 + 264*a**10*b*c**7*d**3 + 495*a**9*b**2*c**8*d**2 + 330*a**8*b**3*c**9*d + 66*a**7*b**4*c**10) + x**4*(30*a**11*c**7*d**3 + 495*a**10*b*c**8*d**2/4 + 275*a**9*b**2*c**9*d/2 + 165*a**8*b**3*c**10/4) + x**3*(15*a**11*c**8*d**2 + 110*a**10*b*c**9*d/3 + 55*a**9*b**2*c**10/3) + x**2*(5*a**11*c**9*d + 11*a**10*b*c**10/2)","B",0
1301,1,1775,0,0.312515," ","integrate((b*x+a)**10*(d*x+c)**10,x)","a^{10} c^{10} x + \frac{b^{10} d^{10} x^{21}}{21} + x^{20} \left(\frac{a b^{9} d^{10}}{2} + \frac{b^{10} c d^{9}}{2}\right) + x^{19} \left(\frac{45 a^{2} b^{8} d^{10}}{19} + \frac{100 a b^{9} c d^{9}}{19} + \frac{45 b^{10} c^{2} d^{8}}{19}\right) + x^{18} \left(\frac{20 a^{3} b^{7} d^{10}}{3} + 25 a^{2} b^{8} c d^{9} + 25 a b^{9} c^{2} d^{8} + \frac{20 b^{10} c^{3} d^{7}}{3}\right) + x^{17} \left(\frac{210 a^{4} b^{6} d^{10}}{17} + \frac{1200 a^{3} b^{7} c d^{9}}{17} + \frac{2025 a^{2} b^{8} c^{2} d^{8}}{17} + \frac{1200 a b^{9} c^{3} d^{7}}{17} + \frac{210 b^{10} c^{4} d^{6}}{17}\right) + x^{16} \left(\frac{63 a^{5} b^{5} d^{10}}{4} + \frac{525 a^{4} b^{6} c d^{9}}{4} + \frac{675 a^{3} b^{7} c^{2} d^{8}}{2} + \frac{675 a^{2} b^{8} c^{3} d^{7}}{2} + \frac{525 a b^{9} c^{4} d^{6}}{4} + \frac{63 b^{10} c^{5} d^{5}}{4}\right) + x^{15} \left(14 a^{6} b^{4} d^{10} + 168 a^{5} b^{5} c d^{9} + 630 a^{4} b^{6} c^{2} d^{8} + 960 a^{3} b^{7} c^{3} d^{7} + 630 a^{2} b^{8} c^{4} d^{6} + 168 a b^{9} c^{5} d^{5} + 14 b^{10} c^{6} d^{4}\right) + x^{14} \left(\frac{60 a^{7} b^{3} d^{10}}{7} + 150 a^{6} b^{4} c d^{9} + 810 a^{5} b^{5} c^{2} d^{8} + 1800 a^{4} b^{6} c^{3} d^{7} + 1800 a^{3} b^{7} c^{4} d^{6} + 810 a^{2} b^{8} c^{5} d^{5} + 150 a b^{9} c^{6} d^{4} + \frac{60 b^{10} c^{7} d^{3}}{7}\right) + x^{13} \left(\frac{45 a^{8} b^{2} d^{10}}{13} + \frac{1200 a^{7} b^{3} c d^{9}}{13} + \frac{9450 a^{6} b^{4} c^{2} d^{8}}{13} + \frac{30240 a^{5} b^{5} c^{3} d^{7}}{13} + \frac{44100 a^{4} b^{6} c^{4} d^{6}}{13} + \frac{30240 a^{3} b^{7} c^{5} d^{5}}{13} + \frac{9450 a^{2} b^{8} c^{6} d^{4}}{13} + \frac{1200 a b^{9} c^{7} d^{3}}{13} + \frac{45 b^{10} c^{8} d^{2}}{13}\right) + x^{12} \left(\frac{5 a^{9} b d^{10}}{6} + \frac{75 a^{8} b^{2} c d^{9}}{2} + 450 a^{7} b^{3} c^{2} d^{8} + 2100 a^{6} b^{4} c^{3} d^{7} + 4410 a^{5} b^{5} c^{4} d^{6} + 4410 a^{4} b^{6} c^{5} d^{5} + 2100 a^{3} b^{7} c^{6} d^{4} + 450 a^{2} b^{8} c^{7} d^{3} + \frac{75 a b^{9} c^{8} d^{2}}{2} + \frac{5 b^{10} c^{9} d}{6}\right) + x^{11} \left(\frac{a^{10} d^{10}}{11} + \frac{100 a^{9} b c d^{9}}{11} + \frac{2025 a^{8} b^{2} c^{2} d^{8}}{11} + \frac{14400 a^{7} b^{3} c^{3} d^{7}}{11} + \frac{44100 a^{6} b^{4} c^{4} d^{6}}{11} + \frac{63504 a^{5} b^{5} c^{5} d^{5}}{11} + \frac{44100 a^{4} b^{6} c^{6} d^{4}}{11} + \frac{14400 a^{3} b^{7} c^{7} d^{3}}{11} + \frac{2025 a^{2} b^{8} c^{8} d^{2}}{11} + \frac{100 a b^{9} c^{9} d}{11} + \frac{b^{10} c^{10}}{11}\right) + x^{10} \left(a^{10} c d^{9} + 45 a^{9} b c^{2} d^{8} + 540 a^{8} b^{2} c^{3} d^{7} + 2520 a^{7} b^{3} c^{4} d^{6} + 5292 a^{6} b^{4} c^{5} d^{5} + 5292 a^{5} b^{5} c^{6} d^{4} + 2520 a^{4} b^{6} c^{7} d^{3} + 540 a^{3} b^{7} c^{8} d^{2} + 45 a^{2} b^{8} c^{9} d + a b^{9} c^{10}\right) + x^{9} \left(5 a^{10} c^{2} d^{8} + \frac{400 a^{9} b c^{3} d^{7}}{3} + 1050 a^{8} b^{2} c^{4} d^{6} + 3360 a^{7} b^{3} c^{5} d^{5} + 4900 a^{6} b^{4} c^{6} d^{4} + 3360 a^{5} b^{5} c^{7} d^{3} + 1050 a^{4} b^{6} c^{8} d^{2} + \frac{400 a^{3} b^{7} c^{9} d}{3} + 5 a^{2} b^{8} c^{10}\right) + x^{8} \left(15 a^{10} c^{3} d^{7} + \frac{525 a^{9} b c^{4} d^{6}}{2} + \frac{2835 a^{8} b^{2} c^{5} d^{5}}{2} + 3150 a^{7} b^{3} c^{6} d^{4} + 3150 a^{6} b^{4} c^{7} d^{3} + \frac{2835 a^{5} b^{5} c^{8} d^{2}}{2} + \frac{525 a^{4} b^{6} c^{9} d}{2} + 15 a^{3} b^{7} c^{10}\right) + x^{7} \left(30 a^{10} c^{4} d^{6} + 360 a^{9} b c^{5} d^{5} + 1350 a^{8} b^{2} c^{6} d^{4} + \frac{14400 a^{7} b^{3} c^{7} d^{3}}{7} + 1350 a^{6} b^{4} c^{8} d^{2} + 360 a^{5} b^{5} c^{9} d + 30 a^{4} b^{6} c^{10}\right) + x^{6} \left(42 a^{10} c^{5} d^{5} + 350 a^{9} b c^{6} d^{4} + 900 a^{8} b^{2} c^{7} d^{3} + 900 a^{7} b^{3} c^{8} d^{2} + 350 a^{6} b^{4} c^{9} d + 42 a^{5} b^{5} c^{10}\right) + x^{5} \left(42 a^{10} c^{6} d^{4} + 240 a^{9} b c^{7} d^{3} + 405 a^{8} b^{2} c^{8} d^{2} + 240 a^{7} b^{3} c^{9} d + 42 a^{6} b^{4} c^{10}\right) + x^{4} \left(30 a^{10} c^{7} d^{3} + \frac{225 a^{9} b c^{8} d^{2}}{2} + \frac{225 a^{8} b^{2} c^{9} d}{2} + 30 a^{7} b^{3} c^{10}\right) + x^{3} \left(15 a^{10} c^{8} d^{2} + \frac{100 a^{9} b c^{9} d}{3} + 15 a^{8} b^{2} c^{10}\right) + x^{2} \left(5 a^{10} c^{9} d + 5 a^{9} b c^{10}\right)"," ",0,"a**10*c**10*x + b**10*d**10*x**21/21 + x**20*(a*b**9*d**10/2 + b**10*c*d**9/2) + x**19*(45*a**2*b**8*d**10/19 + 100*a*b**9*c*d**9/19 + 45*b**10*c**2*d**8/19) + x**18*(20*a**3*b**7*d**10/3 + 25*a**2*b**8*c*d**9 + 25*a*b**9*c**2*d**8 + 20*b**10*c**3*d**7/3) + x**17*(210*a**4*b**6*d**10/17 + 1200*a**3*b**7*c*d**9/17 + 2025*a**2*b**8*c**2*d**8/17 + 1200*a*b**9*c**3*d**7/17 + 210*b**10*c**4*d**6/17) + x**16*(63*a**5*b**5*d**10/4 + 525*a**4*b**6*c*d**9/4 + 675*a**3*b**7*c**2*d**8/2 + 675*a**2*b**8*c**3*d**7/2 + 525*a*b**9*c**4*d**6/4 + 63*b**10*c**5*d**5/4) + x**15*(14*a**6*b**4*d**10 + 168*a**5*b**5*c*d**9 + 630*a**4*b**6*c**2*d**8 + 960*a**3*b**7*c**3*d**7 + 630*a**2*b**8*c**4*d**6 + 168*a*b**9*c**5*d**5 + 14*b**10*c**6*d**4) + x**14*(60*a**7*b**3*d**10/7 + 150*a**6*b**4*c*d**9 + 810*a**5*b**5*c**2*d**8 + 1800*a**4*b**6*c**3*d**7 + 1800*a**3*b**7*c**4*d**6 + 810*a**2*b**8*c**5*d**5 + 150*a*b**9*c**6*d**4 + 60*b**10*c**7*d**3/7) + x**13*(45*a**8*b**2*d**10/13 + 1200*a**7*b**3*c*d**9/13 + 9450*a**6*b**4*c**2*d**8/13 + 30240*a**5*b**5*c**3*d**7/13 + 44100*a**4*b**6*c**4*d**6/13 + 30240*a**3*b**7*c**5*d**5/13 + 9450*a**2*b**8*c**6*d**4/13 + 1200*a*b**9*c**7*d**3/13 + 45*b**10*c**8*d**2/13) + x**12*(5*a**9*b*d**10/6 + 75*a**8*b**2*c*d**9/2 + 450*a**7*b**3*c**2*d**8 + 2100*a**6*b**4*c**3*d**7 + 4410*a**5*b**5*c**4*d**6 + 4410*a**4*b**6*c**5*d**5 + 2100*a**3*b**7*c**6*d**4 + 450*a**2*b**8*c**7*d**3 + 75*a*b**9*c**8*d**2/2 + 5*b**10*c**9*d/6) + x**11*(a**10*d**10/11 + 100*a**9*b*c*d**9/11 + 2025*a**8*b**2*c**2*d**8/11 + 14400*a**7*b**3*c**3*d**7/11 + 44100*a**6*b**4*c**4*d**6/11 + 63504*a**5*b**5*c**5*d**5/11 + 44100*a**4*b**6*c**6*d**4/11 + 14400*a**3*b**7*c**7*d**3/11 + 2025*a**2*b**8*c**8*d**2/11 + 100*a*b**9*c**9*d/11 + b**10*c**10/11) + x**10*(a**10*c*d**9 + 45*a**9*b*c**2*d**8 + 540*a**8*b**2*c**3*d**7 + 2520*a**7*b**3*c**4*d**6 + 5292*a**6*b**4*c**5*d**5 + 5292*a**5*b**5*c**6*d**4 + 2520*a**4*b**6*c**7*d**3 + 540*a**3*b**7*c**8*d**2 + 45*a**2*b**8*c**9*d + a*b**9*c**10) + x**9*(5*a**10*c**2*d**8 + 400*a**9*b*c**3*d**7/3 + 1050*a**8*b**2*c**4*d**6 + 3360*a**7*b**3*c**5*d**5 + 4900*a**6*b**4*c**6*d**4 + 3360*a**5*b**5*c**7*d**3 + 1050*a**4*b**6*c**8*d**2 + 400*a**3*b**7*c**9*d/3 + 5*a**2*b**8*c**10) + x**8*(15*a**10*c**3*d**7 + 525*a**9*b*c**4*d**6/2 + 2835*a**8*b**2*c**5*d**5/2 + 3150*a**7*b**3*c**6*d**4 + 3150*a**6*b**4*c**7*d**3 + 2835*a**5*b**5*c**8*d**2/2 + 525*a**4*b**6*c**9*d/2 + 15*a**3*b**7*c**10) + x**7*(30*a**10*c**4*d**6 + 360*a**9*b*c**5*d**5 + 1350*a**8*b**2*c**6*d**4 + 14400*a**7*b**3*c**7*d**3/7 + 1350*a**6*b**4*c**8*d**2 + 360*a**5*b**5*c**9*d + 30*a**4*b**6*c**10) + x**6*(42*a**10*c**5*d**5 + 350*a**9*b*c**6*d**4 + 900*a**8*b**2*c**7*d**3 + 900*a**7*b**3*c**8*d**2 + 350*a**6*b**4*c**9*d + 42*a**5*b**5*c**10) + x**5*(42*a**10*c**6*d**4 + 240*a**9*b*c**7*d**3 + 405*a**8*b**2*c**8*d**2 + 240*a**7*b**3*c**9*d + 42*a**6*b**4*c**10) + x**4*(30*a**10*c**7*d**3 + 225*a**9*b*c**8*d**2/2 + 225*a**8*b**2*c**9*d/2 + 30*a**7*b**3*c**10) + x**3*(15*a**10*c**8*d**2 + 100*a**9*b*c**9*d/3 + 15*a**8*b**2*c**10) + x**2*(5*a**10*c**9*d + 5*a**9*b*c**10)","B",0
1302,1,1598,0,0.295817," ","integrate((b*x+a)**9*(d*x+c)**10,x)","a^{9} c^{10} x + \frac{b^{9} d^{10} x^{20}}{20} + x^{19} \left(\frac{9 a b^{8} d^{10}}{19} + \frac{10 b^{9} c d^{9}}{19}\right) + x^{18} \left(2 a^{2} b^{7} d^{10} + 5 a b^{8} c d^{9} + \frac{5 b^{9} c^{2} d^{8}}{2}\right) + x^{17} \left(\frac{84 a^{3} b^{6} d^{10}}{17} + \frac{360 a^{2} b^{7} c d^{9}}{17} + \frac{405 a b^{8} c^{2} d^{8}}{17} + \frac{120 b^{9} c^{3} d^{7}}{17}\right) + x^{16} \left(\frac{63 a^{4} b^{5} d^{10}}{8} + \frac{105 a^{3} b^{6} c d^{9}}{2} + \frac{405 a^{2} b^{7} c^{2} d^{8}}{4} + \frac{135 a b^{8} c^{3} d^{7}}{2} + \frac{105 b^{9} c^{4} d^{6}}{8}\right) + x^{15} \left(\frac{42 a^{5} b^{4} d^{10}}{5} + 84 a^{4} b^{5} c d^{9} + 252 a^{3} b^{6} c^{2} d^{8} + 288 a^{2} b^{7} c^{3} d^{7} + 126 a b^{8} c^{4} d^{6} + \frac{84 b^{9} c^{5} d^{5}}{5}\right) + x^{14} \left(6 a^{6} b^{3} d^{10} + 90 a^{5} b^{4} c d^{9} + 405 a^{4} b^{5} c^{2} d^{8} + 720 a^{3} b^{6} c^{3} d^{7} + 540 a^{2} b^{7} c^{4} d^{6} + 162 a b^{8} c^{5} d^{5} + 15 b^{9} c^{6} d^{4}\right) + x^{13} \left(\frac{36 a^{7} b^{2} d^{10}}{13} + \frac{840 a^{6} b^{3} c d^{9}}{13} + \frac{5670 a^{5} b^{4} c^{2} d^{8}}{13} + \frac{15120 a^{4} b^{5} c^{3} d^{7}}{13} + \frac{17640 a^{3} b^{6} c^{4} d^{6}}{13} + \frac{9072 a^{2} b^{7} c^{5} d^{5}}{13} + \frac{1890 a b^{8} c^{6} d^{4}}{13} + \frac{120 b^{9} c^{7} d^{3}}{13}\right) + x^{12} \left(\frac{3 a^{8} b d^{10}}{4} + 30 a^{7} b^{2} c d^{9} + 315 a^{6} b^{3} c^{2} d^{8} + 1260 a^{5} b^{4} c^{3} d^{7} + 2205 a^{4} b^{5} c^{4} d^{6} + 1764 a^{3} b^{6} c^{5} d^{5} + 630 a^{2} b^{7} c^{6} d^{4} + 90 a b^{8} c^{7} d^{3} + \frac{15 b^{9} c^{8} d^{2}}{4}\right) + x^{11} \left(\frac{a^{9} d^{10}}{11} + \frac{90 a^{8} b c d^{9}}{11} + \frac{1620 a^{7} b^{2} c^{2} d^{8}}{11} + \frac{10080 a^{6} b^{3} c^{3} d^{7}}{11} + \frac{26460 a^{5} b^{4} c^{4} d^{6}}{11} + \frac{31752 a^{4} b^{5} c^{5} d^{5}}{11} + \frac{17640 a^{3} b^{6} c^{6} d^{4}}{11} + \frac{4320 a^{2} b^{7} c^{7} d^{3}}{11} + \frac{405 a b^{8} c^{8} d^{2}}{11} + \frac{10 b^{9} c^{9} d}{11}\right) + x^{10} \left(a^{9} c d^{9} + \frac{81 a^{8} b c^{2} d^{8}}{2} + 432 a^{7} b^{2} c^{3} d^{7} + 1764 a^{6} b^{3} c^{4} d^{6} + \frac{15876 a^{5} b^{4} c^{5} d^{5}}{5} + 2646 a^{4} b^{5} c^{6} d^{4} + 1008 a^{3} b^{6} c^{7} d^{3} + 162 a^{2} b^{7} c^{8} d^{2} + 9 a b^{8} c^{9} d + \frac{b^{9} c^{10}}{10}\right) + x^{9} \left(5 a^{9} c^{2} d^{8} + 120 a^{8} b c^{3} d^{7} + 840 a^{7} b^{2} c^{4} d^{6} + 2352 a^{6} b^{3} c^{5} d^{5} + 2940 a^{5} b^{4} c^{6} d^{4} + 1680 a^{4} b^{5} c^{7} d^{3} + 420 a^{3} b^{6} c^{8} d^{2} + 40 a^{2} b^{7} c^{9} d + a b^{8} c^{10}\right) + x^{8} \left(15 a^{9} c^{3} d^{7} + \frac{945 a^{8} b c^{4} d^{6}}{4} + 1134 a^{7} b^{2} c^{5} d^{5} + 2205 a^{6} b^{3} c^{6} d^{4} + 1890 a^{5} b^{4} c^{7} d^{3} + \frac{2835 a^{4} b^{5} c^{8} d^{2}}{4} + 105 a^{3} b^{6} c^{9} d + \frac{9 a^{2} b^{7} c^{10}}{2}\right) + x^{7} \left(30 a^{9} c^{4} d^{6} + 324 a^{8} b c^{5} d^{5} + 1080 a^{7} b^{2} c^{6} d^{4} + 1440 a^{6} b^{3} c^{7} d^{3} + 810 a^{5} b^{4} c^{8} d^{2} + 180 a^{4} b^{5} c^{9} d + 12 a^{3} b^{6} c^{10}\right) + x^{6} \left(42 a^{9} c^{5} d^{5} + 315 a^{8} b c^{6} d^{4} + 720 a^{7} b^{2} c^{7} d^{3} + 630 a^{6} b^{3} c^{8} d^{2} + 210 a^{5} b^{4} c^{9} d + 21 a^{4} b^{5} c^{10}\right) + x^{5} \left(42 a^{9} c^{6} d^{4} + 216 a^{8} b c^{7} d^{3} + 324 a^{7} b^{2} c^{8} d^{2} + 168 a^{6} b^{3} c^{9} d + \frac{126 a^{5} b^{4} c^{10}}{5}\right) + x^{4} \left(30 a^{9} c^{7} d^{3} + \frac{405 a^{8} b c^{8} d^{2}}{4} + 90 a^{7} b^{2} c^{9} d + 21 a^{6} b^{3} c^{10}\right) + x^{3} \left(15 a^{9} c^{8} d^{2} + 30 a^{8} b c^{9} d + 12 a^{7} b^{2} c^{10}\right) + x^{2} \left(5 a^{9} c^{9} d + \frac{9 a^{8} b c^{10}}{2}\right)"," ",0,"a**9*c**10*x + b**9*d**10*x**20/20 + x**19*(9*a*b**8*d**10/19 + 10*b**9*c*d**9/19) + x**18*(2*a**2*b**7*d**10 + 5*a*b**8*c*d**9 + 5*b**9*c**2*d**8/2) + x**17*(84*a**3*b**6*d**10/17 + 360*a**2*b**7*c*d**9/17 + 405*a*b**8*c**2*d**8/17 + 120*b**9*c**3*d**7/17) + x**16*(63*a**4*b**5*d**10/8 + 105*a**3*b**6*c*d**9/2 + 405*a**2*b**7*c**2*d**8/4 + 135*a*b**8*c**3*d**7/2 + 105*b**9*c**4*d**6/8) + x**15*(42*a**5*b**4*d**10/5 + 84*a**4*b**5*c*d**9 + 252*a**3*b**6*c**2*d**8 + 288*a**2*b**7*c**3*d**7 + 126*a*b**8*c**4*d**6 + 84*b**9*c**5*d**5/5) + x**14*(6*a**6*b**3*d**10 + 90*a**5*b**4*c*d**9 + 405*a**4*b**5*c**2*d**8 + 720*a**3*b**6*c**3*d**7 + 540*a**2*b**7*c**4*d**6 + 162*a*b**8*c**5*d**5 + 15*b**9*c**6*d**4) + x**13*(36*a**7*b**2*d**10/13 + 840*a**6*b**3*c*d**9/13 + 5670*a**5*b**4*c**2*d**8/13 + 15120*a**4*b**5*c**3*d**7/13 + 17640*a**3*b**6*c**4*d**6/13 + 9072*a**2*b**7*c**5*d**5/13 + 1890*a*b**8*c**6*d**4/13 + 120*b**9*c**7*d**3/13) + x**12*(3*a**8*b*d**10/4 + 30*a**7*b**2*c*d**9 + 315*a**6*b**3*c**2*d**8 + 1260*a**5*b**4*c**3*d**7 + 2205*a**4*b**5*c**4*d**6 + 1764*a**3*b**6*c**5*d**5 + 630*a**2*b**7*c**6*d**4 + 90*a*b**8*c**7*d**3 + 15*b**9*c**8*d**2/4) + x**11*(a**9*d**10/11 + 90*a**8*b*c*d**9/11 + 1620*a**7*b**2*c**2*d**8/11 + 10080*a**6*b**3*c**3*d**7/11 + 26460*a**5*b**4*c**4*d**6/11 + 31752*a**4*b**5*c**5*d**5/11 + 17640*a**3*b**6*c**6*d**4/11 + 4320*a**2*b**7*c**7*d**3/11 + 405*a*b**8*c**8*d**2/11 + 10*b**9*c**9*d/11) + x**10*(a**9*c*d**9 + 81*a**8*b*c**2*d**8/2 + 432*a**7*b**2*c**3*d**7 + 1764*a**6*b**3*c**4*d**6 + 15876*a**5*b**4*c**5*d**5/5 + 2646*a**4*b**5*c**6*d**4 + 1008*a**3*b**6*c**7*d**3 + 162*a**2*b**7*c**8*d**2 + 9*a*b**8*c**9*d + b**9*c**10/10) + x**9*(5*a**9*c**2*d**8 + 120*a**8*b*c**3*d**7 + 840*a**7*b**2*c**4*d**6 + 2352*a**6*b**3*c**5*d**5 + 2940*a**5*b**4*c**6*d**4 + 1680*a**4*b**5*c**7*d**3 + 420*a**3*b**6*c**8*d**2 + 40*a**2*b**7*c**9*d + a*b**8*c**10) + x**8*(15*a**9*c**3*d**7 + 945*a**8*b*c**4*d**6/4 + 1134*a**7*b**2*c**5*d**5 + 2205*a**6*b**3*c**6*d**4 + 1890*a**5*b**4*c**7*d**3 + 2835*a**4*b**5*c**8*d**2/4 + 105*a**3*b**6*c**9*d + 9*a**2*b**7*c**10/2) + x**7*(30*a**9*c**4*d**6 + 324*a**8*b*c**5*d**5 + 1080*a**7*b**2*c**6*d**4 + 1440*a**6*b**3*c**7*d**3 + 810*a**5*b**4*c**8*d**2 + 180*a**4*b**5*c**9*d + 12*a**3*b**6*c**10) + x**6*(42*a**9*c**5*d**5 + 315*a**8*b*c**6*d**4 + 720*a**7*b**2*c**7*d**3 + 630*a**6*b**3*c**8*d**2 + 210*a**5*b**4*c**9*d + 21*a**4*b**5*c**10) + x**5*(42*a**9*c**6*d**4 + 216*a**8*b*c**7*d**3 + 324*a**7*b**2*c**8*d**2 + 168*a**6*b**3*c**9*d + 126*a**5*b**4*c**10/5) + x**4*(30*a**9*c**7*d**3 + 405*a**8*b*c**8*d**2/4 + 90*a**7*b**2*c**9*d + 21*a**6*b**3*c**10) + x**3*(15*a**9*c**8*d**2 + 30*a**8*b*c**9*d + 12*a**7*b**2*c**10) + x**2*(5*a**9*c**9*d + 9*a**8*b*c**10/2)","B",0
1303,1,1428,0,0.273119," ","integrate((b*x+a)**8*(d*x+c)**10,x)","a^{8} c^{10} x + \frac{b^{8} d^{10} x^{19}}{19} + x^{18} \left(\frac{4 a b^{7} d^{10}}{9} + \frac{5 b^{8} c d^{9}}{9}\right) + x^{17} \left(\frac{28 a^{2} b^{6} d^{10}}{17} + \frac{80 a b^{7} c d^{9}}{17} + \frac{45 b^{8} c^{2} d^{8}}{17}\right) + x^{16} \left(\frac{7 a^{3} b^{5} d^{10}}{2} + \frac{35 a^{2} b^{6} c d^{9}}{2} + \frac{45 a b^{7} c^{2} d^{8}}{2} + \frac{15 b^{8} c^{3} d^{7}}{2}\right) + x^{15} \left(\frac{14 a^{4} b^{4} d^{10}}{3} + \frac{112 a^{3} b^{5} c d^{9}}{3} + 84 a^{2} b^{6} c^{2} d^{8} + 64 a b^{7} c^{3} d^{7} + 14 b^{8} c^{4} d^{6}\right) + x^{14} \left(4 a^{5} b^{3} d^{10} + 50 a^{4} b^{4} c d^{9} + 180 a^{3} b^{5} c^{2} d^{8} + 240 a^{2} b^{6} c^{3} d^{7} + 120 a b^{7} c^{4} d^{6} + 18 b^{8} c^{5} d^{5}\right) + x^{13} \left(\frac{28 a^{6} b^{2} d^{10}}{13} + \frac{560 a^{5} b^{3} c d^{9}}{13} + \frac{3150 a^{4} b^{4} c^{2} d^{8}}{13} + \frac{6720 a^{3} b^{5} c^{3} d^{7}}{13} + \frac{5880 a^{2} b^{6} c^{4} d^{6}}{13} + \frac{2016 a b^{7} c^{5} d^{5}}{13} + \frac{210 b^{8} c^{6} d^{4}}{13}\right) + x^{12} \left(\frac{2 a^{7} b d^{10}}{3} + \frac{70 a^{6} b^{2} c d^{9}}{3} + 210 a^{5} b^{3} c^{2} d^{8} + 700 a^{4} b^{4} c^{3} d^{7} + 980 a^{3} b^{5} c^{4} d^{6} + 588 a^{2} b^{6} c^{5} d^{5} + 140 a b^{7} c^{6} d^{4} + 10 b^{8} c^{7} d^{3}\right) + x^{11} \left(\frac{a^{8} d^{10}}{11} + \frac{80 a^{7} b c d^{9}}{11} + \frac{1260 a^{6} b^{2} c^{2} d^{8}}{11} + \frac{6720 a^{5} b^{3} c^{3} d^{7}}{11} + \frac{14700 a^{4} b^{4} c^{4} d^{6}}{11} + \frac{14112 a^{3} b^{5} c^{5} d^{5}}{11} + \frac{5880 a^{2} b^{6} c^{6} d^{4}}{11} + \frac{960 a b^{7} c^{7} d^{3}}{11} + \frac{45 b^{8} c^{8} d^{2}}{11}\right) + x^{10} \left(a^{8} c d^{9} + 36 a^{7} b c^{2} d^{8} + 336 a^{6} b^{2} c^{3} d^{7} + 1176 a^{5} b^{3} c^{4} d^{6} + 1764 a^{4} b^{4} c^{5} d^{5} + 1176 a^{3} b^{5} c^{6} d^{4} + 336 a^{2} b^{6} c^{7} d^{3} + 36 a b^{7} c^{8} d^{2} + b^{8} c^{9} d\right) + x^{9} \left(5 a^{8} c^{2} d^{8} + \frac{320 a^{7} b c^{3} d^{7}}{3} + \frac{1960 a^{6} b^{2} c^{4} d^{6}}{3} + 1568 a^{5} b^{3} c^{5} d^{5} + \frac{4900 a^{4} b^{4} c^{6} d^{4}}{3} + \frac{2240 a^{3} b^{5} c^{7} d^{3}}{3} + 140 a^{2} b^{6} c^{8} d^{2} + \frac{80 a b^{7} c^{9} d}{9} + \frac{b^{8} c^{10}}{9}\right) + x^{8} \left(15 a^{8} c^{3} d^{7} + 210 a^{7} b c^{4} d^{6} + 882 a^{6} b^{2} c^{5} d^{5} + 1470 a^{5} b^{3} c^{6} d^{4} + 1050 a^{4} b^{4} c^{7} d^{3} + 315 a^{3} b^{5} c^{8} d^{2} + 35 a^{2} b^{6} c^{9} d + a b^{7} c^{10}\right) + x^{7} \left(30 a^{8} c^{4} d^{6} + 288 a^{7} b c^{5} d^{5} + 840 a^{6} b^{2} c^{6} d^{4} + 960 a^{5} b^{3} c^{7} d^{3} + 450 a^{4} b^{4} c^{8} d^{2} + 80 a^{3} b^{5} c^{9} d + 4 a^{2} b^{6} c^{10}\right) + x^{6} \left(42 a^{8} c^{5} d^{5} + 280 a^{7} b c^{6} d^{4} + 560 a^{6} b^{2} c^{7} d^{3} + 420 a^{5} b^{3} c^{8} d^{2} + \frac{350 a^{4} b^{4} c^{9} d}{3} + \frac{28 a^{3} b^{5} c^{10}}{3}\right) + x^{5} \left(42 a^{8} c^{6} d^{4} + 192 a^{7} b c^{7} d^{3} + 252 a^{6} b^{2} c^{8} d^{2} + 112 a^{5} b^{3} c^{9} d + 14 a^{4} b^{4} c^{10}\right) + x^{4} \left(30 a^{8} c^{7} d^{3} + 90 a^{7} b c^{8} d^{2} + 70 a^{6} b^{2} c^{9} d + 14 a^{5} b^{3} c^{10}\right) + x^{3} \left(15 a^{8} c^{8} d^{2} + \frac{80 a^{7} b c^{9} d}{3} + \frac{28 a^{6} b^{2} c^{10}}{3}\right) + x^{2} \left(5 a^{8} c^{9} d + 4 a^{7} b c^{10}\right)"," ",0,"a**8*c**10*x + b**8*d**10*x**19/19 + x**18*(4*a*b**7*d**10/9 + 5*b**8*c*d**9/9) + x**17*(28*a**2*b**6*d**10/17 + 80*a*b**7*c*d**9/17 + 45*b**8*c**2*d**8/17) + x**16*(7*a**3*b**5*d**10/2 + 35*a**2*b**6*c*d**9/2 + 45*a*b**7*c**2*d**8/2 + 15*b**8*c**3*d**7/2) + x**15*(14*a**4*b**4*d**10/3 + 112*a**3*b**5*c*d**9/3 + 84*a**2*b**6*c**2*d**8 + 64*a*b**7*c**3*d**7 + 14*b**8*c**4*d**6) + x**14*(4*a**5*b**3*d**10 + 50*a**4*b**4*c*d**9 + 180*a**3*b**5*c**2*d**8 + 240*a**2*b**6*c**3*d**7 + 120*a*b**7*c**4*d**6 + 18*b**8*c**5*d**5) + x**13*(28*a**6*b**2*d**10/13 + 560*a**5*b**3*c*d**9/13 + 3150*a**4*b**4*c**2*d**8/13 + 6720*a**3*b**5*c**3*d**7/13 + 5880*a**2*b**6*c**4*d**6/13 + 2016*a*b**7*c**5*d**5/13 + 210*b**8*c**6*d**4/13) + x**12*(2*a**7*b*d**10/3 + 70*a**6*b**2*c*d**9/3 + 210*a**5*b**3*c**2*d**8 + 700*a**4*b**4*c**3*d**7 + 980*a**3*b**5*c**4*d**6 + 588*a**2*b**6*c**5*d**5 + 140*a*b**7*c**6*d**4 + 10*b**8*c**7*d**3) + x**11*(a**8*d**10/11 + 80*a**7*b*c*d**9/11 + 1260*a**6*b**2*c**2*d**8/11 + 6720*a**5*b**3*c**3*d**7/11 + 14700*a**4*b**4*c**4*d**6/11 + 14112*a**3*b**5*c**5*d**5/11 + 5880*a**2*b**6*c**6*d**4/11 + 960*a*b**7*c**7*d**3/11 + 45*b**8*c**8*d**2/11) + x**10*(a**8*c*d**9 + 36*a**7*b*c**2*d**8 + 336*a**6*b**2*c**3*d**7 + 1176*a**5*b**3*c**4*d**6 + 1764*a**4*b**4*c**5*d**5 + 1176*a**3*b**5*c**6*d**4 + 336*a**2*b**6*c**7*d**3 + 36*a*b**7*c**8*d**2 + b**8*c**9*d) + x**9*(5*a**8*c**2*d**8 + 320*a**7*b*c**3*d**7/3 + 1960*a**6*b**2*c**4*d**6/3 + 1568*a**5*b**3*c**5*d**5 + 4900*a**4*b**4*c**6*d**4/3 + 2240*a**3*b**5*c**7*d**3/3 + 140*a**2*b**6*c**8*d**2 + 80*a*b**7*c**9*d/9 + b**8*c**10/9) + x**8*(15*a**8*c**3*d**7 + 210*a**7*b*c**4*d**6 + 882*a**6*b**2*c**5*d**5 + 1470*a**5*b**3*c**6*d**4 + 1050*a**4*b**4*c**7*d**3 + 315*a**3*b**5*c**8*d**2 + 35*a**2*b**6*c**9*d + a*b**7*c**10) + x**7*(30*a**8*c**4*d**6 + 288*a**7*b*c**5*d**5 + 840*a**6*b**2*c**6*d**4 + 960*a**5*b**3*c**7*d**3 + 450*a**4*b**4*c**8*d**2 + 80*a**3*b**5*c**9*d + 4*a**2*b**6*c**10) + x**6*(42*a**8*c**5*d**5 + 280*a**7*b*c**6*d**4 + 560*a**6*b**2*c**7*d**3 + 420*a**5*b**3*c**8*d**2 + 350*a**4*b**4*c**9*d/3 + 28*a**3*b**5*c**10/3) + x**5*(42*a**8*c**6*d**4 + 192*a**7*b*c**7*d**3 + 252*a**6*b**2*c**8*d**2 + 112*a**5*b**3*c**9*d + 14*a**4*b**4*c**10) + x**4*(30*a**8*c**7*d**3 + 90*a**7*b*c**8*d**2 + 70*a**6*b**2*c**9*d + 14*a**5*b**3*c**10) + x**3*(15*a**8*c**8*d**2 + 80*a**7*b*c**9*d/3 + 28*a**6*b**2*c**10/3) + x**2*(5*a**8*c**9*d + 4*a**7*b*c**10)","B",0
1304,1,1280,0,0.245938," ","integrate((b*x+a)**7*(d*x+c)**10,x)","a^{7} c^{10} x + \frac{b^{7} d^{10} x^{18}}{18} + x^{17} \left(\frac{7 a b^{6} d^{10}}{17} + \frac{10 b^{7} c d^{9}}{17}\right) + x^{16} \left(\frac{21 a^{2} b^{5} d^{10}}{16} + \frac{35 a b^{6} c d^{9}}{8} + \frac{45 b^{7} c^{2} d^{8}}{16}\right) + x^{15} \left(\frac{7 a^{3} b^{4} d^{10}}{3} + 14 a^{2} b^{5} c d^{9} + 21 a b^{6} c^{2} d^{8} + 8 b^{7} c^{3} d^{7}\right) + x^{14} \left(\frac{5 a^{4} b^{3} d^{10}}{2} + 25 a^{3} b^{4} c d^{9} + \frac{135 a^{2} b^{5} c^{2} d^{8}}{2} + 60 a b^{6} c^{3} d^{7} + 15 b^{7} c^{4} d^{6}\right) + x^{13} \left(\frac{21 a^{5} b^{2} d^{10}}{13} + \frac{350 a^{4} b^{3} c d^{9}}{13} + \frac{1575 a^{3} b^{4} c^{2} d^{8}}{13} + \frac{2520 a^{2} b^{5} c^{3} d^{7}}{13} + \frac{1470 a b^{6} c^{4} d^{6}}{13} + \frac{252 b^{7} c^{5} d^{5}}{13}\right) + x^{12} \left(\frac{7 a^{6} b d^{10}}{12} + \frac{35 a^{5} b^{2} c d^{9}}{2} + \frac{525 a^{4} b^{3} c^{2} d^{8}}{4} + 350 a^{3} b^{4} c^{3} d^{7} + \frac{735 a^{2} b^{5} c^{4} d^{6}}{2} + 147 a b^{6} c^{5} d^{5} + \frac{35 b^{7} c^{6} d^{4}}{2}\right) + x^{11} \left(\frac{a^{7} d^{10}}{11} + \frac{70 a^{6} b c d^{9}}{11} + \frac{945 a^{5} b^{2} c^{2} d^{8}}{11} + \frac{4200 a^{4} b^{3} c^{3} d^{7}}{11} + \frac{7350 a^{3} b^{4} c^{4} d^{6}}{11} + \frac{5292 a^{2} b^{5} c^{5} d^{5}}{11} + \frac{1470 a b^{6} c^{6} d^{4}}{11} + \frac{120 b^{7} c^{7} d^{3}}{11}\right) + x^{10} \left(a^{7} c d^{9} + \frac{63 a^{6} b c^{2} d^{8}}{2} + 252 a^{5} b^{2} c^{3} d^{7} + 735 a^{4} b^{3} c^{4} d^{6} + 882 a^{3} b^{4} c^{5} d^{5} + 441 a^{2} b^{5} c^{6} d^{4} + 84 a b^{6} c^{7} d^{3} + \frac{9 b^{7} c^{8} d^{2}}{2}\right) + x^{9} \left(5 a^{7} c^{2} d^{8} + \frac{280 a^{6} b c^{3} d^{7}}{3} + 490 a^{5} b^{2} c^{4} d^{6} + 980 a^{4} b^{3} c^{5} d^{5} + \frac{2450 a^{3} b^{4} c^{6} d^{4}}{3} + 280 a^{2} b^{5} c^{7} d^{3} + 35 a b^{6} c^{8} d^{2} + \frac{10 b^{7} c^{9} d}{9}\right) + x^{8} \left(15 a^{7} c^{3} d^{7} + \frac{735 a^{6} b c^{4} d^{6}}{4} + \frac{1323 a^{5} b^{2} c^{5} d^{5}}{2} + \frac{3675 a^{4} b^{3} c^{6} d^{4}}{4} + 525 a^{3} b^{4} c^{7} d^{3} + \frac{945 a^{2} b^{5} c^{8} d^{2}}{8} + \frac{35 a b^{6} c^{9} d}{4} + \frac{b^{7} c^{10}}{8}\right) + x^{7} \left(30 a^{7} c^{4} d^{6} + 252 a^{6} b c^{5} d^{5} + 630 a^{5} b^{2} c^{6} d^{4} + 600 a^{4} b^{3} c^{7} d^{3} + 225 a^{3} b^{4} c^{8} d^{2} + 30 a^{2} b^{5} c^{9} d + a b^{6} c^{10}\right) + x^{6} \left(42 a^{7} c^{5} d^{5} + 245 a^{6} b c^{6} d^{4} + 420 a^{5} b^{2} c^{7} d^{3} + \frac{525 a^{4} b^{3} c^{8} d^{2}}{2} + \frac{175 a^{3} b^{4} c^{9} d}{3} + \frac{7 a^{2} b^{5} c^{10}}{2}\right) + x^{5} \left(42 a^{7} c^{6} d^{4} + 168 a^{6} b c^{7} d^{3} + 189 a^{5} b^{2} c^{8} d^{2} + 70 a^{4} b^{3} c^{9} d + 7 a^{3} b^{4} c^{10}\right) + x^{4} \left(30 a^{7} c^{7} d^{3} + \frac{315 a^{6} b c^{8} d^{2}}{4} + \frac{105 a^{5} b^{2} c^{9} d}{2} + \frac{35 a^{4} b^{3} c^{10}}{4}\right) + x^{3} \left(15 a^{7} c^{8} d^{2} + \frac{70 a^{6} b c^{9} d}{3} + 7 a^{5} b^{2} c^{10}\right) + x^{2} \left(5 a^{7} c^{9} d + \frac{7 a^{6} b c^{10}}{2}\right)"," ",0,"a**7*c**10*x + b**7*d**10*x**18/18 + x**17*(7*a*b**6*d**10/17 + 10*b**7*c*d**9/17) + x**16*(21*a**2*b**5*d**10/16 + 35*a*b**6*c*d**9/8 + 45*b**7*c**2*d**8/16) + x**15*(7*a**3*b**4*d**10/3 + 14*a**2*b**5*c*d**9 + 21*a*b**6*c**2*d**8 + 8*b**7*c**3*d**7) + x**14*(5*a**4*b**3*d**10/2 + 25*a**3*b**4*c*d**9 + 135*a**2*b**5*c**2*d**8/2 + 60*a*b**6*c**3*d**7 + 15*b**7*c**4*d**6) + x**13*(21*a**5*b**2*d**10/13 + 350*a**4*b**3*c*d**9/13 + 1575*a**3*b**4*c**2*d**8/13 + 2520*a**2*b**5*c**3*d**7/13 + 1470*a*b**6*c**4*d**6/13 + 252*b**7*c**5*d**5/13) + x**12*(7*a**6*b*d**10/12 + 35*a**5*b**2*c*d**9/2 + 525*a**4*b**3*c**2*d**8/4 + 350*a**3*b**4*c**3*d**7 + 735*a**2*b**5*c**4*d**6/2 + 147*a*b**6*c**5*d**5 + 35*b**7*c**6*d**4/2) + x**11*(a**7*d**10/11 + 70*a**6*b*c*d**9/11 + 945*a**5*b**2*c**2*d**8/11 + 4200*a**4*b**3*c**3*d**7/11 + 7350*a**3*b**4*c**4*d**6/11 + 5292*a**2*b**5*c**5*d**5/11 + 1470*a*b**6*c**6*d**4/11 + 120*b**7*c**7*d**3/11) + x**10*(a**7*c*d**9 + 63*a**6*b*c**2*d**8/2 + 252*a**5*b**2*c**3*d**7 + 735*a**4*b**3*c**4*d**6 + 882*a**3*b**4*c**5*d**5 + 441*a**2*b**5*c**6*d**4 + 84*a*b**6*c**7*d**3 + 9*b**7*c**8*d**2/2) + x**9*(5*a**7*c**2*d**8 + 280*a**6*b*c**3*d**7/3 + 490*a**5*b**2*c**4*d**6 + 980*a**4*b**3*c**5*d**5 + 2450*a**3*b**4*c**6*d**4/3 + 280*a**2*b**5*c**7*d**3 + 35*a*b**6*c**8*d**2 + 10*b**7*c**9*d/9) + x**8*(15*a**7*c**3*d**7 + 735*a**6*b*c**4*d**6/4 + 1323*a**5*b**2*c**5*d**5/2 + 3675*a**4*b**3*c**6*d**4/4 + 525*a**3*b**4*c**7*d**3 + 945*a**2*b**5*c**8*d**2/8 + 35*a*b**6*c**9*d/4 + b**7*c**10/8) + x**7*(30*a**7*c**4*d**6 + 252*a**6*b*c**5*d**5 + 630*a**5*b**2*c**6*d**4 + 600*a**4*b**3*c**7*d**3 + 225*a**3*b**4*c**8*d**2 + 30*a**2*b**5*c**9*d + a*b**6*c**10) + x**6*(42*a**7*c**5*d**5 + 245*a**6*b*c**6*d**4 + 420*a**5*b**2*c**7*d**3 + 525*a**4*b**3*c**8*d**2/2 + 175*a**3*b**4*c**9*d/3 + 7*a**2*b**5*c**10/2) + x**5*(42*a**7*c**6*d**4 + 168*a**6*b*c**7*d**3 + 189*a**5*b**2*c**8*d**2 + 70*a**4*b**3*c**9*d + 7*a**3*b**4*c**10) + x**4*(30*a**7*c**7*d**3 + 315*a**6*b*c**8*d**2/4 + 105*a**5*b**2*c**9*d/2 + 35*a**4*b**3*c**10/4) + x**3*(15*a**7*c**8*d**2 + 70*a**6*b*c**9*d/3 + 7*a**5*b**2*c**10) + x**2*(5*a**7*c**9*d + 7*a**6*b*c**10/2)","B",0
1305,1,1088,0,0.226882," ","integrate((b*x+a)**6*(d*x+c)**10,x)","a^{6} c^{10} x + \frac{b^{6} d^{10} x^{17}}{17} + x^{16} \left(\frac{3 a b^{5} d^{10}}{8} + \frac{5 b^{6} c d^{9}}{8}\right) + x^{15} \left(a^{2} b^{4} d^{10} + 4 a b^{5} c d^{9} + 3 b^{6} c^{2} d^{8}\right) + x^{14} \left(\frac{10 a^{3} b^{3} d^{10}}{7} + \frac{75 a^{2} b^{4} c d^{9}}{7} + \frac{135 a b^{5} c^{2} d^{8}}{7} + \frac{60 b^{6} c^{3} d^{7}}{7}\right) + x^{13} \left(\frac{15 a^{4} b^{2} d^{10}}{13} + \frac{200 a^{3} b^{3} c d^{9}}{13} + \frac{675 a^{2} b^{4} c^{2} d^{8}}{13} + \frac{720 a b^{5} c^{3} d^{7}}{13} + \frac{210 b^{6} c^{4} d^{6}}{13}\right) + x^{12} \left(\frac{a^{5} b d^{10}}{2} + \frac{25 a^{4} b^{2} c d^{9}}{2} + 75 a^{3} b^{3} c^{2} d^{8} + 150 a^{2} b^{4} c^{3} d^{7} + 105 a b^{5} c^{4} d^{6} + 21 b^{6} c^{5} d^{5}\right) + x^{11} \left(\frac{a^{6} d^{10}}{11} + \frac{60 a^{5} b c d^{9}}{11} + \frac{675 a^{4} b^{2} c^{2} d^{8}}{11} + \frac{2400 a^{3} b^{3} c^{3} d^{7}}{11} + \frac{3150 a^{2} b^{4} c^{4} d^{6}}{11} + \frac{1512 a b^{5} c^{5} d^{5}}{11} + \frac{210 b^{6} c^{6} d^{4}}{11}\right) + x^{10} \left(a^{6} c d^{9} + 27 a^{5} b c^{2} d^{8} + 180 a^{4} b^{2} c^{3} d^{7} + 420 a^{3} b^{3} c^{4} d^{6} + 378 a^{2} b^{4} c^{5} d^{5} + 126 a b^{5} c^{6} d^{4} + 12 b^{6} c^{7} d^{3}\right) + x^{9} \left(5 a^{6} c^{2} d^{8} + 80 a^{5} b c^{3} d^{7} + 350 a^{4} b^{2} c^{4} d^{6} + 560 a^{3} b^{3} c^{5} d^{5} + 350 a^{2} b^{4} c^{6} d^{4} + 80 a b^{5} c^{7} d^{3} + 5 b^{6} c^{8} d^{2}\right) + x^{8} \left(15 a^{6} c^{3} d^{7} + \frac{315 a^{5} b c^{4} d^{6}}{2} + \frac{945 a^{4} b^{2} c^{5} d^{5}}{2} + 525 a^{3} b^{3} c^{6} d^{4} + 225 a^{2} b^{4} c^{7} d^{3} + \frac{135 a b^{5} c^{8} d^{2}}{4} + \frac{5 b^{6} c^{9} d}{4}\right) + x^{7} \left(30 a^{6} c^{4} d^{6} + 216 a^{5} b c^{5} d^{5} + 450 a^{4} b^{2} c^{6} d^{4} + \frac{2400 a^{3} b^{3} c^{7} d^{3}}{7} + \frac{675 a^{2} b^{4} c^{8} d^{2}}{7} + \frac{60 a b^{5} c^{9} d}{7} + \frac{b^{6} c^{10}}{7}\right) + x^{6} \left(42 a^{6} c^{5} d^{5} + 210 a^{5} b c^{6} d^{4} + 300 a^{4} b^{2} c^{7} d^{3} + 150 a^{3} b^{3} c^{8} d^{2} + 25 a^{2} b^{4} c^{9} d + a b^{5} c^{10}\right) + x^{5} \left(42 a^{6} c^{6} d^{4} + 144 a^{5} b c^{7} d^{3} + 135 a^{4} b^{2} c^{8} d^{2} + 40 a^{3} b^{3} c^{9} d + 3 a^{2} b^{4} c^{10}\right) + x^{4} \left(30 a^{6} c^{7} d^{3} + \frac{135 a^{5} b c^{8} d^{2}}{2} + \frac{75 a^{4} b^{2} c^{9} d}{2} + 5 a^{3} b^{3} c^{10}\right) + x^{3} \left(15 a^{6} c^{8} d^{2} + 20 a^{5} b c^{9} d + 5 a^{4} b^{2} c^{10}\right) + x^{2} \left(5 a^{6} c^{9} d + 3 a^{5} b c^{10}\right)"," ",0,"a**6*c**10*x + b**6*d**10*x**17/17 + x**16*(3*a*b**5*d**10/8 + 5*b**6*c*d**9/8) + x**15*(a**2*b**4*d**10 + 4*a*b**5*c*d**9 + 3*b**6*c**2*d**8) + x**14*(10*a**3*b**3*d**10/7 + 75*a**2*b**4*c*d**9/7 + 135*a*b**5*c**2*d**8/7 + 60*b**6*c**3*d**7/7) + x**13*(15*a**4*b**2*d**10/13 + 200*a**3*b**3*c*d**9/13 + 675*a**2*b**4*c**2*d**8/13 + 720*a*b**5*c**3*d**7/13 + 210*b**6*c**4*d**6/13) + x**12*(a**5*b*d**10/2 + 25*a**4*b**2*c*d**9/2 + 75*a**3*b**3*c**2*d**8 + 150*a**2*b**4*c**3*d**7 + 105*a*b**5*c**4*d**6 + 21*b**6*c**5*d**5) + x**11*(a**6*d**10/11 + 60*a**5*b*c*d**9/11 + 675*a**4*b**2*c**2*d**8/11 + 2400*a**3*b**3*c**3*d**7/11 + 3150*a**2*b**4*c**4*d**6/11 + 1512*a*b**5*c**5*d**5/11 + 210*b**6*c**6*d**4/11) + x**10*(a**6*c*d**9 + 27*a**5*b*c**2*d**8 + 180*a**4*b**2*c**3*d**7 + 420*a**3*b**3*c**4*d**6 + 378*a**2*b**4*c**5*d**5 + 126*a*b**5*c**6*d**4 + 12*b**6*c**7*d**3) + x**9*(5*a**6*c**2*d**8 + 80*a**5*b*c**3*d**7 + 350*a**4*b**2*c**4*d**6 + 560*a**3*b**3*c**5*d**5 + 350*a**2*b**4*c**6*d**4 + 80*a*b**5*c**7*d**3 + 5*b**6*c**8*d**2) + x**8*(15*a**6*c**3*d**7 + 315*a**5*b*c**4*d**6/2 + 945*a**4*b**2*c**5*d**5/2 + 525*a**3*b**3*c**6*d**4 + 225*a**2*b**4*c**7*d**3 + 135*a*b**5*c**8*d**2/4 + 5*b**6*c**9*d/4) + x**7*(30*a**6*c**4*d**6 + 216*a**5*b*c**5*d**5 + 450*a**4*b**2*c**6*d**4 + 2400*a**3*b**3*c**7*d**3/7 + 675*a**2*b**4*c**8*d**2/7 + 60*a*b**5*c**9*d/7 + b**6*c**10/7) + x**6*(42*a**6*c**5*d**5 + 210*a**5*b*c**6*d**4 + 300*a**4*b**2*c**7*d**3 + 150*a**3*b**3*c**8*d**2 + 25*a**2*b**4*c**9*d + a*b**5*c**10) + x**5*(42*a**6*c**6*d**4 + 144*a**5*b*c**7*d**3 + 135*a**4*b**2*c**8*d**2 + 40*a**3*b**3*c**9*d + 3*a**2*b**4*c**10) + x**4*(30*a**6*c**7*d**3 + 135*a**5*b*c**8*d**2/2 + 75*a**4*b**2*c**9*d/2 + 5*a**3*b**3*c**10) + x**3*(15*a**6*c**8*d**2 + 20*a**5*b*c**9*d + 5*a**4*b**2*c**10) + x**2*(5*a**6*c**9*d + 3*a**5*b*c**10)","B",0
1306,1,940,0,0.209475," ","integrate((b*x+a)**5*(d*x+c)**10,x)","a^{5} c^{10} x + \frac{b^{5} d^{10} x^{16}}{16} + x^{15} \left(\frac{a b^{4} d^{10}}{3} + \frac{2 b^{5} c d^{9}}{3}\right) + x^{14} \left(\frac{5 a^{2} b^{3} d^{10}}{7} + \frac{25 a b^{4} c d^{9}}{7} + \frac{45 b^{5} c^{2} d^{8}}{14}\right) + x^{13} \left(\frac{10 a^{3} b^{2} d^{10}}{13} + \frac{100 a^{2} b^{3} c d^{9}}{13} + \frac{225 a b^{4} c^{2} d^{8}}{13} + \frac{120 b^{5} c^{3} d^{7}}{13}\right) + x^{12} \left(\frac{5 a^{4} b d^{10}}{12} + \frac{25 a^{3} b^{2} c d^{9}}{3} + \frac{75 a^{2} b^{3} c^{2} d^{8}}{2} + 50 a b^{4} c^{3} d^{7} + \frac{35 b^{5} c^{4} d^{6}}{2}\right) + x^{11} \left(\frac{a^{5} d^{10}}{11} + \frac{50 a^{4} b c d^{9}}{11} + \frac{450 a^{3} b^{2} c^{2} d^{8}}{11} + \frac{1200 a^{2} b^{3} c^{3} d^{7}}{11} + \frac{1050 a b^{4} c^{4} d^{6}}{11} + \frac{252 b^{5} c^{5} d^{5}}{11}\right) + x^{10} \left(a^{5} c d^{9} + \frac{45 a^{4} b c^{2} d^{8}}{2} + 120 a^{3} b^{2} c^{3} d^{7} + 210 a^{2} b^{3} c^{4} d^{6} + 126 a b^{4} c^{5} d^{5} + 21 b^{5} c^{6} d^{4}\right) + x^{9} \left(5 a^{5} c^{2} d^{8} + \frac{200 a^{4} b c^{3} d^{7}}{3} + \frac{700 a^{3} b^{2} c^{4} d^{6}}{3} + 280 a^{2} b^{3} c^{5} d^{5} + \frac{350 a b^{4} c^{6} d^{4}}{3} + \frac{40 b^{5} c^{7} d^{3}}{3}\right) + x^{8} \left(15 a^{5} c^{3} d^{7} + \frac{525 a^{4} b c^{4} d^{6}}{4} + 315 a^{3} b^{2} c^{5} d^{5} + \frac{525 a^{2} b^{3} c^{6} d^{4}}{2} + 75 a b^{4} c^{7} d^{3} + \frac{45 b^{5} c^{8} d^{2}}{8}\right) + x^{7} \left(30 a^{5} c^{4} d^{6} + 180 a^{4} b c^{5} d^{5} + 300 a^{3} b^{2} c^{6} d^{4} + \frac{1200 a^{2} b^{3} c^{7} d^{3}}{7} + \frac{225 a b^{4} c^{8} d^{2}}{7} + \frac{10 b^{5} c^{9} d}{7}\right) + x^{6} \left(42 a^{5} c^{5} d^{5} + 175 a^{4} b c^{6} d^{4} + 200 a^{3} b^{2} c^{7} d^{3} + 75 a^{2} b^{3} c^{8} d^{2} + \frac{25 a b^{4} c^{9} d}{3} + \frac{b^{5} c^{10}}{6}\right) + x^{5} \left(42 a^{5} c^{6} d^{4} + 120 a^{4} b c^{7} d^{3} + 90 a^{3} b^{2} c^{8} d^{2} + 20 a^{2} b^{3} c^{9} d + a b^{4} c^{10}\right) + x^{4} \left(30 a^{5} c^{7} d^{3} + \frac{225 a^{4} b c^{8} d^{2}}{4} + 25 a^{3} b^{2} c^{9} d + \frac{5 a^{2} b^{3} c^{10}}{2}\right) + x^{3} \left(15 a^{5} c^{8} d^{2} + \frac{50 a^{4} b c^{9} d}{3} + \frac{10 a^{3} b^{2} c^{10}}{3}\right) + x^{2} \left(5 a^{5} c^{9} d + \frac{5 a^{4} b c^{10}}{2}\right)"," ",0,"a**5*c**10*x + b**5*d**10*x**16/16 + x**15*(a*b**4*d**10/3 + 2*b**5*c*d**9/3) + x**14*(5*a**2*b**3*d**10/7 + 25*a*b**4*c*d**9/7 + 45*b**5*c**2*d**8/14) + x**13*(10*a**3*b**2*d**10/13 + 100*a**2*b**3*c*d**9/13 + 225*a*b**4*c**2*d**8/13 + 120*b**5*c**3*d**7/13) + x**12*(5*a**4*b*d**10/12 + 25*a**3*b**2*c*d**9/3 + 75*a**2*b**3*c**2*d**8/2 + 50*a*b**4*c**3*d**7 + 35*b**5*c**4*d**6/2) + x**11*(a**5*d**10/11 + 50*a**4*b*c*d**9/11 + 450*a**3*b**2*c**2*d**8/11 + 1200*a**2*b**3*c**3*d**7/11 + 1050*a*b**4*c**4*d**6/11 + 252*b**5*c**5*d**5/11) + x**10*(a**5*c*d**9 + 45*a**4*b*c**2*d**8/2 + 120*a**3*b**2*c**3*d**7 + 210*a**2*b**3*c**4*d**6 + 126*a*b**4*c**5*d**5 + 21*b**5*c**6*d**4) + x**9*(5*a**5*c**2*d**8 + 200*a**4*b*c**3*d**7/3 + 700*a**3*b**2*c**4*d**6/3 + 280*a**2*b**3*c**5*d**5 + 350*a*b**4*c**6*d**4/3 + 40*b**5*c**7*d**3/3) + x**8*(15*a**5*c**3*d**7 + 525*a**4*b*c**4*d**6/4 + 315*a**3*b**2*c**5*d**5 + 525*a**2*b**3*c**6*d**4/2 + 75*a*b**4*c**7*d**3 + 45*b**5*c**8*d**2/8) + x**7*(30*a**5*c**4*d**6 + 180*a**4*b*c**5*d**5 + 300*a**3*b**2*c**6*d**4 + 1200*a**2*b**3*c**7*d**3/7 + 225*a*b**4*c**8*d**2/7 + 10*b**5*c**9*d/7) + x**6*(42*a**5*c**5*d**5 + 175*a**4*b*c**6*d**4 + 200*a**3*b**2*c**7*d**3 + 75*a**2*b**3*c**8*d**2 + 25*a*b**4*c**9*d/3 + b**5*c**10/6) + x**5*(42*a**5*c**6*d**4 + 120*a**4*b*c**7*d**3 + 90*a**3*b**2*c**8*d**2 + 20*a**2*b**3*c**9*d + a*b**4*c**10) + x**4*(30*a**5*c**7*d**3 + 225*a**4*b*c**8*d**2/4 + 25*a**3*b**2*c**9*d + 5*a**2*b**3*c**10/2) + x**3*(15*a**5*c**8*d**2 + 50*a**4*b*c**9*d/3 + 10*a**3*b**2*c**10/3) + x**2*(5*a**5*c**9*d + 5*a**4*b*c**10/2)","B",0
1307,1,748,0,0.182787," ","integrate((b*x+a)**4*(d*x+c)**10,x)","a^{4} c^{10} x + \frac{b^{4} d^{10} x^{15}}{15} + x^{14} \left(\frac{2 a b^{3} d^{10}}{7} + \frac{5 b^{4} c d^{9}}{7}\right) + x^{13} \left(\frac{6 a^{2} b^{2} d^{10}}{13} + \frac{40 a b^{3} c d^{9}}{13} + \frac{45 b^{4} c^{2} d^{8}}{13}\right) + x^{12} \left(\frac{a^{3} b d^{10}}{3} + 5 a^{2} b^{2} c d^{9} + 15 a b^{3} c^{2} d^{8} + 10 b^{4} c^{3} d^{7}\right) + x^{11} \left(\frac{a^{4} d^{10}}{11} + \frac{40 a^{3} b c d^{9}}{11} + \frac{270 a^{2} b^{2} c^{2} d^{8}}{11} + \frac{480 a b^{3} c^{3} d^{7}}{11} + \frac{210 b^{4} c^{4} d^{6}}{11}\right) + x^{10} \left(a^{4} c d^{9} + 18 a^{3} b c^{2} d^{8} + 72 a^{2} b^{2} c^{3} d^{7} + 84 a b^{3} c^{4} d^{6} + \frac{126 b^{4} c^{5} d^{5}}{5}\right) + x^{9} \left(5 a^{4} c^{2} d^{8} + \frac{160 a^{3} b c^{3} d^{7}}{3} + 140 a^{2} b^{2} c^{4} d^{6} + 112 a b^{3} c^{5} d^{5} + \frac{70 b^{4} c^{6} d^{4}}{3}\right) + x^{8} \left(15 a^{4} c^{3} d^{7} + 105 a^{3} b c^{4} d^{6} + 189 a^{2} b^{2} c^{5} d^{5} + 105 a b^{3} c^{6} d^{4} + 15 b^{4} c^{7} d^{3}\right) + x^{7} \left(30 a^{4} c^{4} d^{6} + 144 a^{3} b c^{5} d^{5} + 180 a^{2} b^{2} c^{6} d^{4} + \frac{480 a b^{3} c^{7} d^{3}}{7} + \frac{45 b^{4} c^{8} d^{2}}{7}\right) + x^{6} \left(42 a^{4} c^{5} d^{5} + 140 a^{3} b c^{6} d^{4} + 120 a^{2} b^{2} c^{7} d^{3} + 30 a b^{3} c^{8} d^{2} + \frac{5 b^{4} c^{9} d}{3}\right) + x^{5} \left(42 a^{4} c^{6} d^{4} + 96 a^{3} b c^{7} d^{3} + 54 a^{2} b^{2} c^{8} d^{2} + 8 a b^{3} c^{9} d + \frac{b^{4} c^{10}}{5}\right) + x^{4} \left(30 a^{4} c^{7} d^{3} + 45 a^{3} b c^{8} d^{2} + 15 a^{2} b^{2} c^{9} d + a b^{3} c^{10}\right) + x^{3} \left(15 a^{4} c^{8} d^{2} + \frac{40 a^{3} b c^{9} d}{3} + 2 a^{2} b^{2} c^{10}\right) + x^{2} \left(5 a^{4} c^{9} d + 2 a^{3} b c^{10}\right)"," ",0,"a**4*c**10*x + b**4*d**10*x**15/15 + x**14*(2*a*b**3*d**10/7 + 5*b**4*c*d**9/7) + x**13*(6*a**2*b**2*d**10/13 + 40*a*b**3*c*d**9/13 + 45*b**4*c**2*d**8/13) + x**12*(a**3*b*d**10/3 + 5*a**2*b**2*c*d**9 + 15*a*b**3*c**2*d**8 + 10*b**4*c**3*d**7) + x**11*(a**4*d**10/11 + 40*a**3*b*c*d**9/11 + 270*a**2*b**2*c**2*d**8/11 + 480*a*b**3*c**3*d**7/11 + 210*b**4*c**4*d**6/11) + x**10*(a**4*c*d**9 + 18*a**3*b*c**2*d**8 + 72*a**2*b**2*c**3*d**7 + 84*a*b**3*c**4*d**6 + 126*b**4*c**5*d**5/5) + x**9*(5*a**4*c**2*d**8 + 160*a**3*b*c**3*d**7/3 + 140*a**2*b**2*c**4*d**6 + 112*a*b**3*c**5*d**5 + 70*b**4*c**6*d**4/3) + x**8*(15*a**4*c**3*d**7 + 105*a**3*b*c**4*d**6 + 189*a**2*b**2*c**5*d**5 + 105*a*b**3*c**6*d**4 + 15*b**4*c**7*d**3) + x**7*(30*a**4*c**4*d**6 + 144*a**3*b*c**5*d**5 + 180*a**2*b**2*c**6*d**4 + 480*a*b**3*c**7*d**3/7 + 45*b**4*c**8*d**2/7) + x**6*(42*a**4*c**5*d**5 + 140*a**3*b*c**6*d**4 + 120*a**2*b**2*c**7*d**3 + 30*a*b**3*c**8*d**2 + 5*b**4*c**9*d/3) + x**5*(42*a**4*c**6*d**4 + 96*a**3*b*c**7*d**3 + 54*a**2*b**2*c**8*d**2 + 8*a*b**3*c**9*d + b**4*c**10/5) + x**4*(30*a**4*c**7*d**3 + 45*a**3*b*c**8*d**2 + 15*a**2*b**2*c**9*d + a*b**3*c**10) + x**3*(15*a**4*c**8*d**2 + 40*a**3*b*c**9*d/3 + 2*a**2*b**2*c**10) + x**2*(5*a**4*c**9*d + 2*a**3*b*c**10)","B",0
1308,1,586,0,0.162438," ","integrate((b*x+a)**3*(d*x+c)**10,x)","a^{3} c^{10} x + \frac{b^{3} d^{10} x^{14}}{14} + x^{13} \left(\frac{3 a b^{2} d^{10}}{13} + \frac{10 b^{3} c d^{9}}{13}\right) + x^{12} \left(\frac{a^{2} b d^{10}}{4} + \frac{5 a b^{2} c d^{9}}{2} + \frac{15 b^{3} c^{2} d^{8}}{4}\right) + x^{11} \left(\frac{a^{3} d^{10}}{11} + \frac{30 a^{2} b c d^{9}}{11} + \frac{135 a b^{2} c^{2} d^{8}}{11} + \frac{120 b^{3} c^{3} d^{7}}{11}\right) + x^{10} \left(a^{3} c d^{9} + \frac{27 a^{2} b c^{2} d^{8}}{2} + 36 a b^{2} c^{3} d^{7} + 21 b^{3} c^{4} d^{6}\right) + x^{9} \left(5 a^{3} c^{2} d^{8} + 40 a^{2} b c^{3} d^{7} + 70 a b^{2} c^{4} d^{6} + 28 b^{3} c^{5} d^{5}\right) + x^{8} \left(15 a^{3} c^{3} d^{7} + \frac{315 a^{2} b c^{4} d^{6}}{4} + \frac{189 a b^{2} c^{5} d^{5}}{2} + \frac{105 b^{3} c^{6} d^{4}}{4}\right) + x^{7} \left(30 a^{3} c^{4} d^{6} + 108 a^{2} b c^{5} d^{5} + 90 a b^{2} c^{6} d^{4} + \frac{120 b^{3} c^{7} d^{3}}{7}\right) + x^{6} \left(42 a^{3} c^{5} d^{5} + 105 a^{2} b c^{6} d^{4} + 60 a b^{2} c^{7} d^{3} + \frac{15 b^{3} c^{8} d^{2}}{2}\right) + x^{5} \left(42 a^{3} c^{6} d^{4} + 72 a^{2} b c^{7} d^{3} + 27 a b^{2} c^{8} d^{2} + 2 b^{3} c^{9} d\right) + x^{4} \left(30 a^{3} c^{7} d^{3} + \frac{135 a^{2} b c^{8} d^{2}}{4} + \frac{15 a b^{2} c^{9} d}{2} + \frac{b^{3} c^{10}}{4}\right) + x^{3} \left(15 a^{3} c^{8} d^{2} + 10 a^{2} b c^{9} d + a b^{2} c^{10}\right) + x^{2} \left(5 a^{3} c^{9} d + \frac{3 a^{2} b c^{10}}{2}\right)"," ",0,"a**3*c**10*x + b**3*d**10*x**14/14 + x**13*(3*a*b**2*d**10/13 + 10*b**3*c*d**9/13) + x**12*(a**2*b*d**10/4 + 5*a*b**2*c*d**9/2 + 15*b**3*c**2*d**8/4) + x**11*(a**3*d**10/11 + 30*a**2*b*c*d**9/11 + 135*a*b**2*c**2*d**8/11 + 120*b**3*c**3*d**7/11) + x**10*(a**3*c*d**9 + 27*a**2*b*c**2*d**8/2 + 36*a*b**2*c**3*d**7 + 21*b**3*c**4*d**6) + x**9*(5*a**3*c**2*d**8 + 40*a**2*b*c**3*d**7 + 70*a*b**2*c**4*d**6 + 28*b**3*c**5*d**5) + x**8*(15*a**3*c**3*d**7 + 315*a**2*b*c**4*d**6/4 + 189*a*b**2*c**5*d**5/2 + 105*b**3*c**6*d**4/4) + x**7*(30*a**3*c**4*d**6 + 108*a**2*b*c**5*d**5 + 90*a*b**2*c**6*d**4 + 120*b**3*c**7*d**3/7) + x**6*(42*a**3*c**5*d**5 + 105*a**2*b*c**6*d**4 + 60*a*b**2*c**7*d**3 + 15*b**3*c**8*d**2/2) + x**5*(42*a**3*c**6*d**4 + 72*a**2*b*c**7*d**3 + 27*a*b**2*c**8*d**2 + 2*b**3*c**9*d) + x**4*(30*a**3*c**7*d**3 + 135*a**2*b*c**8*d**2/4 + 15*a*b**2*c**9*d/2 + b**3*c**10/4) + x**3*(15*a**3*c**8*d**2 + 10*a**2*b*c**9*d + a*b**2*c**10) + x**2*(5*a**3*c**9*d + 3*a**2*b*c**10/2)","B",0
1309,1,415,0,0.144595," ","integrate((b*x+a)**2*(d*x+c)**10,x)","a^{2} c^{10} x + \frac{b^{2} d^{10} x^{13}}{13} + x^{12} \left(\frac{a b d^{10}}{6} + \frac{5 b^{2} c d^{9}}{6}\right) + x^{11} \left(\frac{a^{2} d^{10}}{11} + \frac{20 a b c d^{9}}{11} + \frac{45 b^{2} c^{2} d^{8}}{11}\right) + x^{10} \left(a^{2} c d^{9} + 9 a b c^{2} d^{8} + 12 b^{2} c^{3} d^{7}\right) + x^{9} \left(5 a^{2} c^{2} d^{8} + \frac{80 a b c^{3} d^{7}}{3} + \frac{70 b^{2} c^{4} d^{6}}{3}\right) + x^{8} \left(15 a^{2} c^{3} d^{7} + \frac{105 a b c^{4} d^{6}}{2} + \frac{63 b^{2} c^{5} d^{5}}{2}\right) + x^{7} \left(30 a^{2} c^{4} d^{6} + 72 a b c^{5} d^{5} + 30 b^{2} c^{6} d^{4}\right) + x^{6} \left(42 a^{2} c^{5} d^{5} + 70 a b c^{6} d^{4} + 20 b^{2} c^{7} d^{3}\right) + x^{5} \left(42 a^{2} c^{6} d^{4} + 48 a b c^{7} d^{3} + 9 b^{2} c^{8} d^{2}\right) + x^{4} \left(30 a^{2} c^{7} d^{3} + \frac{45 a b c^{8} d^{2}}{2} + \frac{5 b^{2} c^{9} d}{2}\right) + x^{3} \left(15 a^{2} c^{8} d^{2} + \frac{20 a b c^{9} d}{3} + \frac{b^{2} c^{10}}{3}\right) + x^{2} \left(5 a^{2} c^{9} d + a b c^{10}\right)"," ",0,"a**2*c**10*x + b**2*d**10*x**13/13 + x**12*(a*b*d**10/6 + 5*b**2*c*d**9/6) + x**11*(a**2*d**10/11 + 20*a*b*c*d**9/11 + 45*b**2*c**2*d**8/11) + x**10*(a**2*c*d**9 + 9*a*b*c**2*d**8 + 12*b**2*c**3*d**7) + x**9*(5*a**2*c**2*d**8 + 80*a*b*c**3*d**7/3 + 70*b**2*c**4*d**6/3) + x**8*(15*a**2*c**3*d**7 + 105*a*b*c**4*d**6/2 + 63*b**2*c**5*d**5/2) + x**7*(30*a**2*c**4*d**6 + 72*a*b*c**5*d**5 + 30*b**2*c**6*d**4) + x**6*(42*a**2*c**5*d**5 + 70*a*b*c**6*d**4 + 20*b**2*c**7*d**3) + x**5*(42*a**2*c**6*d**4 + 48*a*b*c**7*d**3 + 9*b**2*c**8*d**2) + x**4*(30*a**2*c**7*d**3 + 45*a*b*c**8*d**2/2 + 5*b**2*c**9*d/2) + x**3*(15*a**2*c**8*d**2 + 20*a*b*c**9*d/3 + b**2*c**10/3) + x**2*(5*a**2*c**9*d + a*b*c**10)","B",0
1310,1,248,0,0.119243," ","integrate((b*x+a)*(d*x+c)**10,x)","a c^{10} x + \frac{b d^{10} x^{12}}{12} + x^{11} \left(\frac{a d^{10}}{11} + \frac{10 b c d^{9}}{11}\right) + x^{10} \left(a c d^{9} + \frac{9 b c^{2} d^{8}}{2}\right) + x^{9} \left(5 a c^{2} d^{8} + \frac{40 b c^{3} d^{7}}{3}\right) + x^{8} \left(15 a c^{3} d^{7} + \frac{105 b c^{4} d^{6}}{4}\right) + x^{7} \left(30 a c^{4} d^{6} + 36 b c^{5} d^{5}\right) + x^{6} \left(42 a c^{5} d^{5} + 35 b c^{6} d^{4}\right) + x^{5} \left(42 a c^{6} d^{4} + 24 b c^{7} d^{3}\right) + x^{4} \left(30 a c^{7} d^{3} + \frac{45 b c^{8} d^{2}}{4}\right) + x^{3} \left(15 a c^{8} d^{2} + \frac{10 b c^{9} d}{3}\right) + x^{2} \left(5 a c^{9} d + \frac{b c^{10}}{2}\right)"," ",0,"a*c**10*x + b*d**10*x**12/12 + x**11*(a*d**10/11 + 10*b*c*d**9/11) + x**10*(a*c*d**9 + 9*b*c**2*d**8/2) + x**9*(5*a*c**2*d**8 + 40*b*c**3*d**7/3) + x**8*(15*a*c**3*d**7 + 105*b*c**4*d**6/4) + x**7*(30*a*c**4*d**6 + 36*b*c**5*d**5) + x**6*(42*a*c**5*d**5 + 35*b*c**6*d**4) + x**5*(42*a*c**6*d**4 + 24*b*c**7*d**3) + x**4*(30*a*c**7*d**3 + 45*b*c**8*d**2/4) + x**3*(15*a*c**8*d**2 + 10*b*c**9*d/3) + x**2*(5*a*c**9*d + b*c**10/2)","B",0
1311,1,114,0,0.087501," ","integrate((d*x+c)**10,x)","c^{10} x + 5 c^{9} d x^{2} + 15 c^{8} d^{2} x^{3} + 30 c^{7} d^{3} x^{4} + 42 c^{6} d^{4} x^{5} + 42 c^{5} d^{5} x^{6} + 30 c^{4} d^{6} x^{7} + 15 c^{3} d^{7} x^{8} + 5 c^{2} d^{8} x^{9} + c d^{9} x^{10} + \frac{d^{10} x^{11}}{11}"," ",0,"c**10*x + 5*c**9*d*x**2 + 15*c**8*d**2*x**3 + 30*c**7*d**3*x**4 + 42*c**6*d**4*x**5 + 42*c**5*d**5*x**6 + 30*c**4*d**6*x**7 + 15*c**3*d**7*x**8 + 5*c**2*d**8*x**9 + c*d**9*x**10 + d**10*x**11/11","B",0
1312,1,799,0,1.415004," ","integrate((d*x+c)**10/(b*x+a),x)","x^{9} \left(- \frac{a d^{10}}{9 b^{2}} + \frac{10 c d^{9}}{9 b}\right) + x^{8} \left(\frac{a^{2} d^{10}}{8 b^{3}} - \frac{5 a c d^{9}}{4 b^{2}} + \frac{45 c^{2} d^{8}}{8 b}\right) + x^{7} \left(- \frac{a^{3} d^{10}}{7 b^{4}} + \frac{10 a^{2} c d^{9}}{7 b^{3}} - \frac{45 a c^{2} d^{8}}{7 b^{2}} + \frac{120 c^{3} d^{7}}{7 b}\right) + x^{6} \left(\frac{a^{4} d^{10}}{6 b^{5}} - \frac{5 a^{3} c d^{9}}{3 b^{4}} + \frac{15 a^{2} c^{2} d^{8}}{2 b^{3}} - \frac{20 a c^{3} d^{7}}{b^{2}} + \frac{35 c^{4} d^{6}}{b}\right) + x^{5} \left(- \frac{a^{5} d^{10}}{5 b^{6}} + \frac{2 a^{4} c d^{9}}{b^{5}} - \frac{9 a^{3} c^{2} d^{8}}{b^{4}} + \frac{24 a^{2} c^{3} d^{7}}{b^{3}} - \frac{42 a c^{4} d^{6}}{b^{2}} + \frac{252 c^{5} d^{5}}{5 b}\right) + x^{4} \left(\frac{a^{6} d^{10}}{4 b^{7}} - \frac{5 a^{5} c d^{9}}{2 b^{6}} + \frac{45 a^{4} c^{2} d^{8}}{4 b^{5}} - \frac{30 a^{3} c^{3} d^{7}}{b^{4}} + \frac{105 a^{2} c^{4} d^{6}}{2 b^{3}} - \frac{63 a c^{5} d^{5}}{b^{2}} + \frac{105 c^{6} d^{4}}{2 b}\right) + x^{3} \left(- \frac{a^{7} d^{10}}{3 b^{8}} + \frac{10 a^{6} c d^{9}}{3 b^{7}} - \frac{15 a^{5} c^{2} d^{8}}{b^{6}} + \frac{40 a^{4} c^{3} d^{7}}{b^{5}} - \frac{70 a^{3} c^{4} d^{6}}{b^{4}} + \frac{84 a^{2} c^{5} d^{5}}{b^{3}} - \frac{70 a c^{6} d^{4}}{b^{2}} + \frac{40 c^{7} d^{3}}{b}\right) + x^{2} \left(\frac{a^{8} d^{10}}{2 b^{9}} - \frac{5 a^{7} c d^{9}}{b^{8}} + \frac{45 a^{6} c^{2} d^{8}}{2 b^{7}} - \frac{60 a^{5} c^{3} d^{7}}{b^{6}} + \frac{105 a^{4} c^{4} d^{6}}{b^{5}} - \frac{126 a^{3} c^{5} d^{5}}{b^{4}} + \frac{105 a^{2} c^{6} d^{4}}{b^{3}} - \frac{60 a c^{7} d^{3}}{b^{2}} + \frac{45 c^{8} d^{2}}{2 b}\right) + x \left(- \frac{a^{9} d^{10}}{b^{10}} + \frac{10 a^{8} c d^{9}}{b^{9}} - \frac{45 a^{7} c^{2} d^{8}}{b^{8}} + \frac{120 a^{6} c^{3} d^{7}}{b^{7}} - \frac{210 a^{5} c^{4} d^{6}}{b^{6}} + \frac{252 a^{4} c^{5} d^{5}}{b^{5}} - \frac{210 a^{3} c^{6} d^{4}}{b^{4}} + \frac{120 a^{2} c^{7} d^{3}}{b^{3}} - \frac{45 a c^{8} d^{2}}{b^{2}} + \frac{10 c^{9} d}{b}\right) + \frac{d^{10} x^{10}}{10 b} + \frac{\left(a d - b c\right)^{10} \log{\left(a + b x \right)}}{b^{11}}"," ",0,"x**9*(-a*d**10/(9*b**2) + 10*c*d**9/(9*b)) + x**8*(a**2*d**10/(8*b**3) - 5*a*c*d**9/(4*b**2) + 45*c**2*d**8/(8*b)) + x**7*(-a**3*d**10/(7*b**4) + 10*a**2*c*d**9/(7*b**3) - 45*a*c**2*d**8/(7*b**2) + 120*c**3*d**7/(7*b)) + x**6*(a**4*d**10/(6*b**5) - 5*a**3*c*d**9/(3*b**4) + 15*a**2*c**2*d**8/(2*b**3) - 20*a*c**3*d**7/b**2 + 35*c**4*d**6/b) + x**5*(-a**5*d**10/(5*b**6) + 2*a**4*c*d**9/b**5 - 9*a**3*c**2*d**8/b**4 + 24*a**2*c**3*d**7/b**3 - 42*a*c**4*d**6/b**2 + 252*c**5*d**5/(5*b)) + x**4*(a**6*d**10/(4*b**7) - 5*a**5*c*d**9/(2*b**6) + 45*a**4*c**2*d**8/(4*b**5) - 30*a**3*c**3*d**7/b**4 + 105*a**2*c**4*d**6/(2*b**3) - 63*a*c**5*d**5/b**2 + 105*c**6*d**4/(2*b)) + x**3*(-a**7*d**10/(3*b**8) + 10*a**6*c*d**9/(3*b**7) - 15*a**5*c**2*d**8/b**6 + 40*a**4*c**3*d**7/b**5 - 70*a**3*c**4*d**6/b**4 + 84*a**2*c**5*d**5/b**3 - 70*a*c**6*d**4/b**2 + 40*c**7*d**3/b) + x**2*(a**8*d**10/(2*b**9) - 5*a**7*c*d**9/b**8 + 45*a**6*c**2*d**8/(2*b**7) - 60*a**5*c**3*d**7/b**6 + 105*a**4*c**4*d**6/b**5 - 126*a**3*c**5*d**5/b**4 + 105*a**2*c**6*d**4/b**3 - 60*a*c**7*d**3/b**2 + 45*c**8*d**2/(2*b)) + x*(-a**9*d**10/b**10 + 10*a**8*c*d**9/b**9 - 45*a**7*c**2*d**8/b**8 + 120*a**6*c**3*d**7/b**7 - 210*a**5*c**4*d**6/b**6 + 252*a**4*c**5*d**5/b**5 - 210*a**3*c**6*d**4/b**4 + 120*a**2*c**7*d**3/b**3 - 45*a*c**8*d**2/b**2 + 10*c**9*d/b) + d**10*x**10/(10*b) + (a*d - b*c)**10*log(a + b*x)/b**11","B",0
1313,1,816,0,2.652726," ","integrate((d*x+c)**10/(b*x+a)**2,x)","x^{8} \left(- \frac{a d^{10}}{4 b^{3}} + \frac{5 c d^{9}}{4 b^{2}}\right) + x^{7} \left(\frac{3 a^{2} d^{10}}{7 b^{4}} - \frac{20 a c d^{9}}{7 b^{3}} + \frac{45 c^{2} d^{8}}{7 b^{2}}\right) + x^{6} \left(- \frac{2 a^{3} d^{10}}{3 b^{5}} + \frac{5 a^{2} c d^{9}}{b^{4}} - \frac{15 a c^{2} d^{8}}{b^{3}} + \frac{20 c^{3} d^{7}}{b^{2}}\right) + x^{5} \left(\frac{a^{4} d^{10}}{b^{6}} - \frac{8 a^{3} c d^{9}}{b^{5}} + \frac{27 a^{2} c^{2} d^{8}}{b^{4}} - \frac{48 a c^{3} d^{7}}{b^{3}} + \frac{42 c^{4} d^{6}}{b^{2}}\right) + x^{4} \left(- \frac{3 a^{5} d^{10}}{2 b^{7}} + \frac{25 a^{4} c d^{9}}{2 b^{6}} - \frac{45 a^{3} c^{2} d^{8}}{b^{5}} + \frac{90 a^{2} c^{3} d^{7}}{b^{4}} - \frac{105 a c^{4} d^{6}}{b^{3}} + \frac{63 c^{5} d^{5}}{b^{2}}\right) + x^{3} \left(\frac{7 a^{6} d^{10}}{3 b^{8}} - \frac{20 a^{5} c d^{9}}{b^{7}} + \frac{75 a^{4} c^{2} d^{8}}{b^{6}} - \frac{160 a^{3} c^{3} d^{7}}{b^{5}} + \frac{210 a^{2} c^{4} d^{6}}{b^{4}} - \frac{168 a c^{5} d^{5}}{b^{3}} + \frac{70 c^{6} d^{4}}{b^{2}}\right) + x^{2} \left(- \frac{4 a^{7} d^{10}}{b^{9}} + \frac{35 a^{6} c d^{9}}{b^{8}} - \frac{135 a^{5} c^{2} d^{8}}{b^{7}} + \frac{300 a^{4} c^{3} d^{7}}{b^{6}} - \frac{420 a^{3} c^{4} d^{6}}{b^{5}} + \frac{378 a^{2} c^{5} d^{5}}{b^{4}} - \frac{210 a c^{6} d^{4}}{b^{3}} + \frac{60 c^{7} d^{3}}{b^{2}}\right) + x \left(\frac{9 a^{8} d^{10}}{b^{10}} - \frac{80 a^{7} c d^{9}}{b^{9}} + \frac{315 a^{6} c^{2} d^{8}}{b^{8}} - \frac{720 a^{5} c^{3} d^{7}}{b^{7}} + \frac{1050 a^{4} c^{4} d^{6}}{b^{6}} - \frac{1008 a^{3} c^{5} d^{5}}{b^{5}} + \frac{630 a^{2} c^{6} d^{4}}{b^{4}} - \frac{240 a c^{7} d^{3}}{b^{3}} + \frac{45 c^{8} d^{2}}{b^{2}}\right) + \frac{- a^{10} d^{10} + 10 a^{9} b c d^{9} - 45 a^{8} b^{2} c^{2} d^{8} + 120 a^{7} b^{3} c^{3} d^{7} - 210 a^{6} b^{4} c^{4} d^{6} + 252 a^{5} b^{5} c^{5} d^{5} - 210 a^{4} b^{6} c^{6} d^{4} + 120 a^{3} b^{7} c^{7} d^{3} - 45 a^{2} b^{8} c^{8} d^{2} + 10 a b^{9} c^{9} d - b^{10} c^{10}}{a b^{11} + b^{12} x} + \frac{d^{10} x^{9}}{9 b^{2}} - \frac{10 d \left(a d - b c\right)^{9} \log{\left(a + b x \right)}}{b^{11}}"," ",0,"x**8*(-a*d**10/(4*b**3) + 5*c*d**9/(4*b**2)) + x**7*(3*a**2*d**10/(7*b**4) - 20*a*c*d**9/(7*b**3) + 45*c**2*d**8/(7*b**2)) + x**6*(-2*a**3*d**10/(3*b**5) + 5*a**2*c*d**9/b**4 - 15*a*c**2*d**8/b**3 + 20*c**3*d**7/b**2) + x**5*(a**4*d**10/b**6 - 8*a**3*c*d**9/b**5 + 27*a**2*c**2*d**8/b**4 - 48*a*c**3*d**7/b**3 + 42*c**4*d**6/b**2) + x**4*(-3*a**5*d**10/(2*b**7) + 25*a**4*c*d**9/(2*b**6) - 45*a**3*c**2*d**8/b**5 + 90*a**2*c**3*d**7/b**4 - 105*a*c**4*d**6/b**3 + 63*c**5*d**5/b**2) + x**3*(7*a**6*d**10/(3*b**8) - 20*a**5*c*d**9/b**7 + 75*a**4*c**2*d**8/b**6 - 160*a**3*c**3*d**7/b**5 + 210*a**2*c**4*d**6/b**4 - 168*a*c**5*d**5/b**3 + 70*c**6*d**4/b**2) + x**2*(-4*a**7*d**10/b**9 + 35*a**6*c*d**9/b**8 - 135*a**5*c**2*d**8/b**7 + 300*a**4*c**3*d**7/b**6 - 420*a**3*c**4*d**6/b**5 + 378*a**2*c**5*d**5/b**4 - 210*a*c**6*d**4/b**3 + 60*c**7*d**3/b**2) + x*(9*a**8*d**10/b**10 - 80*a**7*c*d**9/b**9 + 315*a**6*c**2*d**8/b**8 - 720*a**5*c**3*d**7/b**7 + 1050*a**4*c**4*d**6/b**6 - 1008*a**3*c**5*d**5/b**5 + 630*a**2*c**6*d**4/b**4 - 240*a*c**7*d**3/b**3 + 45*c**8*d**2/b**2) + (-a**10*d**10 + 10*a**9*b*c*d**9 - 45*a**8*b**2*c**2*d**8 + 120*a**7*b**3*c**3*d**7 - 210*a**6*b**4*c**4*d**6 + 252*a**5*b**5*c**5*d**5 - 210*a**4*b**6*c**6*d**4 + 120*a**3*b**7*c**7*d**3 - 45*a**2*b**8*c**8*d**2 + 10*a*b**9*c**9*d - b**10*c**10)/(a*b**11 + b**12*x) + d**10*x**9/(9*b**2) - 10*d*(a*d - b*c)**9*log(a + b*x)/b**11","B",0
1314,1,843,0,5.671102," ","integrate((d*x+c)**10/(b*x+a)**3,x)","x^{7} \left(- \frac{3 a d^{10}}{7 b^{4}} + \frac{10 c d^{9}}{7 b^{3}}\right) + x^{6} \left(\frac{a^{2} d^{10}}{b^{5}} - \frac{5 a c d^{9}}{b^{4}} + \frac{15 c^{2} d^{8}}{2 b^{3}}\right) + x^{5} \left(- \frac{2 a^{3} d^{10}}{b^{6}} + \frac{12 a^{2} c d^{9}}{b^{5}} - \frac{27 a c^{2} d^{8}}{b^{4}} + \frac{24 c^{3} d^{7}}{b^{3}}\right) + x^{4} \left(\frac{15 a^{4} d^{10}}{4 b^{7}} - \frac{25 a^{3} c d^{9}}{b^{6}} + \frac{135 a^{2} c^{2} d^{8}}{2 b^{5}} - \frac{90 a c^{3} d^{7}}{b^{4}} + \frac{105 c^{4} d^{6}}{2 b^{3}}\right) + x^{3} \left(- \frac{7 a^{5} d^{10}}{b^{8}} + \frac{50 a^{4} c d^{9}}{b^{7}} - \frac{150 a^{3} c^{2} d^{8}}{b^{6}} + \frac{240 a^{2} c^{3} d^{7}}{b^{5}} - \frac{210 a c^{4} d^{6}}{b^{4}} + \frac{84 c^{5} d^{5}}{b^{3}}\right) + x^{2} \left(\frac{14 a^{6} d^{10}}{b^{9}} - \frac{105 a^{5} c d^{9}}{b^{8}} + \frac{675 a^{4} c^{2} d^{8}}{2 b^{7}} - \frac{600 a^{3} c^{3} d^{7}}{b^{6}} + \frac{630 a^{2} c^{4} d^{6}}{b^{5}} - \frac{378 a c^{5} d^{5}}{b^{4}} + \frac{105 c^{6} d^{4}}{b^{3}}\right) + x \left(- \frac{36 a^{7} d^{10}}{b^{10}} + \frac{280 a^{6} c d^{9}}{b^{9}} - \frac{945 a^{5} c^{2} d^{8}}{b^{8}} + \frac{1800 a^{4} c^{3} d^{7}}{b^{7}} - \frac{2100 a^{3} c^{4} d^{6}}{b^{6}} + \frac{1512 a^{2} c^{5} d^{5}}{b^{5}} - \frac{630 a c^{6} d^{4}}{b^{4}} + \frac{120 c^{7} d^{3}}{b^{3}}\right) + \frac{19 a^{10} d^{10} - 170 a^{9} b c d^{9} + 675 a^{8} b^{2} c^{2} d^{8} - 1560 a^{7} b^{3} c^{3} d^{7} + 2310 a^{6} b^{4} c^{4} d^{6} - 2268 a^{5} b^{5} c^{5} d^{5} + 1470 a^{4} b^{6} c^{6} d^{4} - 600 a^{3} b^{7} c^{7} d^{3} + 135 a^{2} b^{8} c^{8} d^{2} - 10 a b^{9} c^{9} d - b^{10} c^{10} + x \left(20 a^{9} b d^{10} - 180 a^{8} b^{2} c d^{9} + 720 a^{7} b^{3} c^{2} d^{8} - 1680 a^{6} b^{4} c^{3} d^{7} + 2520 a^{5} b^{5} c^{4} d^{6} - 2520 a^{4} b^{6} c^{5} d^{5} + 1680 a^{3} b^{7} c^{6} d^{4} - 720 a^{2} b^{8} c^{7} d^{3} + 180 a b^{9} c^{8} d^{2} - 20 b^{10} c^{9} d\right)}{2 a^{2} b^{11} + 4 a b^{12} x + 2 b^{13} x^{2}} + \frac{d^{10} x^{8}}{8 b^{3}} + \frac{45 d^{2} \left(a d - b c\right)^{8} \log{\left(a + b x \right)}}{b^{11}}"," ",0,"x**7*(-3*a*d**10/(7*b**4) + 10*c*d**9/(7*b**3)) + x**6*(a**2*d**10/b**5 - 5*a*c*d**9/b**4 + 15*c**2*d**8/(2*b**3)) + x**5*(-2*a**3*d**10/b**6 + 12*a**2*c*d**9/b**5 - 27*a*c**2*d**8/b**4 + 24*c**3*d**7/b**3) + x**4*(15*a**4*d**10/(4*b**7) - 25*a**3*c*d**9/b**6 + 135*a**2*c**2*d**8/(2*b**5) - 90*a*c**3*d**7/b**4 + 105*c**4*d**6/(2*b**3)) + x**3*(-7*a**5*d**10/b**8 + 50*a**4*c*d**9/b**7 - 150*a**3*c**2*d**8/b**6 + 240*a**2*c**3*d**7/b**5 - 210*a*c**4*d**6/b**4 + 84*c**5*d**5/b**3) + x**2*(14*a**6*d**10/b**9 - 105*a**5*c*d**9/b**8 + 675*a**4*c**2*d**8/(2*b**7) - 600*a**3*c**3*d**7/b**6 + 630*a**2*c**4*d**6/b**5 - 378*a*c**5*d**5/b**4 + 105*c**6*d**4/b**3) + x*(-36*a**7*d**10/b**10 + 280*a**6*c*d**9/b**9 - 945*a**5*c**2*d**8/b**8 + 1800*a**4*c**3*d**7/b**7 - 2100*a**3*c**4*d**6/b**6 + 1512*a**2*c**5*d**5/b**5 - 630*a*c**6*d**4/b**4 + 120*c**7*d**3/b**3) + (19*a**10*d**10 - 170*a**9*b*c*d**9 + 675*a**8*b**2*c**2*d**8 - 1560*a**7*b**3*c**3*d**7 + 2310*a**6*b**4*c**4*d**6 - 2268*a**5*b**5*c**5*d**5 + 1470*a**4*b**6*c**6*d**4 - 600*a**3*b**7*c**7*d**3 + 135*a**2*b**8*c**8*d**2 - 10*a*b**9*c**9*d - b**10*c**10 + x*(20*a**9*b*d**10 - 180*a**8*b**2*c*d**9 + 720*a**7*b**3*c**2*d**8 - 1680*a**6*b**4*c**3*d**7 + 2520*a**5*b**5*c**4*d**6 - 2520*a**4*b**6*c**5*d**5 + 1680*a**3*b**7*c**6*d**4 - 720*a**2*b**8*c**7*d**3 + 180*a*b**9*c**8*d**2 - 20*b**10*c**9*d))/(2*a**2*b**11 + 4*a*b**12*x + 2*b**13*x**2) + d**10*x**8/(8*b**3) + 45*d**2*(a*d - b*c)**8*log(a + b*x)/b**11","B",0
1315,1,867,0,32.528177," ","integrate((d*x+c)**10/(b*x+a)**4,x)","x^{6} \left(- \frac{2 a d^{10}}{3 b^{5}} + \frac{5 c d^{9}}{3 b^{4}}\right) + x^{5} \left(\frac{2 a^{2} d^{10}}{b^{6}} - \frac{8 a c d^{9}}{b^{5}} + \frac{9 c^{2} d^{8}}{b^{4}}\right) + x^{4} \left(- \frac{5 a^{3} d^{10}}{b^{7}} + \frac{25 a^{2} c d^{9}}{b^{6}} - \frac{45 a c^{2} d^{8}}{b^{5}} + \frac{30 c^{3} d^{7}}{b^{4}}\right) + x^{3} \left(\frac{35 a^{4} d^{10}}{3 b^{8}} - \frac{200 a^{3} c d^{9}}{3 b^{7}} + \frac{150 a^{2} c^{2} d^{8}}{b^{6}} - \frac{160 a c^{3} d^{7}}{b^{5}} + \frac{70 c^{4} d^{6}}{b^{4}}\right) + x^{2} \left(- \frac{28 a^{5} d^{10}}{b^{9}} + \frac{175 a^{4} c d^{9}}{b^{8}} - \frac{450 a^{3} c^{2} d^{8}}{b^{7}} + \frac{600 a^{2} c^{3} d^{7}}{b^{6}} - \frac{420 a c^{4} d^{6}}{b^{5}} + \frac{126 c^{5} d^{5}}{b^{4}}\right) + x \left(\frac{84 a^{6} d^{10}}{b^{10}} - \frac{560 a^{5} c d^{9}}{b^{9}} + \frac{1575 a^{4} c^{2} d^{8}}{b^{8}} - \frac{2400 a^{3} c^{3} d^{7}}{b^{7}} + \frac{2100 a^{2} c^{4} d^{6}}{b^{6}} - \frac{1008 a c^{5} d^{5}}{b^{5}} + \frac{210 c^{6} d^{4}}{b^{4}}\right) + \frac{- 121 a^{10} d^{10} + 955 a^{9} b c d^{9} - 3285 a^{8} b^{2} c^{2} d^{8} + 6420 a^{7} b^{3} c^{3} d^{7} - 7770 a^{6} b^{4} c^{4} d^{6} + 5922 a^{5} b^{5} c^{5} d^{5} - 2730 a^{4} b^{6} c^{6} d^{4} + 660 a^{3} b^{7} c^{7} d^{3} - 45 a^{2} b^{8} c^{8} d^{2} - 5 a b^{9} c^{9} d - b^{10} c^{10} + x^{2} \left(- 135 a^{8} b^{2} d^{10} + 1080 a^{7} b^{3} c d^{9} - 3780 a^{6} b^{4} c^{2} d^{8} + 7560 a^{5} b^{5} c^{3} d^{7} - 9450 a^{4} b^{6} c^{4} d^{6} + 7560 a^{3} b^{7} c^{5} d^{5} - 3780 a^{2} b^{8} c^{6} d^{4} + 1080 a b^{9} c^{7} d^{3} - 135 b^{10} c^{8} d^{2}\right) + x \left(- 255 a^{9} b d^{10} + 2025 a^{8} b^{2} c d^{9} - 7020 a^{7} b^{3} c^{2} d^{8} + 13860 a^{6} b^{4} c^{3} d^{7} - 17010 a^{5} b^{5} c^{4} d^{6} + 13230 a^{4} b^{6} c^{5} d^{5} - 6300 a^{3} b^{7} c^{6} d^{4} + 1620 a^{2} b^{8} c^{7} d^{3} - 135 a b^{9} c^{8} d^{2} - 15 b^{10} c^{9} d\right)}{3 a^{3} b^{11} + 9 a^{2} b^{12} x + 9 a b^{13} x^{2} + 3 b^{14} x^{3}} + \frac{d^{10} x^{7}}{7 b^{4}} - \frac{120 d^{3} \left(a d - b c\right)^{7} \log{\left(a + b x \right)}}{b^{11}}"," ",0,"x**6*(-2*a*d**10/(3*b**5) + 5*c*d**9/(3*b**4)) + x**5*(2*a**2*d**10/b**6 - 8*a*c*d**9/b**5 + 9*c**2*d**8/b**4) + x**4*(-5*a**3*d**10/b**7 + 25*a**2*c*d**9/b**6 - 45*a*c**2*d**8/b**5 + 30*c**3*d**7/b**4) + x**3*(35*a**4*d**10/(3*b**8) - 200*a**3*c*d**9/(3*b**7) + 150*a**2*c**2*d**8/b**6 - 160*a*c**3*d**7/b**5 + 70*c**4*d**6/b**4) + x**2*(-28*a**5*d**10/b**9 + 175*a**4*c*d**9/b**8 - 450*a**3*c**2*d**8/b**7 + 600*a**2*c**3*d**7/b**6 - 420*a*c**4*d**6/b**5 + 126*c**5*d**5/b**4) + x*(84*a**6*d**10/b**10 - 560*a**5*c*d**9/b**9 + 1575*a**4*c**2*d**8/b**8 - 2400*a**3*c**3*d**7/b**7 + 2100*a**2*c**4*d**6/b**6 - 1008*a*c**5*d**5/b**5 + 210*c**6*d**4/b**4) + (-121*a**10*d**10 + 955*a**9*b*c*d**9 - 3285*a**8*b**2*c**2*d**8 + 6420*a**7*b**3*c**3*d**7 - 7770*a**6*b**4*c**4*d**6 + 5922*a**5*b**5*c**5*d**5 - 2730*a**4*b**6*c**6*d**4 + 660*a**3*b**7*c**7*d**3 - 45*a**2*b**8*c**8*d**2 - 5*a*b**9*c**9*d - b**10*c**10 + x**2*(-135*a**8*b**2*d**10 + 1080*a**7*b**3*c*d**9 - 3780*a**6*b**4*c**2*d**8 + 7560*a**5*b**5*c**3*d**7 - 9450*a**4*b**6*c**4*d**6 + 7560*a**3*b**7*c**5*d**5 - 3780*a**2*b**8*c**6*d**4 + 1080*a*b**9*c**7*d**3 - 135*b**10*c**8*d**2) + x*(-255*a**9*b*d**10 + 2025*a**8*b**2*c*d**9 - 7020*a**7*b**3*c**2*d**8 + 13860*a**6*b**4*c**3*d**7 - 17010*a**5*b**5*c**4*d**6 + 13230*a**4*b**6*c**5*d**5 - 6300*a**3*b**7*c**6*d**4 + 1620*a**2*b**8*c**7*d**3 - 135*a*b**9*c**8*d**2 - 15*b**10*c**9*d))/(3*a**3*b**11 + 9*a**2*b**12*x + 9*a*b**13*x**2 + 3*b**14*x**3) + d**10*x**7/(7*b**4) - 120*d**3*(a*d - b*c)**7*log(a + b*x)/b**11","B",0
1316,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1319,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1320,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1321,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1322,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**11,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1323,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**12,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1324,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**13,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1325,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**14,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1326,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**15,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**16,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**17,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**18,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**19,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1331,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**20,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1332,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**21,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,-1,0,0,0.000000," ","integrate((d*x+c)**10/(b*x+a)**22,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1334,1,209,0,0.499520," ","integrate((b*x+a)**5/(d*x+c),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
1335,1,136,0,0.391541," ","integrate((b*x+a)**4/(d*x+c),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
1336,1,83,0,0.298635," ","integrate((b*x+a)**3/(d*x+c),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
1337,1,44,0,0.218633," ","integrate((b*x+a)**2/(d*x+c),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
1338,1,20,0,0.147956," ","integrate((b*x+a)/(d*x+c),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
1339,1,7,0,0.061546," ","integrate(1/(d*x+c),x)","\frac{\log{\left(c + d x \right)}}{d}"," ",0,"log(c + d*x)/d","A",0
1340,1,128,0,0.328197," ","integrate(1/(b*x+a)/(d*x+c),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
1341,1,233,0,0.681860," ","integrate(1/(b*x+a)**2/(d*x+c),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
1342,1,381,0,1.064266," ","integrate(1/(b*x+a)**3/(d*x+c),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
1343,1,231,0,0.885798," ","integrate((b*x+a)**5/(d*x+c)**2,x)","\frac{b^{5} x^{4}}{4 d^{2}} + \frac{5 b \left(a d - b c\right)^{4} \log{\left(c + d x \right)}}{d^{6}} + x^{3} \left(\frac{5 a b^{4}}{3 d^{2}} - \frac{2 b^{5} c}{3 d^{3}}\right) + x^{2} \left(\frac{5 a^{2} b^{3}}{d^{2}} - \frac{5 a b^{4} c}{d^{3}} + \frac{3 b^{5} c^{2}}{2 d^{4}}\right) + x \left(\frac{10 a^{3} b^{2}}{d^{2}} - \frac{20 a^{2} b^{3} c}{d^{3}} + \frac{15 a b^{4} c^{2}}{d^{4}} - \frac{4 b^{5} c^{3}}{d^{5}}\right) + \frac{- a^{5} d^{5} + 5 a^{4} b c d^{4} - 10 a^{3} b^{2} c^{2} d^{3} + 10 a^{2} b^{3} c^{3} d^{2} - 5 a b^{4} c^{4} d + b^{5} c^{5}}{c d^{6} + d^{7} x}"," ",0,"b**5*x**4/(4*d**2) + 5*b*(a*d - b*c)**4*log(c + d*x)/d**6 + x**3*(5*a*b**4/(3*d**2) - 2*b**5*c/(3*d**3)) + x**2*(5*a**2*b**3/d**2 - 5*a*b**4*c/d**3 + 3*b**5*c**2/(2*d**4)) + x*(10*a**3*b**2/d**2 - 20*a**2*b**3*c/d**3 + 15*a*b**4*c**2/d**4 - 4*b**5*c**3/d**5) + (-a**5*d**5 + 5*a**4*b*c*d**4 - 10*a**3*b**2*c**2*d**3 + 10*a**2*b**3*c**3*d**2 - 5*a*b**4*c**4*d + b**5*c**5)/(c*d**6 + d**7*x)","A",0
1344,1,155,0,0.679953," ","integrate((b*x+a)**4/(d*x+c)**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
1345,1,102,0,0.506305," ","integrate((b*x+a)**3/(d*x+c)**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
1346,1,60,0,0.337614," ","integrate((b*x+a)**2/(d*x+c)**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
1347,1,27,0,0.185308," ","integrate((b*x+a)/(d*x+c)**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
1348,1,10,0,0.127520," ","integrate(1/(d*x+c)**2,x)","- \frac{1}{c d + d^{2} x}"," ",0,"-1/(c*d + d**2*x)","A",0
1349,1,233,0,0.684100," ","integrate(1/(b*x+a)/(d*x+c)**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
1350,1,406,0,1.113129," ","integrate(1/(b*x+a)**2/(d*x+c)**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
1351,1,634,0,1.716658," ","integrate(1/(b*x+a)**3/(d*x+c)**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
1352,1,340,0,2.154383," ","integrate((b*x+a)**6/(d*x+c)**3,x)","\frac{b^{6} x^{4}}{4 d^{3}} + \frac{15 b^{2} \left(a d - b c\right)^{4} \log{\left(c + d x \right)}}{d^{7}} + x^{3} \left(\frac{2 a b^{5}}{d^{3}} - \frac{b^{6} c}{d^{4}}\right) + x^{2} \left(\frac{15 a^{2} b^{4}}{2 d^{3}} - \frac{9 a b^{5} c}{d^{4}} + \frac{3 b^{6} c^{2}}{d^{5}}\right) + x \left(\frac{20 a^{3} b^{3}}{d^{3}} - \frac{45 a^{2} b^{4} c}{d^{4}} + \frac{36 a b^{5} c^{2}}{d^{5}} - \frac{10 b^{6} c^{3}}{d^{6}}\right) + \frac{- a^{6} d^{6} - 6 a^{5} b c d^{5} + 45 a^{4} b^{2} c^{2} d^{4} - 100 a^{3} b^{3} c^{3} d^{3} + 105 a^{2} b^{4} c^{4} d^{2} - 54 a b^{5} c^{5} d + 11 b^{6} c^{6} + x \left(- 12 a^{5} b d^{6} + 60 a^{4} b^{2} c d^{5} - 120 a^{3} b^{3} c^{2} d^{4} + 120 a^{2} b^{4} c^{3} d^{3} - 60 a b^{5} c^{4} d^{2} + 12 b^{6} c^{5} d\right)}{2 c^{2} d^{7} + 4 c d^{8} x + 2 d^{9} x^{2}}"," ",0,"b**6*x**4/(4*d**3) + 15*b**2*(a*d - b*c)**4*log(c + d*x)/d**7 + x**3*(2*a*b**5/d**3 - b**6*c/d**4) + x**2*(15*a**2*b**4/(2*d**3) - 9*a*b**5*c/d**4 + 3*b**6*c**2/d**5) + x*(20*a**3*b**3/d**3 - 45*a**2*b**4*c/d**4 + 36*a*b**5*c**2/d**5 - 10*b**6*c**3/d**6) + (-a**6*d**6 - 6*a**5*b*c*d**5 + 45*a**4*b**2*c**2*d**4 - 100*a**3*b**3*c**3*d**3 + 105*a**2*b**4*c**4*d**2 - 54*a*b**5*c**5*d + 11*b**6*c**6 + x*(-12*a**5*b*d**6 + 60*a**4*b**2*c*d**5 - 120*a**3*b**3*c**2*d**4 + 120*a**2*b**4*c**3*d**3 - 60*a*b**5*c**4*d**2 + 12*b**6*c**5*d))/(2*c**2*d**7 + 4*c*d**8*x + 2*d**9*x**2)","B",0
1353,1,258,0,1.649670," ","integrate((b*x+a)**5/(d*x+c)**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
1354,1,185,0,1.245831," ","integrate((b*x+a)**4/(d*x+c)**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
1355,1,128,0,0.826764," ","integrate((b*x+a)**3/(d*x+c)**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
1356,1,80,0,0.449962," ","integrate((b*x+a)**2/(d*x+c)**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
1357,1,39,0,0.263206," ","integrate((b*x+a)/(d*x+c)**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
1358,1,26,0,0.181690," ","integrate(1/(d*x+c)**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
1359,1,381,0,1.073646," ","integrate(1/(b*x+a)/(d*x+c)**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
1360,1,632,0,1.720150," ","integrate(1/(b*x+a)**2/(d*x+c)**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
1361,1,881,0,2.419397," ","integrate(1/(b*x+a)**3/(d*x+c)**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
1362,-1,0,0,0.000000," ","integrate((b*x+a)**9/(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1363,-1,0,0,0.000000," ","integrate((b*x+a)**8/(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1364,-1,0,0,0.000000," ","integrate((b*x+a)**7/(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1365,-1,0,0,0.000000," ","integrate((b*x+a)**6/(d*x+c)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1366,1,354,0,54.907641," ","integrate((b*x+a)**5/(d*x+c)**8,x)","\frac{- 6 a^{5} d^{5} - 5 a^{4} b c d^{4} - 4 a^{3} b^{2} c^{2} d^{3} - 3 a^{2} b^{3} c^{3} d^{2} - 2 a b^{4} c^{4} d - b^{5} c^{5} - 21 b^{5} d^{5} x^{5} + x^{4} \left(- 70 a b^{4} d^{5} - 35 b^{5} c d^{4}\right) + x^{3} \left(- 105 a^{2} b^{3} d^{5} - 70 a b^{4} c d^{4} - 35 b^{5} c^{2} d^{3}\right) + x^{2} \left(- 84 a^{3} b^{2} d^{5} - 63 a^{2} b^{3} c d^{4} - 42 a b^{4} c^{2} d^{3} - 21 b^{5} c^{3} d^{2}\right) + x \left(- 35 a^{4} b d^{5} - 28 a^{3} b^{2} c d^{4} - 21 a^{2} b^{3} c^{2} d^{3} - 14 a b^{4} c^{3} d^{2} - 7 b^{5} c^{4} d\right)}{42 c^{7} d^{6} + 294 c^{6} d^{7} x + 882 c^{5} d^{8} x^{2} + 1470 c^{4} d^{9} x^{3} + 1470 c^{3} d^{10} x^{4} + 882 c^{2} d^{11} x^{5} + 294 c d^{12} x^{6} + 42 d^{13} x^{7}}"," ",0,"(-6*a**5*d**5 - 5*a**4*b*c*d**4 - 4*a**3*b**2*c**2*d**3 - 3*a**2*b**3*c**3*d**2 - 2*a*b**4*c**4*d - b**5*c**5 - 21*b**5*d**5*x**5 + x**4*(-70*a*b**4*d**5 - 35*b**5*c*d**4) + x**3*(-105*a**2*b**3*d**5 - 70*a*b**4*c*d**4 - 35*b**5*c**2*d**3) + x**2*(-84*a**3*b**2*d**5 - 63*a**2*b**3*c*d**4 - 42*a*b**4*c**2*d**3 - 21*b**5*c**3*d**2) + x*(-35*a**4*b*d**5 - 28*a**3*b**2*c*d**4 - 21*a**2*b**3*c**2*d**3 - 14*a*b**4*c**3*d**2 - 7*b**5*c**4*d))/(42*c**7*d**6 + 294*c**6*d**7*x + 882*c**5*d**8*x**2 + 1470*c**4*d**9*x**3 + 1470*c**3*d**10*x**4 + 882*c**2*d**11*x**5 + 294*c*d**12*x**6 + 42*d**13*x**7)","B",0
1367,1,267,0,9.644808," ","integrate((b*x+a)**4/(d*x+c)**8,x)","\frac{- 15 a^{4} d^{4} - 10 a^{3} b c d^{3} - 6 a^{2} b^{2} c^{2} d^{2} - 3 a b^{3} c^{3} d - b^{4} c^{4} - 35 b^{4} d^{4} x^{4} + x^{3} \left(- 105 a b^{3} d^{4} - 35 b^{4} c d^{3}\right) + x^{2} \left(- 126 a^{2} b^{2} d^{4} - 63 a b^{3} c d^{3} - 21 b^{4} c^{2} d^{2}\right) + x \left(- 70 a^{3} b d^{4} - 42 a^{2} b^{2} c d^{3} - 21 a b^{3} c^{2} d^{2} - 7 b^{4} c^{3} d\right)}{105 c^{7} d^{5} + 735 c^{6} d^{6} x + 2205 c^{5} d^{7} x^{2} + 3675 c^{4} d^{8} x^{3} + 3675 c^{3} d^{9} x^{4} + 2205 c^{2} d^{10} x^{5} + 735 c d^{11} x^{6} + 105 d^{12} x^{7}}"," ",0,"(-15*a**4*d**4 - 10*a**3*b*c*d**3 - 6*a**2*b**2*c**2*d**2 - 3*a*b**3*c**3*d - b**4*c**4 - 35*b**4*d**4*x**4 + x**3*(-105*a*b**3*d**4 - 35*b**4*c*d**3) + x**2*(-126*a**2*b**2*d**4 - 63*a*b**3*c*d**3 - 21*b**4*c**2*d**2) + x*(-70*a**3*b*d**4 - 42*a**2*b**2*c*d**3 - 21*a*b**3*c**2*d**2 - 7*b**4*c**3*d))/(105*c**7*d**5 + 735*c**6*d**6*x + 2205*c**5*d**7*x**2 + 3675*c**4*d**8*x**3 + 3675*c**3*d**9*x**4 + 2205*c**2*d**10*x**5 + 735*c*d**11*x**6 + 105*d**12*x**7)","B",0
1368,1,196,0,3.100895," ","integrate((b*x+a)**3/(d*x+c)**8,x)","\frac{- 20 a^{3} d^{3} - 10 a^{2} b c d^{2} - 4 a b^{2} c^{2} d - b^{3} c^{3} - 35 b^{3} d^{3} x^{3} + x^{2} \left(- 84 a b^{2} d^{3} - 21 b^{3} c d^{2}\right) + x \left(- 70 a^{2} b d^{3} - 28 a b^{2} c d^{2} - 7 b^{3} c^{2} d\right)}{140 c^{7} d^{4} + 980 c^{6} d^{5} x + 2940 c^{5} d^{6} x^{2} + 4900 c^{4} d^{7} x^{3} + 4900 c^{3} d^{8} x^{4} + 2940 c^{2} d^{9} x^{5} + 980 c d^{10} x^{6} + 140 d^{11} x^{7}}"," ",0,"(-20*a**3*d**3 - 10*a**2*b*c*d**2 - 4*a*b**2*c**2*d - b**3*c**3 - 35*b**3*d**3*x**3 + x**2*(-84*a*b**2*d**3 - 21*b**3*c*d**2) + x*(-70*a**2*b*d**3 - 28*a*b**2*c*d**2 - 7*b**3*c**2*d))/(140*c**7*d**4 + 980*c**6*d**5*x + 2940*c**5*d**6*x**2 + 4900*c**4*d**7*x**3 + 4900*c**3*d**8*x**4 + 2940*c**2*d**9*x**5 + 980*c*d**10*x**6 + 140*d**11*x**7)","B",0
1369,1,139,0,1.390928," ","integrate((b*x+a)**2/(d*x+c)**8,x)","\frac{- 15 a^{2} d^{2} - 5 a b c d - b^{2} c^{2} - 21 b^{2} d^{2} x^{2} + x \left(- 35 a b d^{2} - 7 b^{2} c d\right)}{105 c^{7} d^{3} + 735 c^{6} d^{4} x + 2205 c^{5} d^{5} x^{2} + 3675 c^{4} d^{6} x^{3} + 3675 c^{3} d^{7} x^{4} + 2205 c^{2} d^{8} x^{5} + 735 c d^{9} x^{6} + 105 d^{10} x^{7}}"," ",0,"(-15*a**2*d**2 - 5*a*b*c*d - b**2*c**2 - 21*b**2*d**2*x**2 + x*(-35*a*b*d**2 - 7*b**2*c*d))/(105*c**7*d**3 + 735*c**6*d**4*x + 2205*c**5*d**5*x**2 + 3675*c**4*d**6*x**3 + 3675*c**3*d**7*x**4 + 2205*c**2*d**8*x**5 + 735*c*d**9*x**6 + 105*d**10*x**7)","B",0
1370,1,100,0,0.731462," ","integrate((b*x+a)/(d*x+c)**8,x)","\frac{- 6 a d - b c - 7 b d x}{42 c^{7} d^{2} + 294 c^{6} d^{3} x + 882 c^{5} d^{4} x^{2} + 1470 c^{4} d^{5} x^{3} + 1470 c^{3} d^{6} x^{4} + 882 c^{2} d^{7} x^{5} + 294 c d^{8} x^{6} + 42 d^{9} x^{7}}"," ",0,"(-6*a*d - b*c - 7*b*d*x)/(42*c**7*d**2 + 294*c**6*d**3*x + 882*c**5*d**4*x**2 + 1470*c**4*d**5*x**3 + 1470*c**3*d**6*x**4 + 882*c**2*d**7*x**5 + 294*c*d**8*x**6 + 42*d**9*x**7)","B",0
1371,1,85,0,0.455596," ","integrate(1/(d*x+c)**8,x)","- \frac{1}{7 c^{7} d + 49 c^{6} d^{2} x + 147 c^{5} d^{3} x^{2} + 245 c^{4} d^{4} x^{3} + 245 c^{3} d^{5} x^{4} + 147 c^{2} d^{6} x^{5} + 49 c d^{7} x^{6} + 7 d^{8} x^{7}}"," ",0,"-1/(7*c**7*d + 49*c**6*d**2*x + 147*c**5*d**3*x**2 + 245*c**4*d**4*x**3 + 245*c**3*d**5*x**4 + 147*c**2*d**6*x**5 + 49*c*d**7*x**6 + 7*d**8*x**7)","B",0
1372,1,1776,0,4.488159," ","integrate(1/(b*x+a)/(d*x+c)**8,x)","- \frac{b^{7} \log{\left(x + \frac{- \frac{a^{9} b^{7} d^{9}}{\left(a d - b c\right)^{8}} + \frac{9 a^{8} b^{8} c d^{8}}{\left(a d - b c\right)^{8}} - \frac{36 a^{7} b^{9} c^{2} d^{7}}{\left(a d - b c\right)^{8}} + \frac{84 a^{6} b^{10} c^{3} d^{6}}{\left(a d - b c\right)^{8}} - \frac{126 a^{5} b^{11} c^{4} d^{5}}{\left(a d - b c\right)^{8}} + \frac{126 a^{4} b^{12} c^{5} d^{4}}{\left(a d - b c\right)^{8}} - \frac{84 a^{3} b^{13} c^{6} d^{3}}{\left(a d - b c\right)^{8}} + \frac{36 a^{2} b^{14} c^{7} d^{2}}{\left(a d - b c\right)^{8}} - \frac{9 a b^{15} c^{8} d}{\left(a d - b c\right)^{8}} + a b^{7} d + \frac{b^{16} c^{9}}{\left(a d - b c\right)^{8}} + b^{8} c}{2 b^{8} d} \right)}}{\left(a d - b c\right)^{8}} + \frac{b^{7} \log{\left(x + \frac{\frac{a^{9} b^{7} d^{9}}{\left(a d - b c\right)^{8}} - \frac{9 a^{8} b^{8} c d^{8}}{\left(a d - b c\right)^{8}} + \frac{36 a^{7} b^{9} c^{2} d^{7}}{\left(a d - b c\right)^{8}} - \frac{84 a^{6} b^{10} c^{3} d^{6}}{\left(a d - b c\right)^{8}} + \frac{126 a^{5} b^{11} c^{4} d^{5}}{\left(a d - b c\right)^{8}} - \frac{126 a^{4} b^{12} c^{5} d^{4}}{\left(a d - b c\right)^{8}} + \frac{84 a^{3} b^{13} c^{6} d^{3}}{\left(a d - b c\right)^{8}} - \frac{36 a^{2} b^{14} c^{7} d^{2}}{\left(a d - b c\right)^{8}} + \frac{9 a b^{15} c^{8} d}{\left(a d - b c\right)^{8}} + a b^{7} d - \frac{b^{16} c^{9}}{\left(a d - b c\right)^{8}} + b^{8} c}{2 b^{8} d} \right)}}{\left(a d - b c\right)^{8}} + \frac{- 60 a^{6} d^{6} + 430 a^{5} b c d^{5} - 1334 a^{4} b^{2} c^{2} d^{4} + 2341 a^{3} b^{3} c^{3} d^{3} - 2559 a^{2} b^{4} c^{4} d^{2} + 1851 a b^{5} c^{5} d - 1089 b^{6} c^{6} - 420 b^{6} d^{6} x^{6} + x^{5} \left(210 a b^{5} d^{6} - 2730 b^{6} c d^{5}\right) + x^{4} \left(- 140 a^{2} b^{4} d^{6} + 1330 a b^{5} c d^{5} - 7490 b^{6} c^{2} d^{4}\right) + x^{3} \left(105 a^{3} b^{3} d^{6} - 875 a^{2} b^{4} c d^{5} + 3535 a b^{5} c^{2} d^{4} - 11165 b^{6} c^{3} d^{3}\right) + x^{2} \left(- 84 a^{4} b^{2} d^{6} + 651 a^{3} b^{3} c d^{5} - 2289 a^{2} b^{4} c^{2} d^{4} + 5061 a b^{5} c^{3} d^{3} - 9639 b^{6} c^{4} d^{2}\right) + x \left(70 a^{5} b d^{6} - 518 a^{4} b^{2} c d^{5} + 1687 a^{3} b^{3} c^{2} d^{4} - 3213 a^{2} b^{4} c^{3} d^{3} + 4137 a b^{5} c^{4} d^{2} - 4683 b^{6} c^{5} d\right)}{420 a^{7} c^{7} d^{7} - 2940 a^{6} b c^{8} d^{6} + 8820 a^{5} b^{2} c^{9} d^{5} - 14700 a^{4} b^{3} c^{10} d^{4} + 14700 a^{3} b^{4} c^{11} d^{3} - 8820 a^{2} b^{5} c^{12} d^{2} + 2940 a b^{6} c^{13} d - 420 b^{7} c^{14} + x^{7} \left(420 a^{7} d^{14} - 2940 a^{6} b c d^{13} + 8820 a^{5} b^{2} c^{2} d^{12} - 14700 a^{4} b^{3} c^{3} d^{11} + 14700 a^{3} b^{4} c^{4} d^{10} - 8820 a^{2} b^{5} c^{5} d^{9} + 2940 a b^{6} c^{6} d^{8} - 420 b^{7} c^{7} d^{7}\right) + x^{6} \left(2940 a^{7} c d^{13} - 20580 a^{6} b c^{2} d^{12} + 61740 a^{5} b^{2} c^{3} d^{11} - 102900 a^{4} b^{3} c^{4} d^{10} + 102900 a^{3} b^{4} c^{5} d^{9} - 61740 a^{2} b^{5} c^{6} d^{8} + 20580 a b^{6} c^{7} d^{7} - 2940 b^{7} c^{8} d^{6}\right) + x^{5} \left(8820 a^{7} c^{2} d^{12} - 61740 a^{6} b c^{3} d^{11} + 185220 a^{5} b^{2} c^{4} d^{10} - 308700 a^{4} b^{3} c^{5} d^{9} + 308700 a^{3} b^{4} c^{6} d^{8} - 185220 a^{2} b^{5} c^{7} d^{7} + 61740 a b^{6} c^{8} d^{6} - 8820 b^{7} c^{9} d^{5}\right) + x^{4} \left(14700 a^{7} c^{3} d^{11} - 102900 a^{6} b c^{4} d^{10} + 308700 a^{5} b^{2} c^{5} d^{9} - 514500 a^{4} b^{3} c^{6} d^{8} + 514500 a^{3} b^{4} c^{7} d^{7} - 308700 a^{2} b^{5} c^{8} d^{6} + 102900 a b^{6} c^{9} d^{5} - 14700 b^{7} c^{10} d^{4}\right) + x^{3} \left(14700 a^{7} c^{4} d^{10} - 102900 a^{6} b c^{5} d^{9} + 308700 a^{5} b^{2} c^{6} d^{8} - 514500 a^{4} b^{3} c^{7} d^{7} + 514500 a^{3} b^{4} c^{8} d^{6} - 308700 a^{2} b^{5} c^{9} d^{5} + 102900 a b^{6} c^{10} d^{4} - 14700 b^{7} c^{11} d^{3}\right) + x^{2} \left(8820 a^{7} c^{5} d^{9} - 61740 a^{6} b c^{6} d^{8} + 185220 a^{5} b^{2} c^{7} d^{7} - 308700 a^{4} b^{3} c^{8} d^{6} + 308700 a^{3} b^{4} c^{9} d^{5} - 185220 a^{2} b^{5} c^{10} d^{4} + 61740 a b^{6} c^{11} d^{3} - 8820 b^{7} c^{12} d^{2}\right) + x \left(2940 a^{7} c^{6} d^{8} - 20580 a^{6} b c^{7} d^{7} + 61740 a^{5} b^{2} c^{8} d^{6} - 102900 a^{4} b^{3} c^{9} d^{5} + 102900 a^{3} b^{4} c^{10} d^{4} - 61740 a^{2} b^{5} c^{11} d^{3} + 20580 a b^{6} c^{12} d^{2} - 2940 b^{7} c^{13} d\right)}"," ",0,"-b**7*log(x + (-a**9*b**7*d**9/(a*d - b*c)**8 + 9*a**8*b**8*c*d**8/(a*d - b*c)**8 - 36*a**7*b**9*c**2*d**7/(a*d - b*c)**8 + 84*a**6*b**10*c**3*d**6/(a*d - b*c)**8 - 126*a**5*b**11*c**4*d**5/(a*d - b*c)**8 + 126*a**4*b**12*c**5*d**4/(a*d - b*c)**8 - 84*a**3*b**13*c**6*d**3/(a*d - b*c)**8 + 36*a**2*b**14*c**7*d**2/(a*d - b*c)**8 - 9*a*b**15*c**8*d/(a*d - b*c)**8 + a*b**7*d + b**16*c**9/(a*d - b*c)**8 + b**8*c)/(2*b**8*d))/(a*d - b*c)**8 + b**7*log(x + (a**9*b**7*d**9/(a*d - b*c)**8 - 9*a**8*b**8*c*d**8/(a*d - b*c)**8 + 36*a**7*b**9*c**2*d**7/(a*d - b*c)**8 - 84*a**6*b**10*c**3*d**6/(a*d - b*c)**8 + 126*a**5*b**11*c**4*d**5/(a*d - b*c)**8 - 126*a**4*b**12*c**5*d**4/(a*d - b*c)**8 + 84*a**3*b**13*c**6*d**3/(a*d - b*c)**8 - 36*a**2*b**14*c**7*d**2/(a*d - b*c)**8 + 9*a*b**15*c**8*d/(a*d - b*c)**8 + a*b**7*d - b**16*c**9/(a*d - b*c)**8 + b**8*c)/(2*b**8*d))/(a*d - b*c)**8 + (-60*a**6*d**6 + 430*a**5*b*c*d**5 - 1334*a**4*b**2*c**2*d**4 + 2341*a**3*b**3*c**3*d**3 - 2559*a**2*b**4*c**4*d**2 + 1851*a*b**5*c**5*d - 1089*b**6*c**6 - 420*b**6*d**6*x**6 + x**5*(210*a*b**5*d**6 - 2730*b**6*c*d**5) + x**4*(-140*a**2*b**4*d**6 + 1330*a*b**5*c*d**5 - 7490*b**6*c**2*d**4) + x**3*(105*a**3*b**3*d**6 - 875*a**2*b**4*c*d**5 + 3535*a*b**5*c**2*d**4 - 11165*b**6*c**3*d**3) + x**2*(-84*a**4*b**2*d**6 + 651*a**3*b**3*c*d**5 - 2289*a**2*b**4*c**2*d**4 + 5061*a*b**5*c**3*d**3 - 9639*b**6*c**4*d**2) + x*(70*a**5*b*d**6 - 518*a**4*b**2*c*d**5 + 1687*a**3*b**3*c**2*d**4 - 3213*a**2*b**4*c**3*d**3 + 4137*a*b**5*c**4*d**2 - 4683*b**6*c**5*d))/(420*a**7*c**7*d**7 - 2940*a**6*b*c**8*d**6 + 8820*a**5*b**2*c**9*d**5 - 14700*a**4*b**3*c**10*d**4 + 14700*a**3*b**4*c**11*d**3 - 8820*a**2*b**5*c**12*d**2 + 2940*a*b**6*c**13*d - 420*b**7*c**14 + x**7*(420*a**7*d**14 - 2940*a**6*b*c*d**13 + 8820*a**5*b**2*c**2*d**12 - 14700*a**4*b**3*c**3*d**11 + 14700*a**3*b**4*c**4*d**10 - 8820*a**2*b**5*c**5*d**9 + 2940*a*b**6*c**6*d**8 - 420*b**7*c**7*d**7) + x**6*(2940*a**7*c*d**13 - 20580*a**6*b*c**2*d**12 + 61740*a**5*b**2*c**3*d**11 - 102900*a**4*b**3*c**4*d**10 + 102900*a**3*b**4*c**5*d**9 - 61740*a**2*b**5*c**6*d**8 + 20580*a*b**6*c**7*d**7 - 2940*b**7*c**8*d**6) + x**5*(8820*a**7*c**2*d**12 - 61740*a**6*b*c**3*d**11 + 185220*a**5*b**2*c**4*d**10 - 308700*a**4*b**3*c**5*d**9 + 308700*a**3*b**4*c**6*d**8 - 185220*a**2*b**5*c**7*d**7 + 61740*a*b**6*c**8*d**6 - 8820*b**7*c**9*d**5) + x**4*(14700*a**7*c**3*d**11 - 102900*a**6*b*c**4*d**10 + 308700*a**5*b**2*c**5*d**9 - 514500*a**4*b**3*c**6*d**8 + 514500*a**3*b**4*c**7*d**7 - 308700*a**2*b**5*c**8*d**6 + 102900*a*b**6*c**9*d**5 - 14700*b**7*c**10*d**4) + x**3*(14700*a**7*c**4*d**10 - 102900*a**6*b*c**5*d**9 + 308700*a**5*b**2*c**6*d**8 - 514500*a**4*b**3*c**7*d**7 + 514500*a**3*b**4*c**8*d**6 - 308700*a**2*b**5*c**9*d**5 + 102900*a*b**6*c**10*d**4 - 14700*b**7*c**11*d**3) + x**2*(8820*a**7*c**5*d**9 - 61740*a**6*b*c**6*d**8 + 185220*a**5*b**2*c**7*d**7 - 308700*a**4*b**3*c**8*d**6 + 308700*a**3*b**4*c**9*d**5 - 185220*a**2*b**5*c**10*d**4 + 61740*a*b**6*c**11*d**3 - 8820*b**7*c**12*d**2) + x*(2940*a**7*c**6*d**8 - 20580*a**6*b*c**7*d**7 + 61740*a**5*b**2*c**8*d**6 - 102900*a**4*b**3*c**9*d**5 + 102900*a**3*b**4*c**10*d**4 - 61740*a**2*b**5*c**11*d**3 + 20580*a*b**6*c**12*d**2 - 2940*b**7*c**13*d))","B",0
1373,1,2336,0,7.745099," ","integrate(1/(b*x+a)**2/(d*x+c)**8,x)","- \frac{8 b^{7} d \log{\left(x + \frac{- \frac{8 a^{10} b^{7} d^{11}}{\left(a d - b c\right)^{9}} + \frac{80 a^{9} b^{8} c d^{10}}{\left(a d - b c\right)^{9}} - \frac{360 a^{8} b^{9} c^{2} d^{9}}{\left(a d - b c\right)^{9}} + \frac{960 a^{7} b^{10} c^{3} d^{8}}{\left(a d - b c\right)^{9}} - \frac{1680 a^{6} b^{11} c^{4} d^{7}}{\left(a d - b c\right)^{9}} + \frac{2016 a^{5} b^{12} c^{5} d^{6}}{\left(a d - b c\right)^{9}} - \frac{1680 a^{4} b^{13} c^{6} d^{5}}{\left(a d - b c\right)^{9}} + \frac{960 a^{3} b^{14} c^{7} d^{4}}{\left(a d - b c\right)^{9}} - \frac{360 a^{2} b^{15} c^{8} d^{3}}{\left(a d - b c\right)^{9}} + \frac{80 a b^{16} c^{9} d^{2}}{\left(a d - b c\right)^{9}} + 8 a b^{7} d^{2} - \frac{8 b^{17} c^{10} d}{\left(a d - b c\right)^{9}} + 8 b^{8} c d}{16 b^{8} d^{2}} \right)}}{\left(a d - b c\right)^{9}} + \frac{8 b^{7} d \log{\left(x + \frac{\frac{8 a^{10} b^{7} d^{11}}{\left(a d - b c\right)^{9}} - \frac{80 a^{9} b^{8} c d^{10}}{\left(a d - b c\right)^{9}} + \frac{360 a^{8} b^{9} c^{2} d^{9}}{\left(a d - b c\right)^{9}} - \frac{960 a^{7} b^{10} c^{3} d^{8}}{\left(a d - b c\right)^{9}} + \frac{1680 a^{6} b^{11} c^{4} d^{7}}{\left(a d - b c\right)^{9}} - \frac{2016 a^{5} b^{12} c^{5} d^{6}}{\left(a d - b c\right)^{9}} + \frac{1680 a^{4} b^{13} c^{6} d^{5}}{\left(a d - b c\right)^{9}} - \frac{960 a^{3} b^{14} c^{7} d^{4}}{\left(a d - b c\right)^{9}} + \frac{360 a^{2} b^{15} c^{8} d^{3}}{\left(a d - b c\right)^{9}} - \frac{80 a b^{16} c^{9} d^{2}}{\left(a d - b c\right)^{9}} + 8 a b^{7} d^{2} + \frac{8 b^{17} c^{10} d}{\left(a d - b c\right)^{9}} + 8 b^{8} c d}{16 b^{8} d^{2}} \right)}}{\left(a d - b c\right)^{9}} + \frac{- 15 a^{7} d^{7} + 125 a^{6} b c d^{6} - 463 a^{5} b^{2} c^{2} d^{5} + 1007 a^{4} b^{3} c^{3} d^{4} - 1443 a^{3} b^{4} c^{4} d^{3} + 1497 a^{2} b^{5} c^{5} d^{2} - 1443 a b^{6} c^{6} d - 105 b^{7} c^{7} - 840 b^{7} d^{7} x^{7} + x^{6} \left(- 420 a b^{6} d^{7} - 5460 b^{7} c d^{6}\right) + x^{5} \left(140 a^{2} b^{5} d^{7} - 2800 a b^{6} c d^{6} - 14980 b^{7} c^{2} d^{5}\right) + x^{4} \left(- 70 a^{3} b^{4} d^{7} + 910 a^{2} b^{5} c d^{6} - 7910 a b^{6} c^{2} d^{5} - 22330 b^{7} c^{3} d^{4}\right) + x^{3} \left(42 a^{4} b^{3} d^{7} - 448 a^{3} b^{4} c d^{6} + 2492 a^{2} b^{5} c^{2} d^{5} - 12208 a b^{6} c^{3} d^{4} - 19278 b^{7} c^{4} d^{3}\right) + x^{2} \left(- 28 a^{5} b^{2} d^{7} + 266 a^{4} b^{3} c d^{6} - 1204 a^{3} b^{4} c^{2} d^{5} + 3696 a^{2} b^{5} c^{3} d^{4} - 11004 a b^{6} c^{4} d^{3} - 9366 b^{7} c^{5} d^{2}\right) + x \left(20 a^{6} b d^{7} - 176 a^{5} b^{2} c d^{6} + 706 a^{4} b^{3} c^{2} d^{5} - 1744 a^{3} b^{4} c^{3} d^{4} + 3156 a^{2} b^{5} c^{4} d^{3} - 5664 a b^{6} c^{5} d^{2} - 2178 b^{7} c^{6} d\right)}{105 a^{9} c^{7} d^{8} - 840 a^{8} b c^{8} d^{7} + 2940 a^{7} b^{2} c^{9} d^{6} - 5880 a^{6} b^{3} c^{10} d^{5} + 7350 a^{5} b^{4} c^{11} d^{4} - 5880 a^{4} b^{5} c^{12} d^{3} + 2940 a^{3} b^{6} c^{13} d^{2} - 840 a^{2} b^{7} c^{14} d + 105 a b^{8} c^{15} + x^{8} \left(105 a^{8} b d^{15} - 840 a^{7} b^{2} c d^{14} + 2940 a^{6} b^{3} c^{2} d^{13} - 5880 a^{5} b^{4} c^{3} d^{12} + 7350 a^{4} b^{5} c^{4} d^{11} - 5880 a^{3} b^{6} c^{5} d^{10} + 2940 a^{2} b^{7} c^{6} d^{9} - 840 a b^{8} c^{7} d^{8} + 105 b^{9} c^{8} d^{7}\right) + x^{7} \left(105 a^{9} d^{15} - 105 a^{8} b c d^{14} - 2940 a^{7} b^{2} c^{2} d^{13} + 14700 a^{6} b^{3} c^{3} d^{12} - 33810 a^{5} b^{4} c^{4} d^{11} + 45570 a^{4} b^{5} c^{5} d^{10} - 38220 a^{3} b^{6} c^{6} d^{9} + 19740 a^{2} b^{7} c^{7} d^{8} - 5775 a b^{8} c^{8} d^{7} + 735 b^{9} c^{9} d^{6}\right) + x^{6} \left(735 a^{9} c d^{14} - 3675 a^{8} b c^{2} d^{13} + 2940 a^{7} b^{2} c^{3} d^{12} + 20580 a^{6} b^{3} c^{4} d^{11} - 72030 a^{5} b^{4} c^{5} d^{10} + 113190 a^{4} b^{5} c^{6} d^{9} - 102900 a^{3} b^{6} c^{7} d^{8} + 55860 a^{2} b^{7} c^{8} d^{7} - 16905 a b^{8} c^{9} d^{6} + 2205 b^{9} c^{10} d^{5}\right) + x^{5} \left(2205 a^{9} c^{2} d^{13} - 13965 a^{8} b c^{3} d^{12} + 32340 a^{7} b^{2} c^{4} d^{11} - 20580 a^{6} b^{3} c^{5} d^{10} - 51450 a^{5} b^{4} c^{6} d^{9} + 133770 a^{4} b^{5} c^{7} d^{8} - 144060 a^{3} b^{6} c^{8} d^{7} + 85260 a^{2} b^{7} c^{9} d^{6} - 27195 a b^{8} c^{10} d^{5} + 3675 b^{9} c^{11} d^{4}\right) + x^{4} \left(3675 a^{9} c^{3} d^{12} - 25725 a^{8} b c^{4} d^{11} + 73500 a^{7} b^{2} c^{5} d^{10} - 102900 a^{6} b^{3} c^{6} d^{9} + 51450 a^{5} b^{4} c^{7} d^{8} + 51450 a^{4} b^{5} c^{8} d^{7} - 102900 a^{3} b^{6} c^{9} d^{6} + 73500 a^{2} b^{7} c^{10} d^{5} - 25725 a b^{8} c^{11} d^{4} + 3675 b^{9} c^{12} d^{3}\right) + x^{3} \left(3675 a^{9} c^{4} d^{11} - 27195 a^{8} b c^{5} d^{10} + 85260 a^{7} b^{2} c^{6} d^{9} - 144060 a^{6} b^{3} c^{7} d^{8} + 133770 a^{5} b^{4} c^{8} d^{7} - 51450 a^{4} b^{5} c^{9} d^{6} - 20580 a^{3} b^{6} c^{10} d^{5} + 32340 a^{2} b^{7} c^{11} d^{4} - 13965 a b^{8} c^{12} d^{3} + 2205 b^{9} c^{13} d^{2}\right) + x^{2} \left(2205 a^{9} c^{5} d^{10} - 16905 a^{8} b c^{6} d^{9} + 55860 a^{7} b^{2} c^{7} d^{8} - 102900 a^{6} b^{3} c^{8} d^{7} + 113190 a^{5} b^{4} c^{9} d^{6} - 72030 a^{4} b^{5} c^{10} d^{5} + 20580 a^{3} b^{6} c^{11} d^{4} + 2940 a^{2} b^{7} c^{12} d^{3} - 3675 a b^{8} c^{13} d^{2} + 735 b^{9} c^{14} d\right) + x \left(735 a^{9} c^{6} d^{9} - 5775 a^{8} b c^{7} d^{8} + 19740 a^{7} b^{2} c^{8} d^{7} - 38220 a^{6} b^{3} c^{9} d^{6} + 45570 a^{5} b^{4} c^{10} d^{5} - 33810 a^{4} b^{5} c^{11} d^{4} + 14700 a^{3} b^{6} c^{12} d^{3} - 2940 a^{2} b^{7} c^{13} d^{2} - 105 a b^{8} c^{14} d + 105 b^{9} c^{15}\right)}"," ",0,"-8*b**7*d*log(x + (-8*a**10*b**7*d**11/(a*d - b*c)**9 + 80*a**9*b**8*c*d**10/(a*d - b*c)**9 - 360*a**8*b**9*c**2*d**9/(a*d - b*c)**9 + 960*a**7*b**10*c**3*d**8/(a*d - b*c)**9 - 1680*a**6*b**11*c**4*d**7/(a*d - b*c)**9 + 2016*a**5*b**12*c**5*d**6/(a*d - b*c)**9 - 1680*a**4*b**13*c**6*d**5/(a*d - b*c)**9 + 960*a**3*b**14*c**7*d**4/(a*d - b*c)**9 - 360*a**2*b**15*c**8*d**3/(a*d - b*c)**9 + 80*a*b**16*c**9*d**2/(a*d - b*c)**9 + 8*a*b**7*d**2 - 8*b**17*c**10*d/(a*d - b*c)**9 + 8*b**8*c*d)/(16*b**8*d**2))/(a*d - b*c)**9 + 8*b**7*d*log(x + (8*a**10*b**7*d**11/(a*d - b*c)**9 - 80*a**9*b**8*c*d**10/(a*d - b*c)**9 + 360*a**8*b**9*c**2*d**9/(a*d - b*c)**9 - 960*a**7*b**10*c**3*d**8/(a*d - b*c)**9 + 1680*a**6*b**11*c**4*d**7/(a*d - b*c)**9 - 2016*a**5*b**12*c**5*d**6/(a*d - b*c)**9 + 1680*a**4*b**13*c**6*d**5/(a*d - b*c)**9 - 960*a**3*b**14*c**7*d**4/(a*d - b*c)**9 + 360*a**2*b**15*c**8*d**3/(a*d - b*c)**9 - 80*a*b**16*c**9*d**2/(a*d - b*c)**9 + 8*a*b**7*d**2 + 8*b**17*c**10*d/(a*d - b*c)**9 + 8*b**8*c*d)/(16*b**8*d**2))/(a*d - b*c)**9 + (-15*a**7*d**7 + 125*a**6*b*c*d**6 - 463*a**5*b**2*c**2*d**5 + 1007*a**4*b**3*c**3*d**4 - 1443*a**3*b**4*c**4*d**3 + 1497*a**2*b**5*c**5*d**2 - 1443*a*b**6*c**6*d - 105*b**7*c**7 - 840*b**7*d**7*x**7 + x**6*(-420*a*b**6*d**7 - 5460*b**7*c*d**6) + x**5*(140*a**2*b**5*d**7 - 2800*a*b**6*c*d**6 - 14980*b**7*c**2*d**5) + x**4*(-70*a**3*b**4*d**7 + 910*a**2*b**5*c*d**6 - 7910*a*b**6*c**2*d**5 - 22330*b**7*c**3*d**4) + x**3*(42*a**4*b**3*d**7 - 448*a**3*b**4*c*d**6 + 2492*a**2*b**5*c**2*d**5 - 12208*a*b**6*c**3*d**4 - 19278*b**7*c**4*d**3) + x**2*(-28*a**5*b**2*d**7 + 266*a**4*b**3*c*d**6 - 1204*a**3*b**4*c**2*d**5 + 3696*a**2*b**5*c**3*d**4 - 11004*a*b**6*c**4*d**3 - 9366*b**7*c**5*d**2) + x*(20*a**6*b*d**7 - 176*a**5*b**2*c*d**6 + 706*a**4*b**3*c**2*d**5 - 1744*a**3*b**4*c**3*d**4 + 3156*a**2*b**5*c**4*d**3 - 5664*a*b**6*c**5*d**2 - 2178*b**7*c**6*d))/(105*a**9*c**7*d**8 - 840*a**8*b*c**8*d**7 + 2940*a**7*b**2*c**9*d**6 - 5880*a**6*b**3*c**10*d**5 + 7350*a**5*b**4*c**11*d**4 - 5880*a**4*b**5*c**12*d**3 + 2940*a**3*b**6*c**13*d**2 - 840*a**2*b**7*c**14*d + 105*a*b**8*c**15 + x**8*(105*a**8*b*d**15 - 840*a**7*b**2*c*d**14 + 2940*a**6*b**3*c**2*d**13 - 5880*a**5*b**4*c**3*d**12 + 7350*a**4*b**5*c**4*d**11 - 5880*a**3*b**6*c**5*d**10 + 2940*a**2*b**7*c**6*d**9 - 840*a*b**8*c**7*d**8 + 105*b**9*c**8*d**7) + x**7*(105*a**9*d**15 - 105*a**8*b*c*d**14 - 2940*a**7*b**2*c**2*d**13 + 14700*a**6*b**3*c**3*d**12 - 33810*a**5*b**4*c**4*d**11 + 45570*a**4*b**5*c**5*d**10 - 38220*a**3*b**6*c**6*d**9 + 19740*a**2*b**7*c**7*d**8 - 5775*a*b**8*c**8*d**7 + 735*b**9*c**9*d**6) + x**6*(735*a**9*c*d**14 - 3675*a**8*b*c**2*d**13 + 2940*a**7*b**2*c**3*d**12 + 20580*a**6*b**3*c**4*d**11 - 72030*a**5*b**4*c**5*d**10 + 113190*a**4*b**5*c**6*d**9 - 102900*a**3*b**6*c**7*d**8 + 55860*a**2*b**7*c**8*d**7 - 16905*a*b**8*c**9*d**6 + 2205*b**9*c**10*d**5) + x**5*(2205*a**9*c**2*d**13 - 13965*a**8*b*c**3*d**12 + 32340*a**7*b**2*c**4*d**11 - 20580*a**6*b**3*c**5*d**10 - 51450*a**5*b**4*c**6*d**9 + 133770*a**4*b**5*c**7*d**8 - 144060*a**3*b**6*c**8*d**7 + 85260*a**2*b**7*c**9*d**6 - 27195*a*b**8*c**10*d**5 + 3675*b**9*c**11*d**4) + x**4*(3675*a**9*c**3*d**12 - 25725*a**8*b*c**4*d**11 + 73500*a**7*b**2*c**5*d**10 - 102900*a**6*b**3*c**6*d**9 + 51450*a**5*b**4*c**7*d**8 + 51450*a**4*b**5*c**8*d**7 - 102900*a**3*b**6*c**9*d**6 + 73500*a**2*b**7*c**10*d**5 - 25725*a*b**8*c**11*d**4 + 3675*b**9*c**12*d**3) + x**3*(3675*a**9*c**4*d**11 - 27195*a**8*b*c**5*d**10 + 85260*a**7*b**2*c**6*d**9 - 144060*a**6*b**3*c**7*d**8 + 133770*a**5*b**4*c**8*d**7 - 51450*a**4*b**5*c**9*d**6 - 20580*a**3*b**6*c**10*d**5 + 32340*a**2*b**7*c**11*d**4 - 13965*a*b**8*c**12*d**3 + 2205*b**9*c**13*d**2) + x**2*(2205*a**9*c**5*d**10 - 16905*a**8*b*c**6*d**9 + 55860*a**7*b**2*c**7*d**8 - 102900*a**6*b**3*c**8*d**7 + 113190*a**5*b**4*c**9*d**6 - 72030*a**4*b**5*c**10*d**5 + 20580*a**3*b**6*c**11*d**4 + 2940*a**2*b**7*c**12*d**3 - 3675*a*b**8*c**13*d**2 + 735*b**9*c**14*d) + x*(735*a**9*c**6*d**9 - 5775*a**8*b*c**7*d**8 + 19740*a**7*b**2*c**8*d**7 - 38220*a**6*b**3*c**9*d**6 + 45570*a**5*b**4*c**10*d**5 - 33810*a**4*b**5*c**11*d**4 + 14700*a**3*b**6*c**12*d**3 - 2940*a**2*b**7*c**13*d**2 - 105*a*b**8*c**14*d + 105*b**9*c**15))","B",0
1374,1,2917,0,20.657869," ","integrate(1/(b*x+a)**3/(d*x+c)**8,x)","- \frac{36 b^{7} d^{2} \log{\left(x + \frac{- \frac{36 a^{11} b^{7} d^{13}}{\left(a d - b c\right)^{10}} + \frac{396 a^{10} b^{8} c d^{12}}{\left(a d - b c\right)^{10}} - \frac{1980 a^{9} b^{9} c^{2} d^{11}}{\left(a d - b c\right)^{10}} + \frac{5940 a^{8} b^{10} c^{3} d^{10}}{\left(a d - b c\right)^{10}} - \frac{11880 a^{7} b^{11} c^{4} d^{9}}{\left(a d - b c\right)^{10}} + \frac{16632 a^{6} b^{12} c^{5} d^{8}}{\left(a d - b c\right)^{10}} - \frac{16632 a^{5} b^{13} c^{6} d^{7}}{\left(a d - b c\right)^{10}} + \frac{11880 a^{4} b^{14} c^{7} d^{6}}{\left(a d - b c\right)^{10}} - \frac{5940 a^{3} b^{15} c^{8} d^{5}}{\left(a d - b c\right)^{10}} + \frac{1980 a^{2} b^{16} c^{9} d^{4}}{\left(a d - b c\right)^{10}} - \frac{396 a b^{17} c^{10} d^{3}}{\left(a d - b c\right)^{10}} + 36 a b^{7} d^{3} + \frac{36 b^{18} c^{11} d^{2}}{\left(a d - b c\right)^{10}} + 36 b^{8} c d^{2}}{72 b^{8} d^{3}} \right)}}{\left(a d - b c\right)^{10}} + \frac{36 b^{7} d^{2} \log{\left(x + \frac{\frac{36 a^{11} b^{7} d^{13}}{\left(a d - b c\right)^{10}} - \frac{396 a^{10} b^{8} c d^{12}}{\left(a d - b c\right)^{10}} + \frac{1980 a^{9} b^{9} c^{2} d^{11}}{\left(a d - b c\right)^{10}} - \frac{5940 a^{8} b^{10} c^{3} d^{10}}{\left(a d - b c\right)^{10}} + \frac{11880 a^{7} b^{11} c^{4} d^{9}}{\left(a d - b c\right)^{10}} - \frac{16632 a^{6} b^{12} c^{5} d^{8}}{\left(a d - b c\right)^{10}} + \frac{16632 a^{5} b^{13} c^{6} d^{7}}{\left(a d - b c\right)^{10}} - \frac{11880 a^{4} b^{14} c^{7} d^{6}}{\left(a d - b c\right)^{10}} + \frac{5940 a^{3} b^{15} c^{8} d^{5}}{\left(a d - b c\right)^{10}} - \frac{1980 a^{2} b^{16} c^{9} d^{4}}{\left(a d - b c\right)^{10}} + \frac{396 a b^{17} c^{10} d^{3}}{\left(a d - b c\right)^{10}} + 36 a b^{7} d^{3} - \frac{36 b^{18} c^{11} d^{2}}{\left(a d - b c\right)^{10}} + 36 b^{8} c d^{2}}{72 b^{8} d^{3}} \right)}}{\left(a d - b c\right)^{10}} + \frac{- 10 a^{8} d^{8} + 95 a^{7} b c d^{7} - 409 a^{6} b^{2} c^{2} d^{6} + 1061 a^{5} b^{3} c^{3} d^{5} - 1879 a^{4} b^{4} c^{4} d^{4} + 2531 a^{3} b^{5} c^{5} d^{3} - 3349 a^{2} b^{6} c^{6} d^{2} - 595 a b^{7} c^{7} d + 35 b^{8} c^{8} - 2520 b^{8} d^{8} x^{8} + x^{7} \left(- 3780 a b^{7} d^{8} - 16380 b^{8} c d^{7}\right) + x^{6} \left(- 840 a^{2} b^{6} d^{8} - 24780 a b^{7} c d^{7} - 44940 b^{8} c^{2} d^{6}\right) + x^{5} \left(210 a^{3} b^{5} d^{8} - 5670 a^{2} b^{6} c d^{7} - 68670 a b^{7} c^{2} d^{6} - 66990 b^{8} c^{3} d^{5}\right) + x^{4} \left(- 84 a^{4} b^{4} d^{8} + 1386 a^{3} b^{5} c d^{7} - 16254 a^{2} b^{6} c^{2} d^{6} - 103614 a b^{7} c^{3} d^{5} - 57834 b^{8} c^{4} d^{4}\right) + x^{3} \left(42 a^{5} b^{3} d^{8} - 546 a^{4} b^{4} c d^{7} + 3864 a^{3} b^{5} c^{2} d^{6} - 25536 a^{2} b^{6} c^{3} d^{5} - 90846 a b^{7} c^{4} d^{4} - 28098 b^{8} c^{5} d^{3}\right) + x^{2} \left(- 24 a^{6} b^{2} d^{8} + 270 a^{5} b^{3} c d^{7} - 1494 a^{4} b^{4} c^{2} d^{6} + 5856 a^{3} b^{5} c^{3} d^{5} - 23544 a^{2} b^{6} c^{4} d^{4} - 45090 a b^{7} c^{5} d^{3} - 6534 b^{8} c^{6} d^{2}\right) + x \left(15 a^{7} b d^{8} - 153 a^{6} b^{2} c d^{7} + 729 a^{5} b^{3} c^{2} d^{6} - 2211 a^{4} b^{4} c^{3} d^{5} + 5139 a^{3} b^{5} c^{4} d^{4} - 12501 a^{2} b^{6} c^{5} d^{3} - 10863 a b^{7} c^{6} d^{2} - 315 b^{8} c^{7} d\right)}{70 a^{11} c^{7} d^{9} - 630 a^{10} b c^{8} d^{8} + 2520 a^{9} b^{2} c^{9} d^{7} - 5880 a^{8} b^{3} c^{10} d^{6} + 8820 a^{7} b^{4} c^{11} d^{5} - 8820 a^{6} b^{5} c^{12} d^{4} + 5880 a^{5} b^{6} c^{13} d^{3} - 2520 a^{4} b^{7} c^{14} d^{2} + 630 a^{3} b^{8} c^{15} d - 70 a^{2} b^{9} c^{16} + x^{9} \left(70 a^{9} b^{2} d^{16} - 630 a^{8} b^{3} c d^{15} + 2520 a^{7} b^{4} c^{2} d^{14} - 5880 a^{6} b^{5} c^{3} d^{13} + 8820 a^{5} b^{6} c^{4} d^{12} - 8820 a^{4} b^{7} c^{5} d^{11} + 5880 a^{3} b^{8} c^{6} d^{10} - 2520 a^{2} b^{9} c^{7} d^{9} + 630 a b^{10} c^{8} d^{8} - 70 b^{11} c^{9} d^{7}\right) + x^{8} \left(140 a^{10} b d^{16} - 770 a^{9} b^{2} c d^{15} + 630 a^{8} b^{3} c^{2} d^{14} + 5880 a^{7} b^{4} c^{3} d^{13} - 23520 a^{6} b^{5} c^{4} d^{12} + 44100 a^{5} b^{6} c^{5} d^{11} - 49980 a^{4} b^{7} c^{6} d^{10} + 36120 a^{3} b^{8} c^{7} d^{9} - 16380 a^{2} b^{9} c^{8} d^{8} + 4270 a b^{10} c^{9} d^{7} - 490 b^{11} c^{10} d^{6}\right) + x^{7} \left(70 a^{11} d^{16} + 350 a^{10} b c d^{15} - 4830 a^{9} b^{2} c^{2} d^{14} + 16170 a^{8} b^{3} c^{3} d^{13} - 20580 a^{7} b^{4} c^{4} d^{12} - 8820 a^{6} b^{5} c^{5} d^{11} + 67620 a^{5} b^{6} c^{6} d^{10} - 105420 a^{4} b^{7} c^{7} d^{9} + 88830 a^{3} b^{8} c^{8} d^{8} - 44170 a^{2} b^{9} c^{9} d^{7} + 12250 a b^{10} c^{10} d^{6} - 1470 b^{11} c^{11} d^{5}\right) + x^{6} \left(490 a^{11} c d^{15} - 1470 a^{10} b c^{2} d^{14} - 6370 a^{9} b^{2} c^{3} d^{13} + 42630 a^{8} b^{3} c^{4} d^{12} - 97020 a^{7} b^{4} c^{5} d^{11} + 102900 a^{6} b^{5} c^{6} d^{10} - 20580 a^{5} b^{6} c^{7} d^{9} - 79380 a^{4} b^{7} c^{8} d^{8} + 104370 a^{3} b^{8} c^{9} d^{7} - 62230 a^{2} b^{9} c^{10} d^{6} + 19110 a b^{10} c^{11} d^{5} - 2450 b^{11} c^{12} d^{4}\right) + x^{5} \left(1470 a^{11} c^{2} d^{14} - 8330 a^{10} b c^{3} d^{13} + 11270 a^{9} b^{2} c^{4} d^{12} + 30870 a^{8} b^{3} c^{5} d^{11} - 138180 a^{7} b^{4} c^{6} d^{10} + 226380 a^{6} b^{5} c^{7} d^{9} - 185220 a^{5} b^{6} c^{8} d^{8} + 49980 a^{4} b^{7} c^{9} d^{7} + 42630 a^{3} b^{8} c^{10} d^{6} - 45570 a^{2} b^{9} c^{11} d^{5} + 17150 a b^{10} c^{12} d^{4} - 2450 b^{11} c^{13} d^{3}\right) + x^{4} \left(2450 a^{11} c^{3} d^{13} - 17150 a^{10} b c^{4} d^{12} + 45570 a^{9} b^{2} c^{5} d^{11} - 42630 a^{8} b^{3} c^{6} d^{10} - 49980 a^{7} b^{4} c^{7} d^{9} + 185220 a^{6} b^{5} c^{8} d^{8} - 226380 a^{5} b^{6} c^{9} d^{7} + 138180 a^{4} b^{7} c^{10} d^{6} - 30870 a^{3} b^{8} c^{11} d^{5} - 11270 a^{2} b^{9} c^{12} d^{4} + 8330 a b^{10} c^{13} d^{3} - 1470 b^{11} c^{14} d^{2}\right) + x^{3} \left(2450 a^{11} c^{4} d^{12} - 19110 a^{10} b c^{5} d^{11} + 62230 a^{9} b^{2} c^{6} d^{10} - 104370 a^{8} b^{3} c^{7} d^{9} + 79380 a^{7} b^{4} c^{8} d^{8} + 20580 a^{6} b^{5} c^{9} d^{7} - 102900 a^{5} b^{6} c^{10} d^{6} + 97020 a^{4} b^{7} c^{11} d^{5} - 42630 a^{3} b^{8} c^{12} d^{4} + 6370 a^{2} b^{9} c^{13} d^{3} + 1470 a b^{10} c^{14} d^{2} - 490 b^{11} c^{15} d\right) + x^{2} \left(1470 a^{11} c^{5} d^{11} - 12250 a^{10} b c^{6} d^{10} + 44170 a^{9} b^{2} c^{7} d^{9} - 88830 a^{8} b^{3} c^{8} d^{8} + 105420 a^{7} b^{4} c^{9} d^{7} - 67620 a^{6} b^{5} c^{10} d^{6} + 8820 a^{5} b^{6} c^{11} d^{5} + 20580 a^{4} b^{7} c^{12} d^{4} - 16170 a^{3} b^{8} c^{13} d^{3} + 4830 a^{2} b^{9} c^{14} d^{2} - 350 a b^{10} c^{15} d - 70 b^{11} c^{16}\right) + x \left(490 a^{11} c^{6} d^{10} - 4270 a^{10} b c^{7} d^{9} + 16380 a^{9} b^{2} c^{8} d^{8} - 36120 a^{8} b^{3} c^{9} d^{7} + 49980 a^{7} b^{4} c^{10} d^{6} - 44100 a^{6} b^{5} c^{11} d^{5} + 23520 a^{5} b^{6} c^{12} d^{4} - 5880 a^{4} b^{7} c^{13} d^{3} - 630 a^{3} b^{8} c^{14} d^{2} + 770 a^{2} b^{9} c^{15} d - 140 a b^{10} c^{16}\right)}"," ",0,"-36*b**7*d**2*log(x + (-36*a**11*b**7*d**13/(a*d - b*c)**10 + 396*a**10*b**8*c*d**12/(a*d - b*c)**10 - 1980*a**9*b**9*c**2*d**11/(a*d - b*c)**10 + 5940*a**8*b**10*c**3*d**10/(a*d - b*c)**10 - 11880*a**7*b**11*c**4*d**9/(a*d - b*c)**10 + 16632*a**6*b**12*c**5*d**8/(a*d - b*c)**10 - 16632*a**5*b**13*c**6*d**7/(a*d - b*c)**10 + 11880*a**4*b**14*c**7*d**6/(a*d - b*c)**10 - 5940*a**3*b**15*c**8*d**5/(a*d - b*c)**10 + 1980*a**2*b**16*c**9*d**4/(a*d - b*c)**10 - 396*a*b**17*c**10*d**3/(a*d - b*c)**10 + 36*a*b**7*d**3 + 36*b**18*c**11*d**2/(a*d - b*c)**10 + 36*b**8*c*d**2)/(72*b**8*d**3))/(a*d - b*c)**10 + 36*b**7*d**2*log(x + (36*a**11*b**7*d**13/(a*d - b*c)**10 - 396*a**10*b**8*c*d**12/(a*d - b*c)**10 + 1980*a**9*b**9*c**2*d**11/(a*d - b*c)**10 - 5940*a**8*b**10*c**3*d**10/(a*d - b*c)**10 + 11880*a**7*b**11*c**4*d**9/(a*d - b*c)**10 - 16632*a**6*b**12*c**5*d**8/(a*d - b*c)**10 + 16632*a**5*b**13*c**6*d**7/(a*d - b*c)**10 - 11880*a**4*b**14*c**7*d**6/(a*d - b*c)**10 + 5940*a**3*b**15*c**8*d**5/(a*d - b*c)**10 - 1980*a**2*b**16*c**9*d**4/(a*d - b*c)**10 + 396*a*b**17*c**10*d**3/(a*d - b*c)**10 + 36*a*b**7*d**3 - 36*b**18*c**11*d**2/(a*d - b*c)**10 + 36*b**8*c*d**2)/(72*b**8*d**3))/(a*d - b*c)**10 + (-10*a**8*d**8 + 95*a**7*b*c*d**7 - 409*a**6*b**2*c**2*d**6 + 1061*a**5*b**3*c**3*d**5 - 1879*a**4*b**4*c**4*d**4 + 2531*a**3*b**5*c**5*d**3 - 3349*a**2*b**6*c**6*d**2 - 595*a*b**7*c**7*d + 35*b**8*c**8 - 2520*b**8*d**8*x**8 + x**7*(-3780*a*b**7*d**8 - 16380*b**8*c*d**7) + x**6*(-840*a**2*b**6*d**8 - 24780*a*b**7*c*d**7 - 44940*b**8*c**2*d**6) + x**5*(210*a**3*b**5*d**8 - 5670*a**2*b**6*c*d**7 - 68670*a*b**7*c**2*d**6 - 66990*b**8*c**3*d**5) + x**4*(-84*a**4*b**4*d**8 + 1386*a**3*b**5*c*d**7 - 16254*a**2*b**6*c**2*d**6 - 103614*a*b**7*c**3*d**5 - 57834*b**8*c**4*d**4) + x**3*(42*a**5*b**3*d**8 - 546*a**4*b**4*c*d**7 + 3864*a**3*b**5*c**2*d**6 - 25536*a**2*b**6*c**3*d**5 - 90846*a*b**7*c**4*d**4 - 28098*b**8*c**5*d**3) + x**2*(-24*a**6*b**2*d**8 + 270*a**5*b**3*c*d**7 - 1494*a**4*b**4*c**2*d**6 + 5856*a**3*b**5*c**3*d**5 - 23544*a**2*b**6*c**4*d**4 - 45090*a*b**7*c**5*d**3 - 6534*b**8*c**6*d**2) + x*(15*a**7*b*d**8 - 153*a**6*b**2*c*d**7 + 729*a**5*b**3*c**2*d**6 - 2211*a**4*b**4*c**3*d**5 + 5139*a**3*b**5*c**4*d**4 - 12501*a**2*b**6*c**5*d**3 - 10863*a*b**7*c**6*d**2 - 315*b**8*c**7*d))/(70*a**11*c**7*d**9 - 630*a**10*b*c**8*d**8 + 2520*a**9*b**2*c**9*d**7 - 5880*a**8*b**3*c**10*d**6 + 8820*a**7*b**4*c**11*d**5 - 8820*a**6*b**5*c**12*d**4 + 5880*a**5*b**6*c**13*d**3 - 2520*a**4*b**7*c**14*d**2 + 630*a**3*b**8*c**15*d - 70*a**2*b**9*c**16 + x**9*(70*a**9*b**2*d**16 - 630*a**8*b**3*c*d**15 + 2520*a**7*b**4*c**2*d**14 - 5880*a**6*b**5*c**3*d**13 + 8820*a**5*b**6*c**4*d**12 - 8820*a**4*b**7*c**5*d**11 + 5880*a**3*b**8*c**6*d**10 - 2520*a**2*b**9*c**7*d**9 + 630*a*b**10*c**8*d**8 - 70*b**11*c**9*d**7) + x**8*(140*a**10*b*d**16 - 770*a**9*b**2*c*d**15 + 630*a**8*b**3*c**2*d**14 + 5880*a**7*b**4*c**3*d**13 - 23520*a**6*b**5*c**4*d**12 + 44100*a**5*b**6*c**5*d**11 - 49980*a**4*b**7*c**6*d**10 + 36120*a**3*b**8*c**7*d**9 - 16380*a**2*b**9*c**8*d**8 + 4270*a*b**10*c**9*d**7 - 490*b**11*c**10*d**6) + x**7*(70*a**11*d**16 + 350*a**10*b*c*d**15 - 4830*a**9*b**2*c**2*d**14 + 16170*a**8*b**3*c**3*d**13 - 20580*a**7*b**4*c**4*d**12 - 8820*a**6*b**5*c**5*d**11 + 67620*a**5*b**6*c**6*d**10 - 105420*a**4*b**7*c**7*d**9 + 88830*a**3*b**8*c**8*d**8 - 44170*a**2*b**9*c**9*d**7 + 12250*a*b**10*c**10*d**6 - 1470*b**11*c**11*d**5) + x**6*(490*a**11*c*d**15 - 1470*a**10*b*c**2*d**14 - 6370*a**9*b**2*c**3*d**13 + 42630*a**8*b**3*c**4*d**12 - 97020*a**7*b**4*c**5*d**11 + 102900*a**6*b**5*c**6*d**10 - 20580*a**5*b**6*c**7*d**9 - 79380*a**4*b**7*c**8*d**8 + 104370*a**3*b**8*c**9*d**7 - 62230*a**2*b**9*c**10*d**6 + 19110*a*b**10*c**11*d**5 - 2450*b**11*c**12*d**4) + x**5*(1470*a**11*c**2*d**14 - 8330*a**10*b*c**3*d**13 + 11270*a**9*b**2*c**4*d**12 + 30870*a**8*b**3*c**5*d**11 - 138180*a**7*b**4*c**6*d**10 + 226380*a**6*b**5*c**7*d**9 - 185220*a**5*b**6*c**8*d**8 + 49980*a**4*b**7*c**9*d**7 + 42630*a**3*b**8*c**10*d**6 - 45570*a**2*b**9*c**11*d**5 + 17150*a*b**10*c**12*d**4 - 2450*b**11*c**13*d**3) + x**4*(2450*a**11*c**3*d**13 - 17150*a**10*b*c**4*d**12 + 45570*a**9*b**2*c**5*d**11 - 42630*a**8*b**3*c**6*d**10 - 49980*a**7*b**4*c**7*d**9 + 185220*a**6*b**5*c**8*d**8 - 226380*a**5*b**6*c**9*d**7 + 138180*a**4*b**7*c**10*d**6 - 30870*a**3*b**8*c**11*d**5 - 11270*a**2*b**9*c**12*d**4 + 8330*a*b**10*c**13*d**3 - 1470*b**11*c**14*d**2) + x**3*(2450*a**11*c**4*d**12 - 19110*a**10*b*c**5*d**11 + 62230*a**9*b**2*c**6*d**10 - 104370*a**8*b**3*c**7*d**9 + 79380*a**7*b**4*c**8*d**8 + 20580*a**6*b**5*c**9*d**7 - 102900*a**5*b**6*c**10*d**6 + 97020*a**4*b**7*c**11*d**5 - 42630*a**3*b**8*c**12*d**4 + 6370*a**2*b**9*c**13*d**3 + 1470*a*b**10*c**14*d**2 - 490*b**11*c**15*d) + x**2*(1470*a**11*c**5*d**11 - 12250*a**10*b*c**6*d**10 + 44170*a**9*b**2*c**7*d**9 - 88830*a**8*b**3*c**8*d**8 + 105420*a**7*b**4*c**9*d**7 - 67620*a**6*b**5*c**10*d**6 + 8820*a**5*b**6*c**11*d**5 + 20580*a**4*b**7*c**12*d**4 - 16170*a**3*b**8*c**13*d**3 + 4830*a**2*b**9*c**14*d**2 - 350*a*b**10*c**15*d - 70*b**11*c**16) + x*(490*a**11*c**6*d**10 - 4270*a**10*b*c**7*d**9 + 16380*a**9*b**2*c**8*d**8 - 36120*a**8*b**3*c**9*d**7 + 49980*a**7*b**4*c**10*d**6 - 44100*a**6*b**5*c**11*d**5 + 23520*a**5*b**6*c**12*d**4 - 5880*a**4*b**7*c**13*d**3 - 630*a**3*b**8*c**14*d**2 + 770*a**2*b**9*c**15*d - 140*a*b**10*c**16))","B",0
1375,1,314,0,5.116597," ","integrate((b*x+a)**5*(d*x+c)**(1/2),x)","\frac{2 \left(\frac{b^{5} \left(c + d x\right)^{\frac{13}{2}}}{13 d^{5}} + \frac{\left(c + d x\right)^{\frac{11}{2}} \left(5 a b^{4} d - 5 b^{5} c\right)}{11 d^{5}} + \frac{\left(c + d x\right)^{\frac{9}{2}} \left(10 a^{2} b^{3} d^{2} - 20 a b^{4} c d + 10 b^{5} c^{2}\right)}{9 d^{5}} + \frac{\left(c + d x\right)^{\frac{7}{2}} \left(10 a^{3} b^{2} d^{3} - 30 a^{2} b^{3} c d^{2} + 30 a b^{4} c^{2} d - 10 b^{5} c^{3}\right)}{7 d^{5}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(5 a^{4} b d^{4} - 20 a^{3} b^{2} c d^{3} + 30 a^{2} b^{3} c^{2} d^{2} - 20 a b^{4} c^{3} d + 5 b^{5} c^{4}\right)}{5 d^{5}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(a^{5} d^{5} - 5 a^{4} b c d^{4} + 10 a^{3} b^{2} c^{2} d^{3} - 10 a^{2} b^{3} c^{3} d^{2} + 5 a b^{4} c^{4} d - b^{5} c^{5}\right)}{3 d^{5}}\right)}{d}"," ",0,"2*(b**5*(c + d*x)**(13/2)/(13*d**5) + (c + d*x)**(11/2)*(5*a*b**4*d - 5*b**5*c)/(11*d**5) + (c + d*x)**(9/2)*(10*a**2*b**3*d**2 - 20*a*b**4*c*d + 10*b**5*c**2)/(9*d**5) + (c + d*x)**(7/2)*(10*a**3*b**2*d**3 - 30*a**2*b**3*c*d**2 + 30*a*b**4*c**2*d - 10*b**5*c**3)/(7*d**5) + (c + d*x)**(5/2)*(5*a**4*b*d**4 - 20*a**3*b**2*c*d**3 + 30*a**2*b**3*c**2*d**2 - 20*a*b**4*c**3*d + 5*b**5*c**4)/(5*d**5) + (c + d*x)**(3/2)*(a**5*d**5 - 5*a**4*b*c*d**4 + 10*a**3*b**2*c**2*d**3 - 10*a**2*b**3*c**3*d**2 + 5*a*b**4*c**4*d - b**5*c**5)/(3*d**5))/d","B",0
1376,1,223,0,4.194880," ","integrate((b*x+a)**4*(d*x+c)**(1/2),x)","\frac{2 \left(\frac{b^{4} \left(c + d x\right)^{\frac{11}{2}}}{11 d^{4}} + \frac{\left(c + d x\right)^{\frac{9}{2}} \left(4 a b^{3} d - 4 b^{4} c\right)}{9 d^{4}} + \frac{\left(c + d x\right)^{\frac{7}{2}} \left(6 a^{2} b^{2} d^{2} - 12 a b^{3} c d + 6 b^{4} c^{2}\right)}{7 d^{4}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(4 a^{3} b d^{3} - 12 a^{2} b^{2} c d^{2} + 12 a b^{3} c^{2} d - 4 b^{4} c^{3}\right)}{5 d^{4}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(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}\right)}{3 d^{4}}\right)}{d}"," ",0,"2*(b**4*(c + d*x)**(11/2)/(11*d**4) + (c + d*x)**(9/2)*(4*a*b**3*d - 4*b**4*c)/(9*d**4) + (c + d*x)**(7/2)*(6*a**2*b**2*d**2 - 12*a*b**3*c*d + 6*b**4*c**2)/(7*d**4) + (c + d*x)**(5/2)*(4*a**3*b*d**3 - 12*a**2*b**2*c*d**2 + 12*a*b**3*c**2*d - 4*b**4*c**3)/(5*d**4) + (c + d*x)**(3/2)*(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)/(3*d**4))/d","A",0
1377,1,146,0,3.336046," ","integrate((b*x+a)**3*(d*x+c)**(1/2),x)","\frac{2 \left(\frac{b^{3} \left(c + d x\right)^{\frac{9}{2}}}{9 d^{3}} + \frac{\left(c + d x\right)^{\frac{7}{2}} \left(3 a b^{2} d - 3 b^{3} c\right)}{7 d^{3}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(3 a^{2} b d^{2} - 6 a b^{2} c d + 3 b^{3} c^{2}\right)}{5 d^{3}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}\right)}{3 d^{3}}\right)}{d}"," ",0,"2*(b**3*(c + d*x)**(9/2)/(9*d**3) + (c + d*x)**(7/2)*(3*a*b**2*d - 3*b**3*c)/(7*d**3) + (c + d*x)**(5/2)*(3*a**2*b*d**2 - 6*a*b**2*c*d + 3*b**3*c**2)/(5*d**3) + (c + d*x)**(3/2)*(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3)/(3*d**3))/d","A",0
1378,1,85,0,2.694713," ","integrate((b*x+a)**2*(d*x+c)**(1/2),x)","\frac{2 \left(\frac{b^{2} \left(c + d x\right)^{\frac{7}{2}}}{7 d^{2}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(2 a b d - 2 b^{2} c\right)}{5 d^{2}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{3 d^{2}}\right)}{d}"," ",0,"2*(b**2*(c + d*x)**(7/2)/(7*d**2) + (c + d*x)**(5/2)*(2*a*b*d - 2*b**2*c)/(5*d**2) + (c + d*x)**(3/2)*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(3*d**2))/d","A",0
1379,1,36,0,2.122540," ","integrate((b*x+a)*(d*x+c)**(1/2),x)","\frac{2 \left(\frac{b \left(c + d x\right)^{\frac{5}{2}}}{5 d} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(a d - b c\right)}{3 d}\right)}{d}"," ",0,"2*(b*(c + d*x)**(5/2)/(5*d) + (c + d*x)**(3/2)*(a*d - b*c)/(3*d))/d","A",0
1380,1,12,0,0.060359," ","integrate((d*x+c)**(1/2),x)","\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d}"," ",0,"2*(c + d*x)**(3/2)/(3*d)","A",0
1381,1,61,0,4.388633," ","integrate((d*x+c)**(1/2)/(b*x+a),x)","\frac{2 \left(\frac{d \sqrt{c + d x}}{b} - \frac{d \left(a d - b c\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{2} \sqrt{\frac{a d - b c}{b}}}\right)}{d}"," ",0,"2*(d*sqrt(c + d*x)/b - d*(a*d - b*c)*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(b**2*sqrt((a*d - b*c)/b)))/d","A",0
1382,1,573,0,58.579618," ","integrate((d*x+c)**(1/2)/(b*x+a)**2,x)","- \frac{2 a d^{2} \sqrt{c + d x}}{2 a^{2} b d^{2} - 2 a b^{2} c d + 2 a b^{2} d^{2} x - 2 b^{3} c d x} + \frac{a d^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} \log{\left(- a^{2} d^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + 2 a b c d \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} - b^{2} c^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + \sqrt{c + d x} \right)}}{2 b} - \frac{a d^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} \log{\left(a^{2} d^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} - 2 a b c d \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + b^{2} c^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + \sqrt{c + d x} \right)}}{2 b} - \frac{c d \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} \log{\left(- a^{2} d^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + 2 a b c d \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} - b^{2} c^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + \sqrt{c + d x} \right)}}{2} + \frac{c d \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} \log{\left(a^{2} d^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} - 2 a b c d \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + b^{2} c^{2} \sqrt{- \frac{1}{b \left(a d - b c\right)^{3}}} + \sqrt{c + d x} \right)}}{2} + \frac{2 c d \sqrt{c + d x}}{2 a^{2} d^{2} - 2 a b c d + 2 a b d^{2} x - 2 b^{2} c d x} + \frac{2 d \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d}{b} - c}} \right)}}{b^{2} \sqrt{\frac{a d}{b} - c}}"," ",0,"-2*a*d**2*sqrt(c + d*x)/(2*a**2*b*d**2 - 2*a*b**2*c*d + 2*a*b**2*d**2*x - 2*b**3*c*d*x) + a*d**2*sqrt(-1/(b*(a*d - b*c)**3))*log(-a**2*d**2*sqrt(-1/(b*(a*d - b*c)**3)) + 2*a*b*c*d*sqrt(-1/(b*(a*d - b*c)**3)) - b**2*c**2*sqrt(-1/(b*(a*d - b*c)**3)) + sqrt(c + d*x))/(2*b) - a*d**2*sqrt(-1/(b*(a*d - b*c)**3))*log(a**2*d**2*sqrt(-1/(b*(a*d - b*c)**3)) - 2*a*b*c*d*sqrt(-1/(b*(a*d - b*c)**3)) + b**2*c**2*sqrt(-1/(b*(a*d - b*c)**3)) + sqrt(c + d*x))/(2*b) - c*d*sqrt(-1/(b*(a*d - b*c)**3))*log(-a**2*d**2*sqrt(-1/(b*(a*d - b*c)**3)) + 2*a*b*c*d*sqrt(-1/(b*(a*d - b*c)**3)) - b**2*c**2*sqrt(-1/(b*(a*d - b*c)**3)) + sqrt(c + d*x))/2 + c*d*sqrt(-1/(b*(a*d - b*c)**3))*log(a**2*d**2*sqrt(-1/(b*(a*d - b*c)**3)) - 2*a*b*c*d*sqrt(-1/(b*(a*d - b*c)**3)) + b**2*c**2*sqrt(-1/(b*(a*d - b*c)**3)) + sqrt(c + d*x))/2 + 2*c*d*sqrt(c + d*x)/(2*a**2*d**2 - 2*a*b*c*d + 2*a*b*d**2*x - 2*b**2*c*d*x) + 2*d*atan(sqrt(c + d*x)/sqrt(a*d/b - c))/(b**2*sqrt(a*d/b - c))","B",0
1383,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1384,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1385,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1386,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1387,1,763,0,26.419444," ","integrate((b*x+a)**5*(d*x+c)**(3/2),x)","a^{5} c \left(\begin{cases} \sqrt{c} x & \text{for}\: d = 0 \\\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + \frac{2 a^{5} \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{10 a^{4} b c \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} + \frac{10 a^{4} b \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{20 a^{3} b^{2} c \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} + \frac{20 a^{3} b^{2} \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}} + \frac{20 a^{2} b^{3} c \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} + \frac{20 a^{2} b^{3} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{4}} + \frac{10 a b^{4} c \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{5}} + \frac{10 a b^{4} \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{5}} + \frac{2 b^{5} c \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{6}} + \frac{2 b^{5} \left(\frac{c^{6} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{6 c^{5} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{15 c^{4} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{20 c^{3} \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{15 c^{2} \left(c + d x\right)^{\frac{11}{2}}}{11} - \frac{6 c \left(c + d x\right)^{\frac{13}{2}}}{13} + \frac{\left(c + d x\right)^{\frac{15}{2}}}{15}\right)}{d^{6}}"," ",0,"a**5*c*Piecewise((sqrt(c)*x, Eq(d, 0)), (2*(c + d*x)**(3/2)/(3*d), True)) + 2*a**5*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 10*a**4*b*c*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d**2 + 10*a**4*b*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 20*a**3*b**2*c*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**3 + 20*a**3*b**2*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3 + 20*a**2*b**3*c*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**4 + 20*a**2*b**3*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**4 + 10*a*b**4*c*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**5 + 10*a*b**4*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**5 + 2*b**5*c*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**6 + 2*b**5*(c**6*(c + d*x)**(3/2)/3 - 6*c**5*(c + d*x)**(5/2)/5 + 15*c**4*(c + d*x)**(7/2)/7 - 20*c**3*(c + d*x)**(9/2)/9 + 15*c**2*(c + d*x)**(11/2)/11 - 6*c*(c + d*x)**(13/2)/13 + (c + d*x)**(15/2)/15)/d**6","A",0
1388,1,559,0,20.088794," ","integrate((b*x+a)**4*(d*x+c)**(3/2),x)","a^{4} c \left(\begin{cases} \sqrt{c} x & \text{for}\: d = 0 \\\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + \frac{2 a^{4} \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{8 a^{3} b c \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} + \frac{8 a^{3} b \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{12 a^{2} b^{2} c \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} + \frac{12 a^{2} b^{2} \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}} + \frac{8 a b^{3} c \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} + \frac{8 a b^{3} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{4}} + \frac{2 b^{4} c \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{5}} + \frac{2 b^{4} \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{5}}"," ",0,"a**4*c*Piecewise((sqrt(c)*x, Eq(d, 0)), (2*(c + d*x)**(3/2)/(3*d), True)) + 2*a**4*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 8*a**3*b*c*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d**2 + 8*a**3*b*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 12*a**2*b**2*c*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**3 + 12*a**2*b**2*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3 + 8*a*b**3*c*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**4 + 8*a*b**3*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**4 + 2*b**4*c*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**5 + 2*b**4*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**5","A",0
1389,1,386,0,14.379603," ","integrate((b*x+a)**3*(d*x+c)**(3/2),x)","a^{3} c \left(\begin{cases} \sqrt{c} x & \text{for}\: d = 0 \\\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + \frac{2 a^{3} \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{6 a^{2} b c \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} + \frac{6 a^{2} b \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{6 a b^{2} c \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} + \frac{6 a b^{2} \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}} + \frac{2 b^{3} c \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} + \frac{2 b^{3} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{4}}"," ",0,"a**3*c*Piecewise((sqrt(c)*x, Eq(d, 0)), (2*(c + d*x)**(3/2)/(3*d), True)) + 2*a**3*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 6*a**2*b*c*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d**2 + 6*a**2*b*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 6*a*b**2*c*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**3 + 6*a*b**2*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3 + 2*b**3*c*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**4 + 2*b**3*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**4","A",0
1390,1,240,0,9.605896," ","integrate((b*x+a)**2*(d*x+c)**(3/2),x)","a^{2} c \left(\begin{cases} \sqrt{c} x & \text{for}\: d = 0 \\\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + \frac{2 a^{2} \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{4 a b c \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} + \frac{4 a b \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{2 b^{2} c \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} + \frac{2 b^{2} \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}}"," ",0,"a**2*c*Piecewise((sqrt(c)*x, Eq(d, 0)), (2*(c + d*x)**(3/2)/(3*d), True)) + 2*a**2*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 4*a*b*c*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d**2 + 4*a*b*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 2*b**2*c*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**3 + 2*b**2*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3","A",0
1391,1,146,0,0.665837," ","integrate((b*x+a)*(d*x+c)**(3/2),x)","\begin{cases} \frac{2 a c^{2} \sqrt{c + d x}}{5 d} + \frac{4 a c x \sqrt{c + d x}}{5} + \frac{2 a d x^{2} \sqrt{c + d x}}{5} - \frac{4 b c^{3} \sqrt{c + d x}}{35 d^{2}} + \frac{2 b c^{2} x \sqrt{c + d x}}{35 d} + \frac{16 b c x^{2} \sqrt{c + d x}}{35} + \frac{2 b d x^{3} \sqrt{c + d x}}{7} & \text{for}\: d \neq 0 \\c^{\frac{3}{2}} \left(a x + \frac{b x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*c**2*sqrt(c + d*x)/(5*d) + 4*a*c*x*sqrt(c + d*x)/5 + 2*a*d*x**2*sqrt(c + d*x)/5 - 4*b*c**3*sqrt(c + d*x)/(35*d**2) + 2*b*c**2*x*sqrt(c + d*x)/(35*d) + 16*b*c*x**2*sqrt(c + d*x)/35 + 2*b*d*x**3*sqrt(c + d*x)/7, Ne(d, 0)), (c**(3/2)*(a*x + b*x**2/2), True))","A",0
1392,1,12,0,0.061499," ","integrate((d*x+c)**(3/2),x)","\frac{2 \left(c + d x\right)^{\frac{5}{2}}}{5 d}"," ",0,"2*(c + d*x)**(5/2)/(5*d)","A",0
1393,1,82,0,14.699895," ","integrate((d*x+c)**(3/2)/(b*x+a),x)","\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 b} + \frac{\sqrt{c + d x} \left(- 2 a d + 2 b c\right)}{b^{2}} + \frac{2 \left(a d - b c\right)^{2} \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{3} \sqrt{\frac{a d - b c}{b}}}"," ",0,"2*(c + d*x)**(3/2)/(3*b) + sqrt(c + d*x)*(-2*a*d + 2*b*c)/b**2 + 2*(a*d - b*c)**2*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(b**3*sqrt((a*d - b*c)/b))","A",0
1394,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1395,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1396,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1397,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1398,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1399,1,1292,0,43.078748," ","integrate((b*x+a)**5*(d*x+c)**(5/2),x)","a^{5} c^{2} \left(\begin{cases} \sqrt{c} x & \text{for}\: d = 0 \\\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + \frac{4 a^{5} c \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{2 a^{5} \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d} + \frac{10 a^{4} b c^{2} \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} + \frac{20 a^{4} b c \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{10 a^{4} b \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{2}} + \frac{20 a^{3} b^{2} c^{2} \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} + \frac{40 a^{3} b^{2} c \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}} + \frac{20 a^{3} b^{2} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{3}} + \frac{20 a^{2} b^{3} c^{2} \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} + \frac{40 a^{2} b^{3} c \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{4}} + \frac{20 a^{2} b^{3} \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{4}} + \frac{10 a b^{4} c^{2} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{5}} + \frac{20 a b^{4} c \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{5}} + \frac{10 a b^{4} \left(\frac{c^{6} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{6 c^{5} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{15 c^{4} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{20 c^{3} \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{15 c^{2} \left(c + d x\right)^{\frac{11}{2}}}{11} - \frac{6 c \left(c + d x\right)^{\frac{13}{2}}}{13} + \frac{\left(c + d x\right)^{\frac{15}{2}}}{15}\right)}{d^{5}} + \frac{2 b^{5} c^{2} \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{6}} + \frac{4 b^{5} c \left(\frac{c^{6} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{6 c^{5} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{15 c^{4} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{20 c^{3} \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{15 c^{2} \left(c + d x\right)^{\frac{11}{2}}}{11} - \frac{6 c \left(c + d x\right)^{\frac{13}{2}}}{13} + \frac{\left(c + d x\right)^{\frac{15}{2}}}{15}\right)}{d^{6}} + \frac{2 b^{5} \left(- \frac{c^{7} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{7 c^{6} \left(c + d x\right)^{\frac{5}{2}}}{5} - 3 c^{5} \left(c + d x\right)^{\frac{7}{2}} + \frac{35 c^{4} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{35 c^{3} \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{21 c^{2} \left(c + d x\right)^{\frac{13}{2}}}{13} - \frac{7 c \left(c + d x\right)^{\frac{15}{2}}}{15} + \frac{\left(c + d x\right)^{\frac{17}{2}}}{17}\right)}{d^{6}}"," ",0,"a**5*c**2*Piecewise((sqrt(c)*x, Eq(d, 0)), (2*(c + d*x)**(3/2)/(3*d), True)) + 4*a**5*c*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 2*a**5*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d + 10*a**4*b*c**2*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d**2 + 20*a**4*b*c*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 10*a**4*b*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**2 + 20*a**3*b**2*c**2*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**3 + 40*a**3*b**2*c*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3 + 20*a**3*b**2*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**3 + 20*a**2*b**3*c**2*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**4 + 40*a**2*b**3*c*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**4 + 20*a**2*b**3*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**4 + 10*a*b**4*c**2*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**5 + 20*a*b**4*c*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**5 + 10*a*b**4*(c**6*(c + d*x)**(3/2)/3 - 6*c**5*(c + d*x)**(5/2)/5 + 15*c**4*(c + d*x)**(7/2)/7 - 20*c**3*(c + d*x)**(9/2)/9 + 15*c**2*(c + d*x)**(11/2)/11 - 6*c*(c + d*x)**(13/2)/13 + (c + d*x)**(15/2)/15)/d**5 + 2*b**5*c**2*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**6 + 4*b**5*c*(c**6*(c + d*x)**(3/2)/3 - 6*c**5*(c + d*x)**(5/2)/5 + 15*c**4*(c + d*x)**(7/2)/7 - 20*c**3*(c + d*x)**(9/2)/9 + 15*c**2*(c + d*x)**(11/2)/11 - 6*c*(c + d*x)**(13/2)/13 + (c + d*x)**(15/2)/15)/d**6 + 2*b**5*(-c**7*(c + d*x)**(3/2)/3 + 7*c**6*(c + d*x)**(5/2)/5 - 3*c**5*(c + d*x)**(7/2) + 35*c**4*(c + d*x)**(9/2)/9 - 35*c**3*(c + d*x)**(11/2)/11 + 21*c**2*(c + d*x)**(13/2)/13 - 7*c*(c + d*x)**(15/2)/15 + (c + d*x)**(17/2)/17)/d**6","A",0
1400,1,960,0,33.635859," ","integrate((b*x+a)**4*(d*x+c)**(5/2),x)","a^{4} c^{2} \left(\begin{cases} \sqrt{c} x & \text{for}\: d = 0 \\\frac{2 \left(c + d x\right)^{\frac{3}{2}}}{3 d} & \text{otherwise} \end{cases}\right) + \frac{4 a^{4} c \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d} + \frac{2 a^{4} \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d} + \frac{8 a^{3} b c^{2} \left(- \frac{c \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} + \frac{16 a^{3} b c \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{2}} + \frac{8 a^{3} b \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{2}} + \frac{12 a^{2} b^{2} c^{2} \left(\frac{c^{2} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{2 c \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} + \frac{24 a^{2} b^{2} c \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{3}} + \frac{12 a^{2} b^{2} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{3}} + \frac{8 a b^{3} c^{2} \left(- \frac{c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} + \frac{3 c^{2} \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{3 c \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} + \frac{16 a b^{3} c \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{4}} + \frac{8 a b^{3} \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{4}} + \frac{2 b^{4} c^{2} \left(\frac{c^{4} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{4 c^{3} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{6 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{4 c \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{5}} + \frac{4 b^{4} c \left(- \frac{c^{5} \left(c + d x\right)^{\frac{3}{2}}}{3} + c^{4} \left(c + d x\right)^{\frac{5}{2}} - \frac{10 c^{3} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{10 c^{2} \left(c + d x\right)^{\frac{9}{2}}}{9} - \frac{5 c \left(c + d x\right)^{\frac{11}{2}}}{11} + \frac{\left(c + d x\right)^{\frac{13}{2}}}{13}\right)}{d^{5}} + \frac{2 b^{4} \left(\frac{c^{6} \left(c + d x\right)^{\frac{3}{2}}}{3} - \frac{6 c^{5} \left(c + d x\right)^{\frac{5}{2}}}{5} + \frac{15 c^{4} \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{20 c^{3} \left(c + d x\right)^{\frac{9}{2}}}{9} + \frac{15 c^{2} \left(c + d x\right)^{\frac{11}{2}}}{11} - \frac{6 c \left(c + d x\right)^{\frac{13}{2}}}{13} + \frac{\left(c + d x\right)^{\frac{15}{2}}}{15}\right)}{d^{5}}"," ",0,"a**4*c**2*Piecewise((sqrt(c)*x, Eq(d, 0)), (2*(c + d*x)**(3/2)/(3*d), True)) + 4*a**4*c*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d + 2*a**4*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d + 8*a**3*b*c**2*(-c*(c + d*x)**(3/2)/3 + (c + d*x)**(5/2)/5)/d**2 + 16*a**3*b*c*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**2 + 8*a**3*b*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**2 + 12*a**2*b**2*c**2*(c**2*(c + d*x)**(3/2)/3 - 2*c*(c + d*x)**(5/2)/5 + (c + d*x)**(7/2)/7)/d**3 + 24*a**2*b**2*c*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**3 + 12*a**2*b**2*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**3 + 8*a*b**3*c**2*(-c**3*(c + d*x)**(3/2)/3 + 3*c**2*(c + d*x)**(5/2)/5 - 3*c*(c + d*x)**(7/2)/7 + (c + d*x)**(9/2)/9)/d**4 + 16*a*b**3*c*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**4 + 8*a*b**3*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**4 + 2*b**4*c**2*(c**4*(c + d*x)**(3/2)/3 - 4*c**3*(c + d*x)**(5/2)/5 + 6*c**2*(c + d*x)**(7/2)/7 - 4*c*(c + d*x)**(9/2)/9 + (c + d*x)**(11/2)/11)/d**5 + 4*b**4*c*(-c**5*(c + d*x)**(3/2)/3 + c**4*(c + d*x)**(5/2) - 10*c**3*(c + d*x)**(7/2)/7 + 10*c**2*(c + d*x)**(9/2)/9 - 5*c*(c + d*x)**(11/2)/11 + (c + d*x)**(13/2)/13)/d**5 + 2*b**4*(c**6*(c + d*x)**(3/2)/3 - 6*c**5*(c + d*x)**(5/2)/5 + 15*c**4*(c + d*x)**(7/2)/7 - 20*c**3*(c + d*x)**(9/2)/9 + 15*c**2*(c + d*x)**(11/2)/11 - 6*c*(c + d*x)**(13/2)/13 + (c + d*x)**(15/2)/15)/d**5","A",0
1401,1,549,0,4.608888," ","integrate((b*x+a)**3*(d*x+c)**(5/2),x)","\begin{cases} \frac{2 a^{3} c^{3} \sqrt{c + d x}}{7 d} + \frac{6 a^{3} c^{2} x \sqrt{c + d x}}{7} + \frac{6 a^{3} c d x^{2} \sqrt{c + d x}}{7} + \frac{2 a^{3} d^{2} x^{3} \sqrt{c + d x}}{7} - \frac{4 a^{2} b c^{4} \sqrt{c + d x}}{21 d^{2}} + \frac{2 a^{2} b c^{3} x \sqrt{c + d x}}{21 d} + \frac{10 a^{2} b c^{2} x^{2} \sqrt{c + d x}}{7} + \frac{38 a^{2} b c d x^{3} \sqrt{c + d x}}{21} + \frac{2 a^{2} b d^{2} x^{4} \sqrt{c + d x}}{3} + \frac{16 a b^{2} c^{5} \sqrt{c + d x}}{231 d^{3}} - \frac{8 a b^{2} c^{4} x \sqrt{c + d x}}{231 d^{2}} + \frac{2 a b^{2} c^{3} x^{2} \sqrt{c + d x}}{77 d} + \frac{226 a b^{2} c^{2} x^{3} \sqrt{c + d x}}{231} + \frac{46 a b^{2} c d x^{4} \sqrt{c + d x}}{33} + \frac{6 a b^{2} d^{2} x^{5} \sqrt{c + d x}}{11} - \frac{32 b^{3} c^{6} \sqrt{c + d x}}{3003 d^{4}} + \frac{16 b^{3} c^{5} x \sqrt{c + d x}}{3003 d^{3}} - \frac{4 b^{3} c^{4} x^{2} \sqrt{c + d x}}{1001 d^{2}} + \frac{10 b^{3} c^{3} x^{3} \sqrt{c + d x}}{3003 d} + \frac{106 b^{3} c^{2} x^{4} \sqrt{c + d x}}{429} + \frac{54 b^{3} c d x^{5} \sqrt{c + d x}}{143} + \frac{2 b^{3} d^{2} x^{6} \sqrt{c + d x}}{13} & \text{for}\: d \neq 0 \\c^{\frac{5}{2}} \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{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*c**3*sqrt(c + d*x)/(7*d) + 6*a**3*c**2*x*sqrt(c + d*x)/7 + 6*a**3*c*d*x**2*sqrt(c + d*x)/7 + 2*a**3*d**2*x**3*sqrt(c + d*x)/7 - 4*a**2*b*c**4*sqrt(c + d*x)/(21*d**2) + 2*a**2*b*c**3*x*sqrt(c + d*x)/(21*d) + 10*a**2*b*c**2*x**2*sqrt(c + d*x)/7 + 38*a**2*b*c*d*x**3*sqrt(c + d*x)/21 + 2*a**2*b*d**2*x**4*sqrt(c + d*x)/3 + 16*a*b**2*c**5*sqrt(c + d*x)/(231*d**3) - 8*a*b**2*c**4*x*sqrt(c + d*x)/(231*d**2) + 2*a*b**2*c**3*x**2*sqrt(c + d*x)/(77*d) + 226*a*b**2*c**2*x**3*sqrt(c + d*x)/231 + 46*a*b**2*c*d*x**4*sqrt(c + d*x)/33 + 6*a*b**2*d**2*x**5*sqrt(c + d*x)/11 - 32*b**3*c**6*sqrt(c + d*x)/(3003*d**4) + 16*b**3*c**5*x*sqrt(c + d*x)/(3003*d**3) - 4*b**3*c**4*x**2*sqrt(c + d*x)/(1001*d**2) + 10*b**3*c**3*x**3*sqrt(c + d*x)/(3003*d) + 106*b**3*c**2*x**4*sqrt(c + d*x)/429 + 54*b**3*c*d*x**5*sqrt(c + d*x)/143 + 2*b**3*d**2*x**6*sqrt(c + d*x)/13, Ne(d, 0)), (c**(5/2)*(a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4), True))","A",0
1402,1,355,0,3.578918," ","integrate((b*x+a)**2*(d*x+c)**(5/2),x)","\begin{cases} \frac{2 a^{2} c^{3} \sqrt{c + d x}}{7 d} + \frac{6 a^{2} c^{2} x \sqrt{c + d x}}{7} + \frac{6 a^{2} c d x^{2} \sqrt{c + d x}}{7} + \frac{2 a^{2} d^{2} x^{3} \sqrt{c + d x}}{7} - \frac{8 a b c^{4} \sqrt{c + d x}}{63 d^{2}} + \frac{4 a b c^{3} x \sqrt{c + d x}}{63 d} + \frac{20 a b c^{2} x^{2} \sqrt{c + d x}}{21} + \frac{76 a b c d x^{3} \sqrt{c + d x}}{63} + \frac{4 a b d^{2} x^{4} \sqrt{c + d x}}{9} + \frac{16 b^{2} c^{5} \sqrt{c + d x}}{693 d^{3}} - \frac{8 b^{2} c^{4} x \sqrt{c + d x}}{693 d^{2}} + \frac{2 b^{2} c^{3} x^{2} \sqrt{c + d x}}{231 d} + \frac{226 b^{2} c^{2} x^{3} \sqrt{c + d x}}{693} + \frac{46 b^{2} c d x^{4} \sqrt{c + d x}}{99} + \frac{2 b^{2} d^{2} x^{5} \sqrt{c + d x}}{11} & \text{for}\: d \neq 0 \\c^{\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*c**3*sqrt(c + d*x)/(7*d) + 6*a**2*c**2*x*sqrt(c + d*x)/7 + 6*a**2*c*d*x**2*sqrt(c + d*x)/7 + 2*a**2*d**2*x**3*sqrt(c + d*x)/7 - 8*a*b*c**4*sqrt(c + d*x)/(63*d**2) + 4*a*b*c**3*x*sqrt(c + d*x)/(63*d) + 20*a*b*c**2*x**2*sqrt(c + d*x)/21 + 76*a*b*c*d*x**3*sqrt(c + d*x)/63 + 4*a*b*d**2*x**4*sqrt(c + d*x)/9 + 16*b**2*c**5*sqrt(c + d*x)/(693*d**3) - 8*b**2*c**4*x*sqrt(c + d*x)/(693*d**2) + 2*b**2*c**3*x**2*sqrt(c + d*x)/(231*d) + 226*b**2*c**2*x**3*sqrt(c + d*x)/693 + 46*b**2*c*d*x**4*sqrt(c + d*x)/99 + 2*b**2*d**2*x**5*sqrt(c + d*x)/11, Ne(d, 0)), (c**(5/2)*(a**2*x + a*b*x**2 + b**2*x**3/3), True))","A",0
1403,1,194,0,2.363216," ","integrate((b*x+a)*(d*x+c)**(5/2),x)","\begin{cases} \frac{2 a c^{3} \sqrt{c + d x}}{7 d} + \frac{6 a c^{2} x \sqrt{c + d x}}{7} + \frac{6 a c d x^{2} \sqrt{c + d x}}{7} + \frac{2 a d^{2} x^{3} \sqrt{c + d x}}{7} - \frac{4 b c^{4} \sqrt{c + d x}}{63 d^{2}} + \frac{2 b c^{3} x \sqrt{c + d x}}{63 d} + \frac{10 b c^{2} x^{2} \sqrt{c + d x}}{21} + \frac{38 b c d x^{3} \sqrt{c + d x}}{63} + \frac{2 b d^{2} x^{4} \sqrt{c + d x}}{9} & \text{for}\: d \neq 0 \\c^{\frac{5}{2}} \left(a x + \frac{b x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*c**3*sqrt(c + d*x)/(7*d) + 6*a*c**2*x*sqrt(c + d*x)/7 + 6*a*c*d*x**2*sqrt(c + d*x)/7 + 2*a*d**2*x**3*sqrt(c + d*x)/7 - 4*b*c**4*sqrt(c + d*x)/(63*d**2) + 2*b*c**3*x*sqrt(c + d*x)/(63*d) + 10*b*c**2*x**2*sqrt(c + d*x)/21 + 38*b*c*d*x**3*sqrt(c + d*x)/63 + 2*b*d**2*x**4*sqrt(c + d*x)/9, Ne(d, 0)), (c**(5/2)*(a*x + b*x**2/2), True))","A",0
1404,1,12,0,0.064969," ","integrate((d*x+c)**(5/2),x)","\frac{2 \left(c + d x\right)^{\frac{7}{2}}}{7 d}"," ",0,"2*(c + d*x)**(7/2)/(7*d)","A",0
1405,1,121,0,27.012394," ","integrate((d*x+c)**(5/2)/(b*x+a),x)","\frac{2 \left(c + d x\right)^{\frac{5}{2}}}{5 b} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(- 2 a d + 2 b c\right)}{3 b^{2}} + \frac{\sqrt{c + d x} \left(2 a^{2} d^{2} - 4 a b c d + 2 b^{2} c^{2}\right)}{b^{3}} - \frac{2 \left(a d - b c\right)^{3} \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{4} \sqrt{\frac{a d - b c}{b}}}"," ",0,"2*(c + d*x)**(5/2)/(5*b) + (c + d*x)**(3/2)*(-2*a*d + 2*b*c)/(3*b**2) + sqrt(c + d*x)*(2*a**2*d**2 - 4*a*b*c*d + 2*b**2*c**2)/b**3 - 2*(a*d - b*c)**3*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(b**4*sqrt((a*d - b*c)/b))","A",0
1406,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1407,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1408,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1409,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1410,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1411,1,104,0,1.498123," ","integrate((-1+x)**(1/2)/(1+x)**2,x)","\begin{cases} \frac{\sqrt{2} i \operatorname{acosh}{\left(\frac{\sqrt{2}}{\sqrt{x + 1}} \right)}}{2} + \frac{i}{\sqrt{-1 + \frac{2}{x + 1}} \sqrt{x + 1}} - \frac{2 i}{\sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{\frac{3}{2}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{\sqrt{1 - \frac{2}{x + 1}}}{\sqrt{x + 1}} - \frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{2}}{\sqrt{x + 1}} \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(2)*I*acosh(sqrt(2)/sqrt(x + 1))/2 + I/(sqrt(-1 + 2/(x + 1))*sqrt(x + 1)) - 2*I/(sqrt(-1 + 2/(x + 1))*(x + 1)**(3/2)), 2/Abs(x + 1) > 1), (-sqrt(1 - 2/(x + 1))/sqrt(x + 1) - sqrt(2)*asin(sqrt(2)/sqrt(x + 1))/2, True))","A",0
1412,1,167,0,2.609464," ","integrate((-1+x)**(1/2)/(1+x)**3,x)","\begin{cases} \frac{\sqrt{2} i \operatorname{acosh}{\left(\frac{\sqrt{2}}{\sqrt{x + 1}} \right)}}{16} - \frac{i}{8 \sqrt{-1 + \frac{2}{x + 1}} \sqrt{x + 1}} + \frac{3 i}{4 \sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{\frac{3}{2}}} - \frac{i}{\sqrt{-1 + \frac{2}{x + 1}} \left(x + 1\right)^{\frac{5}{2}}} & \text{for}\: \frac{2}{\left|{x + 1}\right|} > 1 \\- \frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{2}}{\sqrt{x + 1}} \right)}}{16} + \frac{1}{8 \sqrt{1 - \frac{2}{x + 1}} \sqrt{x + 1}} - \frac{3}{4 \sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - \frac{2}{x + 1}} \left(x + 1\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(2)*I*acosh(sqrt(2)/sqrt(x + 1))/16 - I/(8*sqrt(-1 + 2/(x + 1))*sqrt(x + 1)) + 3*I/(4*sqrt(-1 + 2/(x + 1))*(x + 1)**(3/2)) - I/(sqrt(-1 + 2/(x + 1))*(x + 1)**(5/2)), 2/Abs(x + 1) > 1), (-sqrt(2)*asin(sqrt(2)/sqrt(x + 1))/16 + 1/(8*sqrt(1 - 2/(x + 1))*sqrt(x + 1)) - 3/(4*sqrt(1 - 2/(x + 1))*(x + 1)**(3/2)) + 1/(sqrt(1 - 2/(x + 1))*(x + 1)**(5/2)), True))","A",0
1413,1,728,0,79.908144," ","integrate((b*x+a)**5/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{5} c}{\sqrt{c + d x}} - 2 a^{5} \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{10 a^{4} b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{10 a^{4} b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{20 a^{3} b^{2} c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{20 a^{3} b^{2} \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{20 a^{2} b^{3} c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{20 a^{2} b^{3} \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{10 a b^{4} c \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{4}} - \frac{10 a b^{4} \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} - \frac{2 b^{5} c \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{5}} - \frac{2 b^{5} \left(\frac{c^{6}}{\sqrt{c + d x}} + 6 c^{5} \sqrt{c + d x} - 5 c^{4} \left(c + d x\right)^{\frac{3}{2}} + 4 c^{3} \left(c + d x\right)^{\frac{5}{2}} - \frac{15 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{2 c \left(c + d x\right)^{\frac{9}{2}}}{3} - \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{5}}}{d} & \text{for}\: d \neq 0 \\\frac{\begin{cases} a^{5} x & \text{for}\: b = 0 \\\frac{\left(a + b x\right)^{6}}{6 b} & \text{otherwise} \end{cases}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**5*c/sqrt(c + d*x) - 2*a**5*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 10*a**4*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 10*a**4*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 20*a**3*b**2*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 20*a**3*b**2*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 20*a**2*b**3*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 20*a**2*b**3*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 10*a*b**4*c*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**4 - 10*a*b**4*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**4 - 2*b**5*c*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**5 - 2*b**5*(c**6/sqrt(c + d*x) + 6*c**5*sqrt(c + d*x) - 5*c**4*(c + d*x)**(3/2) + 4*c**3*(c + d*x)**(5/2) - 15*c**2*(c + d*x)**(7/2)/7 + 2*c*(c + d*x)**(9/2)/3 - (c + d*x)**(11/2)/11)/d**5)/d, Ne(d, 0)), (Piecewise((a**5*x, Eq(b, 0)), ((a + b*x)**6/(6*b), True))/sqrt(c), True))","A",0
1414,1,532,0,56.898395," ","integrate((b*x+a)**4/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{4} c}{\sqrt{c + d x}} - 2 a^{4} \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{8 a^{3} b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{8 a^{3} b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{12 a^{2} b^{2} c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{12 a^{2} b^{2} \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{8 a b^{3} c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{8 a b^{3} \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{2 b^{4} c \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{4}} - \frac{2 b^{4} \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}}}{d} & \text{for}\: d \neq 0 \\\frac{\begin{cases} a^{4} x & \text{for}\: b = 0 \\\frac{\left(a + b x\right)^{5}}{5 b} & \text{otherwise} \end{cases}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**4*c/sqrt(c + d*x) - 2*a**4*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 8*a**3*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 8*a**3*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 12*a**2*b**2*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 12*a**2*b**2*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 8*a*b**3*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 8*a*b**3*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 2*b**4*c*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**4 - 2*b**4*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**4)/d, Ne(d, 0)), (Piecewise((a**4*x, Eq(b, 0)), ((a + b*x)**5/(5*b), True))/sqrt(c), True))","A",0
1415,1,366,0,37.063752," ","integrate((b*x+a)**3/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{3} c}{\sqrt{c + d x}} - 2 a^{3} \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{6 a^{2} b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{6 a^{2} b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{6 a b^{2} c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{6 a b^{2} \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{2 b^{3} c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{2 b^{3} \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}}}{d} & \text{for}\: d \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{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**3*c/sqrt(c + d*x) - 2*a**3*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 6*a**2*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 6*a**2*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 6*a*b**2*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 6*a*b**2*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 2*b**3*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 2*b**3*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3)/d, Ne(d, 0)), (Piecewise((a**3*x, Eq(b, 0)), ((a + b*x)**4/(4*b), True))/sqrt(c), True))","A",0
1416,1,231,0,20.940431," ","integrate((b*x+a)**2/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 a^{2} c}{\sqrt{c + d x}} - 2 a^{2} \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{4 a b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{4 a b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{2 b^{2} c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{2 b^{2} \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}}}{d} & \text{for}\: d \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{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a**2*c/sqrt(c + d*x) - 2*a**2*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 4*a*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 4*a*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 2*b**2*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 2*b**2*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2)/d, Ne(d, 0)), (Piecewise((a**2*x, Eq(b, 0)), ((a + b*x)**3/(3*b), True))/sqrt(c), True))","A",0
1417,1,121,0,4.778368," ","integrate((b*x+a)/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 a c}{\sqrt{c + d x}} - 2 a \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{2 b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{2 b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d}}{d} & \text{for}\: d \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*c/sqrt(c + d*x) - 2*a*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 2*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 2*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d)/d, Ne(d, 0)), ((a*x + b*x**2/2)/sqrt(c), True))","A",0
1418,1,10,0,0.062696," ","integrate(1/(d*x+c)**(1/2),x)","\frac{2 \sqrt{c + d x}}{d}"," ",0,"2*sqrt(c + d*x)/d","A",0
1419,1,44,0,5.408810," ","integrate(1/(b*x+a)/(d*x+c)**(1/2),x)","- \frac{2 \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{b}{a d - b c}} \sqrt{c + d x}} \right)}}{\sqrt{\frac{b}{a d - b c}} \left(a d - b c\right)}"," ",0,"-2*atan(1/(sqrt(b/(a*d - b*c))*sqrt(c + d*x)))/(sqrt(b/(a*d - b*c))*(a*d - b*c))","A",0
1420,0,0,0,0.000000," ","integrate(1/(b*x+a)**2/(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b x\right)^{2} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**2*sqrt(c + d*x)), x)","F",0
1421,-1,0,0,0.000000," ","integrate(1/(b*x+a)**3/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1422,-1,0,0,0.000000," ","integrate(1/(b*x+a)**4/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1423,-1,0,0,0.000000," ","integrate(1/(b*x+a)**5/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1424,1,243,0,47.936776," ","integrate((b*x+a)**5/(d*x+c)**(3/2),x)","\frac{2 b^{5} \left(c + d x\right)^{\frac{9}{2}}}{9 d^{6}} + \frac{\left(c + d x\right)^{\frac{7}{2}} \left(10 a b^{4} d - 10 b^{5} c\right)}{7 d^{6}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(20 a^{2} b^{3} d^{2} - 40 a b^{4} c d + 20 b^{5} c^{2}\right)}{5 d^{6}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(20 a^{3} b^{2} d^{3} - 60 a^{2} b^{3} c d^{2} + 60 a b^{4} c^{2} d - 20 b^{5} c^{3}\right)}{3 d^{6}} + \frac{\sqrt{c + d x} \left(10 a^{4} b d^{4} - 40 a^{3} b^{2} c d^{3} + 60 a^{2} b^{3} c^{2} d^{2} - 40 a b^{4} c^{3} d + 10 b^{5} c^{4}\right)}{d^{6}} - \frac{2 \left(a d - b c\right)^{5}}{d^{6} \sqrt{c + d x}}"," ",0,"2*b**5*(c + d*x)**(9/2)/(9*d**6) + (c + d*x)**(7/2)*(10*a*b**4*d - 10*b**5*c)/(7*d**6) + (c + d*x)**(5/2)*(20*a**2*b**3*d**2 - 40*a*b**4*c*d + 20*b**5*c**2)/(5*d**6) + (c + d*x)**(3/2)*(20*a**3*b**2*d**3 - 60*a**2*b**3*c*d**2 + 60*a*b**4*c**2*d - 20*b**5*c**3)/(3*d**6) + sqrt(c + d*x)*(10*a**4*b*d**4 - 40*a**3*b**2*c*d**3 + 60*a**2*b**3*c**2*d**2 - 40*a*b**4*c**3*d + 10*b**5*c**4)/d**6 - 2*(a*d - b*c)**5/(d**6*sqrt(c + d*x))","A",0
1425,1,168,0,32.865376," ","integrate((b*x+a)**4/(d*x+c)**(3/2),x)","\frac{2 b^{4} \left(c + d x\right)^{\frac{7}{2}}}{7 d^{5}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(8 a b^{3} d - 8 b^{4} c\right)}{5 d^{5}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(12 a^{2} b^{2} d^{2} - 24 a b^{3} c d + 12 b^{4} c^{2}\right)}{3 d^{5}} + \frac{\sqrt{c + d x} \left(8 a^{3} b d^{3} - 24 a^{2} b^{2} c d^{2} + 24 a b^{3} c^{2} d - 8 b^{4} c^{3}\right)}{d^{5}} - \frac{2 \left(a d - b c\right)^{4}}{d^{5} \sqrt{c + d x}}"," ",0,"2*b**4*(c + d*x)**(7/2)/(7*d**5) + (c + d*x)**(5/2)*(8*a*b**3*d - 8*b**4*c)/(5*d**5) + (c + d*x)**(3/2)*(12*a**2*b**2*d**2 - 24*a*b**3*c*d + 12*b**4*c**2)/(3*d**5) + sqrt(c + d*x)*(8*a**3*b*d**3 - 24*a**2*b**2*c*d**2 + 24*a*b**3*c**2*d - 8*b**4*c**3)/d**5 - 2*(a*d - b*c)**4/(d**5*sqrt(c + d*x))","A",0
1426,1,109,0,21.509825," ","integrate((b*x+a)**3/(d*x+c)**(3/2),x)","\frac{2 b^{3} \left(c + d x\right)^{\frac{5}{2}}}{5 d^{4}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(6 a b^{2} d - 6 b^{3} c\right)}{3 d^{4}} + \frac{\sqrt{c + d x} \left(6 a^{2} b d^{2} - 12 a b^{2} c d + 6 b^{3} c^{2}\right)}{d^{4}} - \frac{2 \left(a d - b c\right)^{3}}{d^{4} \sqrt{c + d x}}"," ",0,"2*b**3*(c + d*x)**(5/2)/(5*d**4) + (c + d*x)**(3/2)*(6*a*b**2*d - 6*b**3*c)/(3*d**4) + sqrt(c + d*x)*(6*a**2*b*d**2 - 12*a*b**2*c*d + 6*b**3*c**2)/d**4 - 2*(a*d - b*c)**3/(d**4*sqrt(c + d*x))","A",0
1427,1,65,0,13.292377," ","integrate((b*x+a)**2/(d*x+c)**(3/2),x)","\frac{2 b^{2} \left(c + d x\right)^{\frac{3}{2}}}{3 d^{3}} + \frac{\sqrt{c + d x} \left(4 a b d - 4 b^{2} c\right)}{d^{3}} - \frac{2 \left(a d - b c\right)^{2}}{d^{3} \sqrt{c + d x}}"," ",0,"2*b**2*(c + d*x)**(3/2)/(3*d**3) + sqrt(c + d*x)*(4*a*b*d - 4*b**2*c)/d**3 - 2*(a*d - b*c)**2/(d**3*sqrt(c + d*x))","A",0
1428,1,60,0,0.613669," ","integrate((b*x+a)/(d*x+c)**(3/2),x)","\begin{cases} - \frac{2 a}{d \sqrt{c + d x}} + \frac{4 b c}{d^{2} \sqrt{c + d x}} + \frac{2 b x}{d \sqrt{c + d x}} & \text{for}\: d \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{c^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/(d*sqrt(c + d*x)) + 4*b*c/(d**2*sqrt(c + d*x)) + 2*b*x/(d*sqrt(c + d*x)), Ne(d, 0)), ((a*x + b*x**2/2)/c**(3/2), True))","A",0
1429,1,12,0,0.064327," ","integrate(1/(d*x+c)**(3/2),x)","- \frac{2}{d \sqrt{c + d x}}"," ",0,"-2/(d*sqrt(c + d*x))","A",0
1430,1,60,0,11.486544," ","integrate(1/(b*x+a)/(d*x+c)**(3/2),x)","- \frac{2}{\sqrt{c + d x} \left(a d - b c\right)} - \frac{2 \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{\sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)}"," ",0,"-2/(sqrt(c + d*x)*(a*d - b*c)) - 2*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(sqrt((a*d - b*c)/b)*(a*d - b*c))","A",0
1431,0,0,0,0.000000," ","integrate(1/(b*x+a)**2/(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b x\right)^{2} \left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**2*(c + d*x)**(3/2)), x)","F",0
1432,-1,0,0,0.000000," ","integrate(1/(b*x+a)**3/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1433,-1,0,0,0.000000," ","integrate(1/(b*x+a)**4/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1434,1,196,0,59.926463," ","integrate((b*x+a)**5/(d*x+c)**(5/2),x)","\frac{2 b^{5} \left(c + d x\right)^{\frac{7}{2}}}{7 d^{6}} - \frac{10 b \left(a d - b c\right)^{4}}{d^{6} \sqrt{c + d x}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(10 a b^{4} d - 10 b^{5} c\right)}{5 d^{6}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(20 a^{2} b^{3} d^{2} - 40 a b^{4} c d + 20 b^{5} c^{2}\right)}{3 d^{6}} + \frac{\sqrt{c + d x} \left(20 a^{3} b^{2} d^{3} - 60 a^{2} b^{3} c d^{2} + 60 a b^{4} c^{2} d - 20 b^{5} c^{3}\right)}{d^{6}} - \frac{2 \left(a d - b c\right)^{5}}{3 d^{6} \left(c + d x\right)^{\frac{3}{2}}}"," ",0,"2*b**5*(c + d*x)**(7/2)/(7*d**6) - 10*b*(a*d - b*c)**4/(d**6*sqrt(c + d*x)) + (c + d*x)**(5/2)*(10*a*b**4*d - 10*b**5*c)/(5*d**6) + (c + d*x)**(3/2)*(20*a**2*b**3*d**2 - 40*a*b**4*c*d + 20*b**5*c**2)/(3*d**6) + sqrt(c + d*x)*(20*a**3*b**2*d**3 - 60*a**2*b**3*c*d**2 + 60*a*b**4*c**2*d - 20*b**5*c**3)/d**6 - 2*(a*d - b*c)**5/(3*d**6*(c + d*x)**(3/2))","A",0
1435,1,136,0,43.586351," ","integrate((b*x+a)**4/(d*x+c)**(5/2),x)","\frac{2 b^{4} \left(c + d x\right)^{\frac{5}{2}}}{5 d^{5}} - \frac{8 b \left(a d - b c\right)^{3}}{d^{5} \sqrt{c + d x}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(8 a b^{3} d - 8 b^{4} c\right)}{3 d^{5}} + \frac{\sqrt{c + d x} \left(12 a^{2} b^{2} d^{2} - 24 a b^{3} c d + 12 b^{4} c^{2}\right)}{d^{5}} - \frac{2 \left(a d - b c\right)^{4}}{3 d^{5} \left(c + d x\right)^{\frac{3}{2}}}"," ",0,"2*b**4*(c + d*x)**(5/2)/(5*d**5) - 8*b*(a*d - b*c)**3/(d**5*sqrt(c + d*x)) + (c + d*x)**(3/2)*(8*a*b**3*d - 8*b**4*c)/(3*d**5) + sqrt(c + d*x)*(12*a**2*b**2*d**2 - 24*a*b**3*c*d + 12*b**4*c**2)/d**5 - 2*(a*d - b*c)**4/(3*d**5*(c + d*x)**(3/2))","A",0
1436,1,461,0,1.436377," ","integrate((b*x+a)**3/(d*x+c)**(5/2),x)","\begin{cases} - \frac{2 a^{3} d^{3}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{12 a^{2} b c d^{2}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{18 a^{2} b d^{3} x}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{48 a b^{2} c^{2} d}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{72 a b^{2} c d^{2} x}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{18 a b^{2} d^{3} x^{2}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{32 b^{3} c^{3}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{48 b^{3} c^{2} d x}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{12 b^{3} c d^{2} x^{2}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{2 b^{3} d^{3} x^{3}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} & \text{for}\: d \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}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*d**3/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 12*a**2*b*c*d**2/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 18*a**2*b*d**3*x/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 48*a*b**2*c**2*d/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 72*a*b**2*c*d**2*x/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 18*a*b**2*d**3*x**2/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 32*b**3*c**3/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 48*b**3*c**2*d*x/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 12*b**3*c*d**2*x**2/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 2*b**3*d**3*x**3/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)), Ne(d, 0)), ((a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4)/c**(5/2), True))","A",0
1437,1,265,0,1.265442," ","integrate((b*x+a)**2/(d*x+c)**(5/2),x)","\begin{cases} - \frac{2 a^{2} d^{2}}{3 c d^{3} \sqrt{c + d x} + 3 d^{4} x \sqrt{c + d x}} - \frac{8 a b c d}{3 c d^{3} \sqrt{c + d x} + 3 d^{4} x \sqrt{c + d x}} - \frac{12 a b d^{2} x}{3 c d^{3} \sqrt{c + d x} + 3 d^{4} x \sqrt{c + d x}} + \frac{16 b^{2} c^{2}}{3 c d^{3} \sqrt{c + d x} + 3 d^{4} x \sqrt{c + d x}} + \frac{24 b^{2} c d x}{3 c d^{3} \sqrt{c + d x} + 3 d^{4} x \sqrt{c + d x}} + \frac{6 b^{2} d^{2} x^{2}}{3 c d^{3} \sqrt{c + d x} + 3 d^{4} x \sqrt{c + d x}} & \text{for}\: d \neq 0 \\\frac{a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**2*d**2/(3*c*d**3*sqrt(c + d*x) + 3*d**4*x*sqrt(c + d*x)) - 8*a*b*c*d/(3*c*d**3*sqrt(c + d*x) + 3*d**4*x*sqrt(c + d*x)) - 12*a*b*d**2*x/(3*c*d**3*sqrt(c + d*x) + 3*d**4*x*sqrt(c + d*x)) + 16*b**2*c**2/(3*c*d**3*sqrt(c + d*x) + 3*d**4*x*sqrt(c + d*x)) + 24*b**2*c*d*x/(3*c*d**3*sqrt(c + d*x) + 3*d**4*x*sqrt(c + d*x)) + 6*b**2*d**2*x**2/(3*c*d**3*sqrt(c + d*x) + 3*d**4*x*sqrt(c + d*x)), Ne(d, 0)), ((a**2*x + a*b*x**2 + b**2*x**3/3)/c**(5/2), True))","A",0
1438,1,124,0,1.121663," ","integrate((b*x+a)/(d*x+c)**(5/2),x)","\begin{cases} - \frac{2 a d}{3 c d^{2} \sqrt{c + d x} + 3 d^{3} x \sqrt{c + d x}} - \frac{4 b c}{3 c d^{2} \sqrt{c + d x} + 3 d^{3} x \sqrt{c + d x}} - \frac{6 b d x}{3 c d^{2} \sqrt{c + d x} + 3 d^{3} x \sqrt{c + d x}} & \text{for}\: d \neq 0 \\\frac{a x + \frac{b x^{2}}{2}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*d/(3*c*d**2*sqrt(c + d*x) + 3*d**3*x*sqrt(c + d*x)) - 4*b*c/(3*c*d**2*sqrt(c + d*x) + 3*d**3*x*sqrt(c + d*x)) - 6*b*d*x/(3*c*d**2*sqrt(c + d*x) + 3*d**3*x*sqrt(c + d*x)), Ne(d, 0)), ((a*x + b*x**2/2)/c**(5/2), True))","A",0
1439,1,14,0,0.066461," ","integrate(1/(d*x+c)**(5/2),x)","- \frac{2}{3 d \left(c + d x\right)^{\frac{3}{2}}}"," ",0,"-2/(3*d*(c + d*x)**(3/2))","A",0
1440,1,83,0,13.575479," ","integrate(1/(b*x+a)/(d*x+c)**(5/2),x)","\frac{2 b}{\sqrt{c + d x} \left(a d - b c\right)^{2}} + \frac{2 b \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{\sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)^{2}} - \frac{2}{3 \left(c + d x\right)^{\frac{3}{2}} \left(a d - b c\right)}"," ",0,"2*b/(sqrt(c + d*x)*(a*d - b*c)**2) + 2*b*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(sqrt((a*d - b*c)/b)*(a*d - b*c)**2) - 2/(3*(c + d*x)**(3/2)*(a*d - b*c))","A",0
1441,0,0,0,0.000000," ","integrate(1/(b*x+a)**2/(d*x+c)**(5/2),x)","\int \frac{1}{\left(a + b x\right)^{2} \left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**2*(c + d*x)**(5/2)), x)","F",0
1442,-1,0,0,0.000000," ","integrate(1/(b*x+a)**3/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1443,-1,0,0,0.000000," ","integrate(1/(b*x+a)**4/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1444,1,66,0,1.214557," ","integrate((b*x+a)**5*(b*c*x+a*c)**(3/2),x)","\begin{cases} \frac{2 b^{\frac{13}{2}} c^{\frac{3}{2}} \left(\frac{a}{b} + x\right)^{\frac{15}{2}}}{15} & \text{for}\: \left|{\frac{a}{b} + x}\right| < 1 \\b^{\frac{13}{2}} c^{\frac{3}{2}} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{17}{2} \\\frac{15}{2} & 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)} + b^{\frac{13}{2}} c^{\frac{3}{2}} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{17}{2}, 1 &  \\ & \frac{15}{2}, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(13/2)*c**(3/2)*(a/b + x)**(15/2)/15, Abs(a/b + x) < 1), (b**(13/2)*c**(3/2)*meijerg(((1,), (17/2,)), ((15/2,), (0,)), a/b + x) + b**(13/2)*c**(3/2)*meijerg(((17/2, 1), ()), ((), (15/2, 0)), a/b + x), True))","A",0
1445,1,66,0,1.062748," ","integrate((b*x+a)**5*(b*c*x+a*c)**(1/2),x)","\begin{cases} \frac{2 b^{\frac{11}{2}} \sqrt{c} \left(\frac{a}{b} + x\right)^{\frac{13}{2}}}{13} & \text{for}\: \left|{\frac{a}{b} + x}\right| < 1 \\b^{\frac{11}{2}} \sqrt{c} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{15}{2} \\\frac{13}{2} & 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)} + b^{\frac{11}{2}} \sqrt{c} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{15}{2}, 1 &  \\ & \frac{13}{2}, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(11/2)*sqrt(c)*(a/b + x)**(13/2)/13, Abs(a/b + x) < 1), (b**(11/2)*sqrt(c)*meijerg(((1,), (15/2,)), ((13/2,), (0,)), a/b + x) + b**(11/2)*sqrt(c)*meijerg(((15/2, 1), ()), ((), (13/2, 0)), a/b + x), True))","A",0
1446,1,73,0,1.542390," ","integrate((b*x+a)**5/(b*c*x+a*c)**(1/2),x)","\begin{cases} \frac{2 b^{\frac{9}{2}} \left(\frac{a}{b} + x\right)^{\frac{11}{2}}}{11 \sqrt{c}} & \text{for}\: \left|{\frac{a}{b} + x}\right| > 1 \vee \left|{\frac{a}{b} + x}\right| < 1 \\\frac{b^{\frac{9}{2}} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{13}{2} \\\frac{11}{2} & 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{\sqrt{c}} + \frac{b^{\frac{9}{2}} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{13}{2}, 1 &  \\ & \frac{11}{2}, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(9/2)*(a/b + x)**(11/2)/(11*sqrt(c)), (Abs(a/b + x) > 1) | (Abs(a/b + x) < 1)), (b**(9/2)*meijerg(((1,), (13/2,)), ((11/2,), (0,)), a/b + x)/sqrt(c) + b**(9/2)*meijerg(((13/2, 1), ()), ((), (11/2, 0)), a/b + x)/sqrt(c), True))","A",0
1447,1,73,0,1.645851," ","integrate((b*x+a)**5/(b*c*x+a*c)**(3/2),x)","\begin{cases} \frac{2 b^{\frac{7}{2}} \left(\frac{a}{b} + x\right)^{\frac{9}{2}}}{9 c^{\frac{3}{2}}} & \text{for}\: \left|{\frac{a}{b} + x}\right| > 1 \vee \left|{\frac{a}{b} + x}\right| < 1 \\\frac{b^{\frac{7}{2}} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{11}{2} \\\frac{9}{2} & 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{c^{\frac{3}{2}}} + \frac{b^{\frac{7}{2}} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{11}{2}, 1 &  \\ & \frac{9}{2}, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{c^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(7/2)*(a/b + x)**(9/2)/(9*c**(3/2)), (Abs(a/b + x) > 1) | (Abs(a/b + x) < 1)), (b**(7/2)*meijerg(((1,), (11/2,)), ((9/2,), (0,)), a/b + x)/c**(3/2) + b**(7/2)*meijerg(((11/2, 1), ()), ((), (9/2, 0)), a/b + x)/c**(3/2), True))","A",0
1448,1,73,0,1.615175," ","integrate((b*x+a)**5/(b*c*x+a*c)**(5/2),x)","\begin{cases} \frac{2 b^{\frac{5}{2}} \left(\frac{a}{b} + x\right)^{\frac{7}{2}}}{7 c^{\frac{5}{2}}} & \text{for}\: \left|{\frac{a}{b} + x}\right| > 1 \vee \left|{\frac{a}{b} + x}\right| < 1 \\\frac{b^{\frac{5}{2}} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{9}{2} \\\frac{7}{2} & 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{c^{\frac{5}{2}}} + \frac{b^{\frac{5}{2}} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{9}{2}, 1 &  \\ & \frac{7}{2}, 0 \end{matrix} \middle| {\frac{a}{b} + x} \right)}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b**(5/2)*(a/b + x)**(7/2)/(7*c**(5/2)), (Abs(a/b + x) > 1) | (Abs(a/b + x) < 1)), (b**(5/2)*meijerg(((1,), (9/2,)), ((7/2,), (0,)), a/b + x)/c**(5/2) + b**(5/2)*meijerg(((9/2, 1), ()), ((), (7/2, 0)), a/b + x)/c**(5/2), True))","A",0
1449,1,80,0,4.108082," ","integrate((b*x+a)**5/(b*c*x+a*c)**(7/2),x)","\begin{cases} \frac{2 a^{2} \sqrt{a c + b c x}}{5 b c^{4}} + \frac{4 a x \sqrt{a c + b c x}}{5 c^{4}} + \frac{2 b x^{2} \sqrt{a c + b c x}}{5 c^{4}} & \text{for}\: b \neq 0 \\\frac{a^{5} x}{\left(a c\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*sqrt(a*c + b*c*x)/(5*b*c**4) + 4*a*x*sqrt(a*c + b*c*x)/(5*c**4) + 2*b*x**2*sqrt(a*c + b*c*x)/(5*c**4), Ne(b, 0)), (a**5*x/(a*c)**(7/2), True))","A",0
1450,1,53,0,8.308001," ","integrate((b*x+a)**5/(b*c*x+a*c)**(9/2),x)","\begin{cases} \frac{2 a \sqrt{a c + b c x}}{3 b c^{5}} + \frac{2 x \sqrt{a c + b c x}}{3 c^{5}} & \text{for}\: b \neq 0 \\\frac{a^{5} x}{\left(a c\right)^{\frac{9}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sqrt(a*c + b*c*x)/(3*b*c**5) + 2*x*sqrt(a*c + b*c*x)/(3*c**5), Ne(b, 0)), (a**5*x/(a*c)**(9/2), True))","A",0
1451,1,29,0,15.475663," ","integrate((b*x+a)**5/(b*c*x+a*c)**(11/2),x)","\begin{cases} \frac{2 \sqrt{a c + b c x}}{b c^{6}} & \text{for}\: b \neq 0 \\\frac{a^{5} x}{\left(a c\right)^{\frac{11}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(a*c + b*c*x)/(b*c**6), Ne(b, 0)), (a**5*x/(a*c)**(11/2), True))","A",0
1452,1,48,0,39.428953," ","integrate((b*x+a)**5/(b*c*x+a*c)**(13/2),x)","\begin{cases} - \frac{2 \sqrt{a c + b c x}}{a b c^{7} + b^{2} c^{7} x} & \text{for}\: a \neq 0 \\- \frac{2}{b^{\frac{3}{2}} c^{\frac{13}{2}} \sqrt{x}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(a*c + b*c*x)/(a*b*c**7 + b**2*c**7*x), Ne(a, 0)), (-2/(b**(3/2)*c**(13/2)*sqrt(x)), True))","A",0
1453,1,27,0,0.658609," ","integrate(1/(-2+x)/(2+x)**(1/2),x)","\begin{cases} - \operatorname{acoth}{\left(\frac{\sqrt{x + 2}}{2} \right)} & \text{for}\: \frac{\left|{x + 2}\right|}{4} > 1 \\- \operatorname{atanh}{\left(\frac{\sqrt{x + 2}}{2} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-acoth(sqrt(x + 2)/2), Abs(x + 2)/4 > 1), (-atanh(sqrt(x + 2)/2), True))","A",0
1454,1,61,0,1.123502," ","integrate(1/(2+3*x)/(1+5*x)**(1/2),x)","\begin{cases} \frac{2 \sqrt{21} i \operatorname{acosh}{\left(\frac{\sqrt{105}}{15 \sqrt{x + \frac{2}{3}}} \right)}}{21} & \text{for}\: \frac{7}{15 \left|{x + \frac{2}{3}}\right|} > 1 \\- \frac{2 \sqrt{21} \operatorname{asin}{\left(\frac{\sqrt{105}}{15 \sqrt{x + \frac{2}{3}}} \right)}}{21} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(21)*I*acosh(sqrt(105)/(15*sqrt(x + 2/3)))/21, 7/(15*Abs(x + 2/3)) > 1), (-2*sqrt(21)*asin(sqrt(105)/(15*sqrt(x + 2/3)))/21, True))","A",0
1455,1,170,0,2.256907," ","integrate((1-x)**(1/3)/(1+x),x)","\frac{4 \sqrt[3]{-1} \sqrt[3]{x - 1} \Gamma\left(\frac{4}{3}\right)}{\Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{-2} e^{- \frac{i \pi}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt[3]{x - 1} e^{\frac{i \pi}{3}}}{2} + 1 \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} - \frac{4 \sqrt[3]{-2} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt[3]{x - 1} e^{i \pi}}{2} + 1 \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)} + \frac{4 \sqrt[3]{-2} e^{\frac{i \pi}{3}} \log{\left(- \frac{2^{\frac{2}{3}} \sqrt[3]{x - 1} e^{\frac{5 i \pi}{3}}}{2} + 1 \right)} \Gamma\left(\frac{4}{3}\right)}{3 \Gamma\left(\frac{7}{3}\right)}"," ",0,"4*(-1)**(1/3)*(x - 1)**(1/3)*gamma(4/3)/gamma(7/3) + 4*(-2)**(1/3)*exp(-I*pi/3)*log(-2**(2/3)*(x - 1)**(1/3)*exp_polar(I*pi/3)/2 + 1)*gamma(4/3)/(3*gamma(7/3)) - 4*(-2)**(1/3)*log(-2**(2/3)*(x - 1)**(1/3)*exp_polar(I*pi)/2 + 1)*gamma(4/3)/(3*gamma(7/3)) + 4*(-2)**(1/3)*exp(I*pi/3)*log(-2**(2/3)*(x - 1)**(1/3)*exp_polar(5*I*pi/3)/2 + 1)*gamma(4/3)/(3*gamma(7/3))","C",0
1456,1,114,0,1.092601," ","integrate((3-2*x)**(1/3)*(7+x),x)","\begin{cases} \frac{3 \left(x + 7\right)^{2} \sqrt[3]{2 x - 3} e^{\frac{i \pi}{3}}}{7} - \frac{51 \left(x + 7\right) \sqrt[3]{2 x - 3} e^{\frac{i \pi}{3}}}{56} - \frac{2601 \sqrt[3]{2 x - 3} e^{\frac{i \pi}{3}}}{112} & \text{for}\: \frac{2 \left|{x + 7}\right|}{17} > 1 \\\frac{3 \sqrt[3]{3 - 2 x} \left(x + 7\right)^{2}}{7} - \frac{51 \sqrt[3]{3 - 2 x} \left(x + 7\right)}{56} - \frac{2601 \sqrt[3]{3 - 2 x}}{112} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*(x + 7)**2*(2*x - 3)**(1/3)*exp(I*pi/3)/7 - 51*(x + 7)*(2*x - 3)**(1/3)*exp(I*pi/3)/56 - 2601*(2*x - 3)**(1/3)*exp(I*pi/3)/112, 2*Abs(x + 7)/17 > 1), (3*(3 - 2*x)**(1/3)*(x + 7)**2/7 - 51*(3 - 2*x)**(1/3)*(x + 7)/56 - 2601*(3 - 2*x)**(1/3)/112, True))","A",0
1457,1,146,0,1.518306," ","integrate((1-x)**(1/3)*(1+x)**2,x)","\begin{cases} - \frac{3 \sqrt[3]{x - 1} \left(x + 1\right)^{3} e^{- \frac{2 i \pi}{3}}}{10} + \frac{3 \sqrt[3]{x - 1} \left(x + 1\right)^{2} e^{- \frac{2 i \pi}{3}}}{35} + \frac{9 \sqrt[3]{x - 1} \left(x + 1\right) e^{- \frac{2 i \pi}{3}}}{35} + \frac{54 \sqrt[3]{x - 1} e^{- \frac{2 i \pi}{3}}}{35} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\\frac{3 \sqrt[3]{1 - x} \left(x + 1\right)^{3}}{10} - \frac{3 \sqrt[3]{1 - x} \left(x + 1\right)^{2}}{35} - \frac{9 \sqrt[3]{1 - x} \left(x + 1\right)}{35} - \frac{54 \sqrt[3]{1 - x}}{35} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*(x - 1)**(1/3)*(x + 1)**3*exp(-2*I*pi/3)/10 + 3*(x - 1)**(1/3)*(x + 1)**2*exp(-2*I*pi/3)/35 + 9*(x - 1)**(1/3)*(x + 1)*exp(-2*I*pi/3)/35 + 54*(x - 1)**(1/3)*exp(-2*I*pi/3)/35, Abs(x + 1)/2 > 1), (3*(1 - x)**(1/3)*(x + 1)**3/10 - 3*(1 - x)**(1/3)*(x + 1)**2/35 - 9*(1 - x)**(1/3)*(x + 1)/35 - 54*(1 - x)**(1/3)/35, True))","A",0
1458,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right) \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)*(c + d*x)**(1/3)), x)","F",0
1459,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right) \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)*(c + d*x)**(2/3)), x)","F",0
1460,-1,0,0,0.000000," ","integrate((b*x+a)**(7/2)*(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1461,-1,0,0,0.000000," ","integrate((b*x+a)**(5/2)*(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1462,-1,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1463,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(1/2),x)","\int \sqrt{a + b x} \sqrt{c + d x}\, dx"," ",0,"Integral(sqrt(a + b*x)*sqrt(c + d*x), x)","F",0
1464,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(1/2),x)","\int \frac{\sqrt{c + d x}}{\sqrt{a + b x}}\, dx"," ",0,"Integral(sqrt(c + d*x)/sqrt(a + b*x), x)","F",0
1465,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(3/2),x)","\int \frac{\sqrt{c + d x}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x)/(a + b*x)**(3/2), x)","F",0
1466,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(5/2),x)","\int \frac{\sqrt{c + d x}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x)/(a + b*x)**(5/2), x)","F",0
1467,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1468,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1469,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1470,-1,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(b*x+a)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1471,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)*(d*x+c)**(3/2),x)","\int \left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)**(5/2)*(c + d*x)**(3/2), x)","F",0
1472,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(3/2),x)","\int \left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(3/2), x)","F",0
1473,-1,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1474,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(1/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{2}}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(3/2)/sqrt(a + b*x), x)","F",0
1475,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(3/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{2}}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(3/2)/(a + b*x)**(3/2), x)","F",0
1476,0,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(5/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{2}}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(3/2)/(a + b*x)**(5/2), x)","F",0
1477,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1478,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1479,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1480,-1,0,0,0.000000," ","integrate((d*x+c)**(3/2)/(b*x+a)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1481,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)*(d*x+c)**(5/2),x)","\int \left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)**(5/2)*(c + d*x)**(5/2), x)","F",0
1482,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(5/2),x)","\int \left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(5/2), x)","F",0
1483,-1,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1484,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1485,0,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(3/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{2}}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/2)/(a + b*x)**(3/2), x)","F",0
1486,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1487,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1488,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1489,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1490,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1491,-1,0,0,0.000000," ","integrate((d*x+c)**(5/2)/(b*x+a)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1492,-1,0,0,0.000000," ","integrate((b*x+a)**(7/2)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1493,-1,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1494,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(1/2),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\sqrt{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/sqrt(c + d*x), x)","F",0
1495,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b x}}{\sqrt{c + d x}}\, dx"," ",0,"Integral(sqrt(a + b*x)/sqrt(c + d*x), x)","F",0
1496,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{a + b x} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*sqrt(c + d*x)), x)","F",0
1497,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*sqrt(c + d*x)), x)","F",0
1498,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*sqrt(c + d*x)), x)","F",0
1499,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{2}} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/2)*sqrt(c + d*x)), x)","F",0
1500,0,0,0,0.000000," ","integrate(1/(b*x+a)**(9/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{9}{2}} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(9/2)*sqrt(c + d*x)), x)","F",0
1501,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(11/2)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1502,0,0,0,0.000000," ","integrate((b*x+a)**(7/2)/(d*x+c)**(3/2),x)","\int \frac{\left(a + b x\right)^{\frac{7}{2}}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)**(7/2)/(c + d*x)**(3/2), x)","F",0
1503,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(3/2),x)","\int \frac{\left(a + b x\right)^{\frac{5}{2}}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)**(5/2)/(c + d*x)**(3/2), x)","F",0
1504,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(3/2),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(3/2), x)","F",0
1505,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(3/2), x)","F",0
1506,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(3/2),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(3/2)), x)","F",0
1507,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(3/2)), x)","F",0
1508,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(3/2)), x)","F",0
1509,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/2)/(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{2}} \left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/2)*(c + d*x)**(3/2)), x)","F",0
1510,0,0,0,0.000000," ","integrate(1/(b*x+a)**(9/2)/(d*x+c)**(3/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{9}{2}} \left(c + d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(9/2)*(c + d*x)**(3/2)), x)","F",0
1511,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(11/2)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1512,-1,0,0,0.000000," ","integrate((b*x+a)**(9/2)/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1513,-1,0,0,0.000000," ","integrate((b*x+a)**(7/2)/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1514,-1,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1515,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(5/2),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(5/2), x)","F",0
1516,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(5/2),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(5/2), x)","F",0
1517,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(5/2),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(5/2)), x)","F",0
1518,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(5/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(5/2)), x)","F",0
1519,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(5/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(5/2)), x)","F",0
1520,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/2)/(d*x+c)**(5/2),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{2}} \left(c + d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/2)*(c + d*x)**(5/2)), x)","F",0
1521,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(9/2)/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1522,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(b*x+a+4)**(1/2),x)","\int \frac{1}{\sqrt{a + b x} \sqrt{a + b x + 4}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*sqrt(a + b*x + 4)), x)","F",0
1523,0,0,0,0.000000," ","integrate(1/(b*x+2)**(1/2)/(b*x+6)**(1/2),x)","\int \frac{1}{\sqrt{b x + 2} \sqrt{b x + 6}}\, dx"," ",0,"Integral(1/(sqrt(b*x + 2)*sqrt(b*x + 6)), x)","F",0
1524,0,0,0,0.000000," ","integrate(1/(b*x+1)**(1/2)/(b*x+5)**(1/2),x)","\int \frac{1}{\sqrt{b x + 1} \sqrt{b x + 5}}\, dx"," ",0,"Integral(1/(sqrt(b*x + 1)*sqrt(b*x + 5)), x)","F",0
1525,1,15,0,1.265490," ","integrate(1/(b*x)**(1/2)/(b*x+4)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{b} \sqrt{x}}{2} \right)}}{b}"," ",0,"2*asinh(sqrt(b)*sqrt(x)/2)/b","A",0
1526,0,0,0,0.000000," ","integrate(1/(b*x-1)**(1/2)/(b*x+3)**(1/2),x)","\int \frac{1}{\sqrt{b x - 1} \sqrt{b x + 3}}\, dx"," ",0,"Integral(1/(sqrt(b*x - 1)*sqrt(b*x + 3)), x)","F",0
1527,1,75,0,4.198720," ","integrate(1/(b*x-2)**(1/2)/(b*x+2)**(1/2),x)","\frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{4 e^{2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{4}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b}"," ",0,"meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 4*exp_polar(2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b) + I*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), 4/(b**2*x**2))/(4*pi**(3/2)*b)","C",0
1528,0,0,0,0.000000," ","integrate(1/(b*x-3)**(1/2)/(b*x+1)**(1/2),x)","\int \frac{1}{\sqrt{b x - 3} \sqrt{b x + 1}}\, dx"," ",0,"Integral(1/(sqrt(b*x - 3)*sqrt(b*x + 1)), x)","F",0
1529,0,0,0,0.000000," ","integrate(1/(b*x+2)**(1/2)/(b*x+3)**(1/2),x)","\int \frac{1}{\sqrt{b x + 2} \sqrt{b x + 3}}\, dx"," ",0,"Integral(1/(sqrt(b*x + 2)*sqrt(b*x + 3)), x)","F",0
1530,1,7,0,0.062322," ","integrate(1/(b*x+2),x)","\frac{\log{\left(b x + 2 \right)}}{b}"," ",0,"log(b*x + 2)/b","A",0
1531,0,0,0,0.000000," ","integrate(1/(b*x+1)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{b x + 1} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(b*x + 1)*sqrt(b*x + 2)), x)","F",0
1532,1,20,0,1.349135," ","integrate(1/(b*x)**(1/2)/(b*x+2)**(1/2),x)","\frac{2 \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b}"," ",0,"2*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b","A",0
1533,0,0,0,0.000000," ","integrate(1/(b*x-1)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{b x - 1} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(b*x - 1)*sqrt(b*x + 2)), x)","F",0
1534,1,75,0,4.281751," ","integrate(1/(b*x-2)**(1/2)/(b*x+2)**(1/2),x)","\frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{4 e^{2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{4}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b}"," ",0,"meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 4*exp_polar(2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b) + I*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), 4/(b**2*x**2))/(4*pi**(3/2)*b)","C",0
1535,0,0,0,0.000000," ","integrate(1/(b*x-3)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{b x - 3} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(b*x - 3)*sqrt(b*x + 2)), x)","F",0
1536,0,0,0,0.000000," ","integrate(1/(-b*x+3)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x + 3} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x + 3)*sqrt(b*x + 2)), x)","F",0
1537,1,76,0,4.439957," ","integrate(1/(-b*x+2)**(1/2)/(b*x+2)**(1/2),x)","- \frac{i {G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{4}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b} + \frac{{G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{4 e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b}"," ",0,"-I*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 4/(b**2*x**2))/(4*pi**(3/2)*b) + meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), 4*exp_polar(-2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b)","C",0
1538,0,0,0,0.000000," ","integrate(1/(-b*x+1)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x + 1} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x + 1)*sqrt(b*x + 2)), x)","F",0
1539,1,24,0,1.276785," ","integrate(1/(-b*x)**(1/2)/(b*x+2)**(1/2),x)","- \frac{2 i \operatorname{asinh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b}"," ",0,"-2*I*asinh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b","C",0
1540,0,0,0,0.000000," ","integrate(1/(-b*x-1)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x - 1} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x - 1)*sqrt(b*x + 2)), x)","F",0
1541,1,53,0,1.979949," ","integrate(1/(-b*x-2)**(1/2)/(b*x+2)**(1/2),x)","\begin{cases} - \frac{i \log{\left(x + \frac{2}{b} \right)}}{b} & \text{for}\: \left|{x + \frac{2}{b}}\right| < 1 \\\frac{i \log{\left(\frac{1}{x + \frac{2}{b}} \right)}}{b} & \text{for}\: \frac{1}{\left|{x + \frac{2}{b}}\right|} < 1 \\\frac{i {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x + \frac{2}{b}} \right)}}{b} - \frac{i {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x + \frac{2}{b}} \right)}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*log(x + 2/b)/b, Abs(x + 2/b) < 1), (I*log(1/(x + 2/b))/b, 1/Abs(x + 2/b) < 1), (I*meijerg(((), (1, 1)), ((0, 0), ()), x + 2/b)/b - I*meijerg(((1, 1), ()), ((), (0, 0)), x + 2/b)/b, True))","C",0
1542,0,0,0,0.000000," ","integrate(1/(-b*x-3)**(1/2)/(b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x - 3} \sqrt{b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x - 3)*sqrt(b*x + 2)), x)","F",0
1543,0,0,0,0.000000," ","integrate(1/(-b*x+2)**(1/2)/(-b*x+3)**(1/2),x)","\int \frac{1}{\sqrt{- b x + 2} \sqrt{- b x + 3}}\, dx"," ",0,"Integral(1/(sqrt(-b*x + 2)*sqrt(-b*x + 3)), x)","F",0
1544,1,8,0,0.065809," ","integrate(1/(-b*x+2),x)","- \frac{\log{\left(b x - 2 \right)}}{b}"," ",0,"-log(b*x - 2)/b","A",0
1545,0,0,0,0.000000," ","integrate(1/(-b*x+1)**(1/2)/(-b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x + 1} \sqrt{- b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x + 1)*sqrt(-b*x + 2)), x)","F",0
1546,1,53,0,1.337490," ","integrate(1/(-b*x)**(1/2)/(-b*x+2)**(1/2),x)","\begin{cases} - \frac{2 \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b} & \text{for}\: \frac{\left|{b x}\right|}{2} > 1 \\- \frac{2 i \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{b} \sqrt{x}}{2} \right)}}{b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*acosh(sqrt(2)*sqrt(b)*sqrt(x)/2)/b, Abs(b*x)/2 > 1), (-2*I*asin(sqrt(2)*sqrt(b)*sqrt(x)/2)/b, True))","A",0
1547,0,0,0,0.000000," ","integrate(1/(-b*x-1)**(1/2)/(-b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x - 1} \sqrt{- b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x - 1)*sqrt(-b*x + 2)), x)","F",0
1548,1,78,0,4.625127," ","integrate(1/(-b*x-2)**(1/2)/(-b*x+2)**(1/2),x)","- \frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{4}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b} - \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{4 e^{- 2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b}"," ",0,"-meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 4/(b**2*x**2))/(4*pi**(3/2)*b) - I*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), 4*exp_polar(-2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b)","C",0
1549,0,0,0,0.000000," ","integrate(1/(-b*x-3)**(1/2)/(-b*x+2)**(1/2),x)","\int \frac{1}{\sqrt{- b x - 3} \sqrt{- b x + 2}}\, dx"," ",0,"Integral(1/(sqrt(-b*x - 3)*sqrt(-b*x + 2)), x)","F",0
1550,1,75,0,4.208878," ","integrate(1/(b*x-4)**(1/2)/(b*x+4)**(1/2),x)","\frac{{G_{6, 6}^{6, 2}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} & \frac{1}{2}, \frac{1}{2}, 1, 1 \\0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 0 &  \end{matrix} \middle| {\frac{16 e^{2 i \pi}}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b} + \frac{i {G_{6, 6}^{2, 6}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, 1 &  \\- \frac{1}{4}, \frac{1}{4} & - \frac{1}{2}, 0, 0, 0 \end{matrix} \middle| {\frac{16}{b^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} b}"," ",0,"meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 16*exp_polar(2*I*pi)/(b**2*x**2))/(4*pi**(3/2)*b) + I*meijerg(((-1/2, -1/4, 0, 1/4, 1/2, 1), ()), ((-1/4, 1/4), (-1/2, 0, 0, 0)), 16/(b**2*x**2))/(4*pi**(3/2)*b)","C",0
1551,0,0,0,0.000000," ","integrate(1/((b*c-b)/d+b*x)**(1/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{b \left(\frac{c}{d} + x - \frac{1}{d}\right)} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(b*(c/d + x - 1/d))*sqrt(c + d*x)), x)","F",0
1552,1,44,0,1.028589," ","integrate(1/x**(1/2)/(-3+2*x)**(1/2),x)","\begin{cases} \sqrt{2} \operatorname{acosh}{\left(\frac{\sqrt{6} \sqrt{x}}{3} \right)} & \text{for}\: \frac{2 \left|{x}\right|}{3} > 1 \\- \sqrt{2} i \operatorname{asin}{\left(\frac{\sqrt{6} \sqrt{x}}{3} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(2)*acosh(sqrt(6)*sqrt(x)/3), 2*Abs(x)/3 > 1), (-sqrt(2)*I*asin(sqrt(6)*sqrt(x)/3), True))","A",0
1553,1,58,0,1.091771," ","integrate(1/(-3+2*x)**(1/2)/(2+3*x)**(1/2),x)","\begin{cases} \frac{\sqrt{6} \operatorname{acosh}{\left(\frac{\sqrt{78} \sqrt{x + \frac{2}{3}}}{13} \right)}}{3} & \text{for}\: \frac{6 \left|{x + \frac{2}{3}}\right|}{13} > 1 \\- \frac{\sqrt{6} i \operatorname{asin}{\left(\frac{\sqrt{78} \sqrt{x + \frac{2}{3}}}{13} \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(6)*acosh(sqrt(78)*sqrt(x + 2/3)/13)/3, 6*Abs(x + 2/3)/13 > 1), (-sqrt(6)*I*asin(sqrt(78)*sqrt(x + 2/3)/13)/3, True))","A",0
1554,0,0,0,0.000000," ","integrate(1/((-b*c+b)/d+b*x)**(1/2)/(-d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{b \left(- \frac{c}{d} + x + \frac{1}{d}\right)} \sqrt{c - d x}}\, dx"," ",0,"Integral(1/(sqrt(b*(-c/d + x + 1/d))*sqrt(c - d*x)), x)","F",0
1555,1,26,0,0.992348," ","integrate(1/(4-x)**(1/2)/x**(1/2),x)","\begin{cases} - 2 i \operatorname{acosh}{\left(\frac{\sqrt{x}}{2} \right)} & \text{for}\: \frac{\left|{x}\right|}{4} > 1 \\2 \operatorname{asin}{\left(\frac{\sqrt{x}}{2} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*acosh(sqrt(x)/2), Abs(x)/4 > 1), (2*asin(sqrt(x)/2), True))","A",0
1556,1,44,0,1.003269," ","integrate(1/(3-2*x)**(1/2)/x**(1/2),x)","\begin{cases} - \sqrt{2} i \operatorname{acosh}{\left(\frac{\sqrt{6} \sqrt{x}}{3} \right)} & \text{for}\: \frac{2 \left|{x}\right|}{3} > 1 \\\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{6} \sqrt{x}}{3} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(2)*I*acosh(sqrt(6)*sqrt(x)/3), 2*Abs(x)/3 > 1), (sqrt(2)*asin(sqrt(6)*sqrt(x)/3), True))","A",0
1557,1,58,0,1.068931," ","integrate(1/(3-2*x)**(1/2)/(3+5*x)**(1/2),x)","\begin{cases} - \frac{\sqrt{10} i \operatorname{acosh}{\left(\frac{\sqrt{210} \sqrt{x + \frac{3}{5}}}{21} \right)}}{5} & \text{for}\: \frac{10 \left|{x + \frac{3}{5}}\right|}{21} > 1 \\\frac{\sqrt{10} \operatorname{asin}{\left(\frac{\sqrt{210} \sqrt{x + \frac{3}{5}}}{21} \right)}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sqrt(10)*I*acosh(sqrt(210)*sqrt(x + 3/5)/21)/5, 10*Abs(x + 3/5)/21 > 1), (sqrt(10)*asin(sqrt(210)*sqrt(x + 3/5)/21)/5, True))","A",0
1558,0,0,0,0.000000," ","integrate(1/(-b*x+a)**(1/2)/(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{a - b x} \sqrt{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(a - b*x)*sqrt(c + d*x)), x)","F",0
1559,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(1/3),x)","\int \left(a + b x\right)^{\frac{3}{2}} \sqrt[3]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(1/3), x)","F",0
1560,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(1/3),x)","\int \sqrt{a + b x} \sqrt[3]{c + d x}\, dx"," ",0,"Integral(sqrt(a + b*x)*(c + d*x)**(1/3), x)","F",0
1561,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(1/2),x)","\int \frac{\sqrt[3]{c + d x}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/sqrt(a + b*x), x)","F",0
1562,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(3/2),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(3/2), x)","F",0
1563,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(5/2),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(5/2), x)","F",0
1564,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(7/2),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(7/2), x)","F",0
1565,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(1/3),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(1/3), x)","F",0
1566,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(1/3),x)","\int \frac{\sqrt{a + b x}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(1/3), x)","F",0
1567,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(1/3),x)","\int \frac{1}{\sqrt{a + b x} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(1/3)), x)","F",0
1568,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(1/3)), x)","F",0
1569,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(1/3)), x)","F",0
1570,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(2/3),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(2/3), x)","F",0
1571,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(2/3),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(2/3), x)","F",0
1572,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(2/3),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(2/3)), x)","F",0
1573,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(2/3)), x)","F",0
1574,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(2/3)), x)","F",0
1575,0,0,0,0.000000," ","integrate((b*x+a)**(2/3)*(d*x+c)**(1/3),x)","\int \left(a + b x\right)^{\frac{2}{3}} \sqrt[3]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(2/3)*(c + d*x)**(1/3), x)","F",0
1576,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(1/3),x)","\int \frac{\sqrt[3]{c + d x}}{\sqrt[3]{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(1/3), x)","F",0
1577,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(4/3),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(4/3), x)","F",0
1578,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(7/3),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(7/3), x)","F",0
1579,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(10/3),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{10}{3}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(10/3), x)","F",0
1580,-1,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(13/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1581,-1,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(16/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1582,0,0,0,0.000000," ","integrate((b*x+a)**(4/3)*(d*x+c)**(1/3),x)","\int \left(a + b x\right)^{\frac{4}{3}} \sqrt[3]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(4/3)*(c + d*x)**(1/3), x)","F",0
1583,0,0,0,0.000000," ","integrate((b*x+a)**(1/3)*(d*x+c)**(1/3),x)","\int \sqrt[3]{a + b x} \sqrt[3]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(1/3)*(c + d*x)**(1/3), x)","F",0
1584,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(2/3),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(2/3), x)","F",0
1585,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(5/3),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(5/3), x)","F",0
1586,0,0,0,0.000000," ","integrate((d*x+c)**(1/3)/(b*x+a)**(8/3),x)","\int \frac{\sqrt[3]{c + d x}}{\left(a + b x\right)^{\frac{8}{3}}}\, dx"," ",0,"Integral((c + d*x)**(1/3)/(a + b*x)**(8/3), x)","F",0
1587,0,0,0,0.000000," ","integrate((b*x+a)**(4/3)/(d*x+c)**(1/3),x)","\int \frac{\left(a + b x\right)^{\frac{4}{3}}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(4/3)/(c + d*x)**(1/3), x)","F",0
1588,0,0,0,0.000000," ","integrate((b*x+a)**(1/3)/(d*x+c)**(1/3),x)","\int \frac{\sqrt[3]{a + b x}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(1/3)/(c + d*x)**(1/3), x)","F",0
1589,0,0,0,0.000000," ","integrate(1/(b*x+a)**(2/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{2}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(2/3)*(c + d*x)**(1/3)), x)","F",0
1590,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/3)*(c + d*x)**(1/3)), x)","F",0
1591,0,0,0,0.000000," ","integrate(1/(b*x+a)**(8/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{8}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(8/3)*(c + d*x)**(1/3)), x)","F",0
1592,0,0,0,0.000000," ","integrate(1/(b*x+a)**(11/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{11}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(11/3)*(c + d*x)**(1/3)), x)","F",0
1593,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(14/3)/(d*x+c)**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1594,0,0,0,0.000000," ","integrate((b*x+a)**(8/3)/(d*x+c)**(1/3),x)","\int \frac{\left(a + b x\right)^{\frac{8}{3}}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(8/3)/(c + d*x)**(1/3), x)","F",0
1595,0,0,0,0.000000," ","integrate((b*x+a)**(5/3)/(d*x+c)**(1/3),x)","\int \frac{\left(a + b x\right)^{\frac{5}{3}}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(5/3)/(c + d*x)**(1/3), x)","F",0
1596,0,0,0,0.000000," ","integrate((b*x+a)**(2/3)/(d*x+c)**(1/3),x)","\int \frac{\left(a + b x\right)^{\frac{2}{3}}}{\sqrt[3]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(2/3)/(c + d*x)**(1/3), x)","F",0
1597,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b x} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/3)*(c + d*x)**(1/3)), x)","F",0
1598,0,0,0,0.000000," ","integrate(1/(b*x+a)**(4/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{4}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(4/3)*(c + d*x)**(1/3)), x)","F",0
1599,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/3)*(c + d*x)**(1/3)), x)","F",0
1600,0,0,0,0.000000," ","integrate(1/(b*x+a)**(10/3)/(d*x+c)**(1/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{10}{3}} \sqrt[3]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(10/3)*(c + d*x)**(1/3)), x)","F",0
1601,0,0,0,0.000000," ","integrate((b*x+a)**(5/3)/(d*x+c)**(2/3),x)","\int \frac{\left(a + b x\right)^{\frac{5}{3}}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x)**(5/3)/(c + d*x)**(2/3), x)","F",0
1602,0,0,0,0.000000," ","integrate((b*x+a)**(2/3)/(d*x+c)**(2/3),x)","\int \frac{\left(a + b x\right)^{\frac{2}{3}}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x)**(2/3)/(c + d*x)**(2/3), x)","F",0
1603,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\sqrt[3]{a + b x} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/3)*(c + d*x)**(2/3)), x)","F",0
1604,0,0,0,0.000000," ","integrate(1/(b*x+a)**(4/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{4}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(4/3)*(c + d*x)**(2/3)), x)","F",0
1605,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/3)*(c + d*x)**(2/3)), x)","F",0
1606,0,0,0,0.000000," ","integrate(1/(b*x+a)**(10/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{10}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(10/3)*(c + d*x)**(2/3)), x)","F",0
1607,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(13/3)/(d*x+c)**(2/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1608,0,0,0,0.000000," ","integrate((b*x+a)**(7/3)/(d*x+c)**(2/3),x)","\int \frac{\left(a + b x\right)^{\frac{7}{3}}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x)**(7/3)/(c + d*x)**(2/3), x)","F",0
1609,0,0,0,0.000000," ","integrate((b*x+a)**(4/3)/(d*x+c)**(2/3),x)","\int \frac{\left(a + b x\right)^{\frac{4}{3}}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x)**(4/3)/(c + d*x)**(2/3), x)","F",0
1610,0,0,0,0.000000," ","integrate((b*x+a)**(1/3)/(d*x+c)**(2/3),x)","\int \frac{\sqrt[3]{a + b x}}{\left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*x)**(1/3)/(c + d*x)**(2/3), x)","F",0
1611,0,0,0,0.000000," ","integrate(1/(b*x+a)**(2/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{2}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(2/3)*(c + d*x)**(2/3)), x)","F",0
1612,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/3)*(c + d*x)**(2/3)), x)","F",0
1613,0,0,0,0.000000," ","integrate(1/(b*x+a)**(8/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{8}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(8/3)*(c + d*x)**(2/3)), x)","F",0
1614,0,0,0,0.000000," ","integrate(1/(b*x+a)**(11/3)/(d*x+c)**(2/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{11}{3}} \left(c + d x\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(11/3)*(c + d*x)**(2/3)), x)","F",0
1615,0,0,0,0.000000," ","integrate((b*x+a)**(7/3)/(d*x+c)**(4/3),x)","\int \frac{\left(a + b x\right)^{\frac{7}{3}}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x)**(7/3)/(c + d*x)**(4/3), x)","F",0
1616,0,0,0,0.000000," ","integrate((b*x+a)**(4/3)/(d*x+c)**(4/3),x)","\int \frac{\left(a + b x\right)^{\frac{4}{3}}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x)**(4/3)/(c + d*x)**(4/3), x)","F",0
1617,0,0,0,0.000000," ","integrate((b*x+a)**(1/3)/(d*x+c)**(4/3),x)","\int \frac{\sqrt[3]{a + b x}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x)**(1/3)/(c + d*x)**(4/3), x)","F",0
1618,0,0,0,0.000000," ","integrate(1/(b*x+a)**(2/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{2}{3}} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(2/3)*(c + d*x)**(4/3)), x)","F",0
1619,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{3}} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/3)*(c + d*x)**(4/3)), x)","F",0
1620,0,0,0,0.000000," ","integrate(1/(b*x+a)**(8/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{8}{3}} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(8/3)*(c + d*x)**(4/3)), x)","F",0
1621,0,0,0,0.000000," ","integrate(1/(b*x+a)**(11/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{11}{3}} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(11/3)*(c + d*x)**(4/3)), x)","F",0
1622,0,0,0,0.000000," ","integrate((b*x+a)**(8/3)/(d*x+c)**(4/3),x)","\int \frac{\left(a + b x\right)^{\frac{8}{3}}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x)**(8/3)/(c + d*x)**(4/3), x)","F",0
1623,0,0,0,0.000000," ","integrate((b*x+a)**(5/3)/(d*x+c)**(4/3),x)","\int \frac{\left(a + b x\right)^{\frac{5}{3}}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x)**(5/3)/(c + d*x)**(4/3), x)","F",0
1624,0,0,0,0.000000," ","integrate((b*x+a)**(2/3)/(d*x+c)**(4/3),x)","\int \frac{\left(a + b x\right)^{\frac{2}{3}}}{\left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*x)**(2/3)/(c + d*x)**(4/3), x)","F",0
1625,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\sqrt[3]{a + b x} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/3)*(c + d*x)**(4/3)), x)","F",0
1626,0,0,0,0.000000," ","integrate(1/(b*x+a)**(4/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{4}{3}} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(4/3)*(c + d*x)**(4/3)), x)","F",0
1627,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/3)/(d*x+c)**(4/3),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{3}} \left(c + d x\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/3)*(c + d*x)**(4/3)), x)","F",0
1628,1,39,0,2.548446," ","integrate((-1+x)**(1/3)/(1+x)**(1/3),x)","\frac{2^{\frac{2}{3}} \left(x - 1\right)^{\frac{4}{3}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{\left(x - 1\right) e^{i \pi}}{2}} \right)}}{2 \Gamma\left(\frac{7}{3}\right)}"," ",0,"2**(2/3)*(x - 1)**(4/3)*gamma(4/3)*hyper((1/3, 4/3), (7/3,), (x - 1)*exp_polar(I*pi)/2)/(2*gamma(7/3))","C",0
1629,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(1/4),x)","\int \left(a + b x\right)^{\frac{3}{2}} \sqrt[4]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(1/4), x)","F",0
1630,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(1/4),x)","\int \sqrt{a + b x} \sqrt[4]{c + d x}\, dx"," ",0,"Integral(sqrt(a + b*x)*(c + d*x)**(1/4), x)","F",0
1631,0,0,0,0.000000," ","integrate((d*x+c)**(1/4)/(b*x+a)**(1/2),x)","\int \frac{\sqrt[4]{c + d x}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(1/4)/sqrt(a + b*x), x)","F",0
1632,0,0,0,0.000000," ","integrate((d*x+c)**(1/4)/(b*x+a)**(3/2),x)","\int \frac{\sqrt[4]{c + d x}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/4)/(a + b*x)**(3/2), x)","F",0
1633,0,0,0,0.000000," ","integrate((d*x+c)**(1/4)/(b*x+a)**(5/2),x)","\int \frac{\sqrt[4]{c + d x}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/4)/(a + b*x)**(5/2), x)","F",0
1634,0,0,0,0.000000," ","integrate((d*x+c)**(1/4)/(b*x+a)**(7/2),x)","\int \frac{\sqrt[4]{c + d x}}{\left(a + b x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/4)/(a + b*x)**(7/2), x)","F",0
1635,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(3/4),x)","\int \left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{3}{4}}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(3/4), x)","F",0
1636,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(3/4),x)","\int \sqrt{a + b x} \left(c + d x\right)^{\frac{3}{4}}\, dx"," ",0,"Integral(sqrt(a + b*x)*(c + d*x)**(3/4), x)","F",0
1637,0,0,0,0.000000," ","integrate((d*x+c)**(3/4)/(b*x+a)**(1/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{4}}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(3/4)/sqrt(a + b*x), x)","F",0
1638,0,0,0,0.000000," ","integrate((d*x+c)**(3/4)/(b*x+a)**(3/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{4}}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(3/4)/(a + b*x)**(3/2), x)","F",0
1639,0,0,0,0.000000," ","integrate((d*x+c)**(3/4)/(b*x+a)**(5/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{4}}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(3/4)/(a + b*x)**(5/2), x)","F",0
1640,0,0,0,0.000000," ","integrate((d*x+c)**(3/4)/(b*x+a)**(7/2),x)","\int \frac{\left(c + d x\right)^{\frac{3}{4}}}{\left(a + b x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*x)**(3/4)/(a + b*x)**(7/2), x)","F",0
1641,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(5/4),x)","\int \left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(5/4), x)","F",0
1642,1,218,0,14.769279," ","integrate((b*x+a)**(1/2)*(d*x+c)**(5/4),x)","- \frac{2 a d \left(a + b x\right)^{\frac{3}{2}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a d e^{i \pi}}{b \operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}} + \frac{d x e^{i \pi}}{\operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}}} \right)} \sqrt[4]{\operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}}}{3 b^{2}} + \frac{2 c \left(a + b x\right)^{\frac{3}{2}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{a d e^{i \pi}}{b \operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}} + \frac{d x e^{i \pi}}{\operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}}} \right)} \sqrt[4]{\operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}}}{3 b} + \frac{2 d \left(a + b x\right)^{\frac{5}{2}} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{a d e^{i \pi}}{b \operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}} + \frac{d x e^{i \pi}}{\operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}}} \right)} \sqrt[4]{\operatorname{polar\_lift}{\left(- \frac{a d}{b} + c \right)}}}{5 b^{2}}"," ",0,"-2*a*d*(a + b*x)**(3/2)*hyper((-1/4, 3/2), (5/2,), a*d*exp_polar(I*pi)/(b*polar_lift(-a*d/b + c)) + d*x*exp_polar(I*pi)/polar_lift(-a*d/b + c))*polar_lift(-a*d/b + c)**(1/4)/(3*b**2) + 2*c*(a + b*x)**(3/2)*hyper((-1/4, 3/2), (5/2,), a*d*exp_polar(I*pi)/(b*polar_lift(-a*d/b + c)) + d*x*exp_polar(I*pi)/polar_lift(-a*d/b + c))*polar_lift(-a*d/b + c)**(1/4)/(3*b) + 2*d*(a + b*x)**(5/2)*hyper((-1/4, 5/2), (7/2,), a*d*exp_polar(I*pi)/(b*polar_lift(-a*d/b + c)) + d*x*exp_polar(I*pi)/polar_lift(-a*d/b + c))*polar_lift(-a*d/b + c)**(1/4)/(5*b**2)","A",0
1643,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(1/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/sqrt(a + b*x), x)","F",0
1644,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(3/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(3/2), x)","F",0
1645,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(5/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(5/2), x)","F",0
1646,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(7/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(7/2), x)","F",0
1647,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1648,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(1/4),x)","\int \frac{\left(a + b x\right)^{\frac{5}{2}}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(5/2)/(c + d*x)**(1/4), x)","F",0
1649,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(1/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(1/4), x)","F",0
1650,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(1/4),x)","\int \frac{\sqrt{a + b x}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(1/4), x)","F",0
1651,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(1/4),x)","\int \frac{1}{\sqrt{a + b x} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(1/4)), x)","F",0
1652,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(1/4)), x)","F",0
1653,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(1/4)), x)","F",0
1654,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(3/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(3/4), x)","F",0
1655,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(3/4),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(3/4), x)","F",0
1656,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(3/4),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(3/4)), x)","F",0
1657,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(3/4)), x)","F",0
1658,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(3/4)), x)","F",0
1659,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(5/4),x)","\int \frac{\left(a + b x\right)^{\frac{5}{2}}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x)**(5/2)/(c + d*x)**(5/4), x)","F",0
1660,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(5/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(5/4), x)","F",0
1661,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(5/4),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(5/4), x)","F",0
1662,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(5/4),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(5/4)), x)","F",0
1663,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(5/4)), x)","F",0
1664,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(5/4)), x)","F",0
1665,0,0,0,0.000000," ","integrate((b*x+a)**(7/2)/(d*x+c)**(7/4),x)","\int \frac{\left(a + b x\right)^{\frac{7}{2}}}{\left(c + d x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((a + b*x)**(7/2)/(c + d*x)**(7/4), x)","F",0
1666,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(7/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(7/4), x)","F",0
1667,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(7/4),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(7/4), x)","F",0
1668,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(7/4),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(7/4)), x)","F",0
1669,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(7/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(7/4)), x)","F",0
1670,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(7/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(7/4)), x)","F",0
1671,-1,0,0,0.000000," ","integrate((b*x+a)**(7/2)/(d*x+c)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1672,-1,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(9/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1673,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(9/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(9/4), x)","F",0
1674,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(9/4),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(9/4), x)","F",0
1675,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(9/4),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(9/4)), x)","F",0
1676,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(9/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(9/4)), x)","F",0
1677,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(9/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(9/4)), x)","F",0
1678,0,0,0,0.000000," ","integrate((b*x+a)**(3/4)*(d*x+c)**(5/4),x)","\int \left(a + b x\right)^{\frac{3}{4}} \left(c + d x\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((a + b*x)**(3/4)*(c + d*x)**(5/4), x)","F",0
1679,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(1/4),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\sqrt[4]{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(1/4), x)","F",0
1680,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(5/4),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(5/4), x)","F",0
1681,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(9/4),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{9}{4}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(9/4), x)","F",0
1682,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(13/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1683,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(17/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1684,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(21/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1685,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(25/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1686,0,0,0,0.000000," ","integrate((b*x+a)**(5/4)*(d*x+c)**(5/4),x)","\int \left(a + b x\right)^{\frac{5}{4}} \left(c + d x\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((a + b*x)**(5/4)*(c + d*x)**(5/4), x)","F",0
1687,0,0,0,0.000000," ","integrate((b*x+a)**(1/4)*(d*x+c)**(5/4),x)","\int \sqrt[4]{a + b x} \left(c + d x\right)^{\frac{5}{4}}\, dx"," ",0,"Integral((a + b*x)**(1/4)*(c + d*x)**(5/4), x)","F",0
1688,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(3/4),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(3/4), x)","F",0
1689,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(7/4),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{7}{4}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(7/4), x)","F",0
1690,0,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(11/4),x)","\int \frac{\left(c + d x\right)^{\frac{5}{4}}}{\left(a + b x\right)^{\frac{11}{4}}}\, dx"," ",0,"Integral((c + d*x)**(5/4)/(a + b*x)**(11/4), x)","F",0
1691,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(15/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1692,-1,0,0,0.000000," ","integrate((d*x+c)**(5/4)/(b*x+a)**(19/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1693,0,0,0,0.000000," ","integrate((b*x+a)**(5/4)/(d*x+c)**(1/4),x)","\int \frac{\left(a + b x\right)^{\frac{5}{4}}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(5/4)/(c + d*x)**(1/4), x)","F",0
1694,0,0,0,0.000000," ","integrate((b*x+a)**(1/4)/(d*x+c)**(1/4),x)","\int \frac{\sqrt[4]{a + b x}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(1/4)/(c + d*x)**(1/4), x)","F",0
1695,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/4)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{4}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/4)*(c + d*x)**(1/4)), x)","F",0
1696,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/4)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{4}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/4)*(c + d*x)**(1/4)), x)","F",0
1697,0,0,0,0.000000," ","integrate(1/(b*x+a)**(11/4)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{11}{4}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(11/4)*(c + d*x)**(1/4)), x)","F",0
1698,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(15/4)/(d*x+c)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1699,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(19/4)/(d*x+c)**(1/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1700,0,0,0,0.000000," ","integrate((b*x+a)**(7/4)/(d*x+c)**(1/4),x)","\int \frac{\left(a + b x\right)^{\frac{7}{4}}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(7/4)/(c + d*x)**(1/4), x)","F",0
1701,0,0,0,0.000000," ","integrate((b*x+a)**(3/4)/(d*x+c)**(1/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{4}}}{\sqrt[4]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(3/4)/(c + d*x)**(1/4), x)","F",0
1702,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/4)/(d*x+c)**(1/4),x)","\int \frac{1}{\sqrt[4]{a + b x} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/4)*(c + d*x)**(1/4)), x)","F",0
1703,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/4)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{4}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/4)*(c + d*x)**(1/4)), x)","F",0
1704,0,0,0,0.000000," ","integrate(1/(b*x+a)**(9/4)/(d*x+c)**(1/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{9}{4}} \sqrt[4]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(9/4)*(c + d*x)**(1/4)), x)","F",0
1705,0,0,0,0.000000," ","integrate((b*x+a)**(7/4)/(d*x+c)**(3/4),x)","\int \frac{\left(a + b x\right)^{\frac{7}{4}}}{\left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a + b*x)**(7/4)/(c + d*x)**(3/4), x)","F",0
1706,0,0,0,0.000000," ","integrate((b*x+a)**(3/4)/(d*x+c)**(3/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{4}}}{\left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a + b*x)**(3/4)/(c + d*x)**(3/4), x)","F",0
1707,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/4)/(d*x+c)**(3/4),x)","\int \frac{1}{\sqrt[4]{a + b x} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/4)*(c + d*x)**(3/4)), x)","F",0
1708,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/4)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{4}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/4)*(c + d*x)**(3/4)), x)","F",0
1709,0,0,0,0.000000," ","integrate(1/(b*x+a)**(9/4)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{9}{4}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(9/4)*(c + d*x)**(3/4)), x)","F",0
1710,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(13/4)/(d*x+c)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1711,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(17/4)/(d*x+c)**(3/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1712,0,0,0,0.000000," ","integrate((b*x+a)**(5/4)/(d*x+c)**(3/4),x)","\int \frac{\left(a + b x\right)^{\frac{5}{4}}}{\left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a + b*x)**(5/4)/(c + d*x)**(3/4), x)","F",0
1713,0,0,0,0.000000," ","integrate((b*x+a)**(1/4)/(d*x+c)**(3/4),x)","\int \frac{\sqrt[4]{a + b x}}{\left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral((a + b*x)**(1/4)/(c + d*x)**(3/4), x)","F",0
1714,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/4)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{4}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/4)*(c + d*x)**(3/4)), x)","F",0
1715,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/4)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{4}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/4)*(c + d*x)**(3/4)), x)","F",0
1716,0,0,0,0.000000," ","integrate(1/(b*x+a)**(11/4)/(d*x+c)**(3/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{11}{4}} \left(c + d x\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(11/4)*(c + d*x)**(3/4)), x)","F",0
1717,0,0,0,0.000000," ","integrate((b*x+a)**(5/4)/(d*x+c)**(5/4),x)","\int \frac{\left(a + b x\right)^{\frac{5}{4}}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x)**(5/4)/(c + d*x)**(5/4), x)","F",0
1718,0,0,0,0.000000," ","integrate((b*x+a)**(1/4)/(d*x+c)**(5/4),x)","\int \frac{\sqrt[4]{a + b x}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x)**(1/4)/(c + d*x)**(5/4), x)","F",0
1719,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/4)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{4}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/4)*(c + d*x)**(5/4)), x)","F",0
1720,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/4)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{4}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/4)*(c + d*x)**(5/4)), x)","F",0
1721,0,0,0,0.000000," ","integrate(1/(b*x+a)**(11/4)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{11}{4}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(11/4)*(c + d*x)**(5/4)), x)","F",0
1722,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(15/4)/(d*x+c)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1723,-1,0,0,0.000000," ","integrate((b*x+a)**(11/4)/(d*x+c)**(5/4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1724,0,0,0,0.000000," ","integrate((b*x+a)**(7/4)/(d*x+c)**(5/4),x)","\int \frac{\left(a + b x\right)^{\frac{7}{4}}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x)**(7/4)/(c + d*x)**(5/4), x)","F",0
1725,0,0,0,0.000000," ","integrate((b*x+a)**(3/4)/(d*x+c)**(5/4),x)","\int \frac{\left(a + b x\right)^{\frac{3}{4}}}{\left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral((a + b*x)**(3/4)/(c + d*x)**(5/4), x)","F",0
1726,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/4)/(d*x+c)**(5/4),x)","\int \frac{1}{\sqrt[4]{a + b x} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/4)*(c + d*x)**(5/4)), x)","F",0
1727,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/4)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{4}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/4)*(c + d*x)**(5/4)), x)","F",0
1728,0,0,0,0.000000," ","integrate(1/(b*x+a)**(9/4)/(d*x+c)**(5/4),x)","\int \frac{1}{\left(a + b x\right)^{\frac{9}{4}} \left(c + d x\right)^{\frac{5}{4}}}\, dx"," ",0,"Integral(1/((a + b*x)**(9/4)*(c + d*x)**(5/4)), x)","F",0
1729,0,0,0,0.000000," ","integrate(1/(-a*x+1)**(1/4)/(b*x+1)**(3/4),x)","\int \frac{1}{\sqrt[4]{- a x + 1} \left(b x + 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((-a*x + 1)**(1/4)*(b*x + 1)**(3/4)), x)","F",0
1730,0,0,0,0.000000," ","integrate(1/(-a*x+1)**(1/4)/(a*x+1)**(3/4),x)","\int \frac{1}{\sqrt[4]{- a x + 1} \left(a x + 1\right)^{\frac{3}{4}}}\, dx"," ",0,"Integral(1/((-a*x + 1)**(1/4)*(a*x + 1)**(3/4)), x)","F",0
1731,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(1/5),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\sqrt[5]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(1/5), x)","F",0
1732,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(1/5),x)","\int \frac{\sqrt{a + b x}}{\sqrt[5]{c + d x}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(1/5), x)","F",0
1733,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(1/5),x)","\int \frac{1}{\sqrt{a + b x} \sqrt[5]{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(1/5)), x)","F",0
1734,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(1/5),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \sqrt[5]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(1/5)), x)","F",0
1735,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(1/5),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \sqrt[5]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(1/5)), x)","F",0
1736,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)*(d*x+c)**(1/6),x)","\int \left(a + b x\right)^{\frac{5}{2}} \sqrt[6]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(5/2)*(c + d*x)**(1/6), x)","F",0
1737,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(1/6),x)","\int \left(a + b x\right)^{\frac{3}{2}} \sqrt[6]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(1/6), x)","F",0
1738,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(1/6),x)","\int \sqrt{a + b x} \sqrt[6]{c + d x}\, dx"," ",0,"Integral(sqrt(a + b*x)*(c + d*x)**(1/6), x)","F",0
1739,0,0,0,0.000000," ","integrate((d*x+c)**(1/6)/(b*x+a)**(1/2),x)","\int \frac{\sqrt[6]{c + d x}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(1/6)/sqrt(a + b*x), x)","F",0
1740,0,0,0,0.000000," ","integrate((d*x+c)**(1/6)/(b*x+a)**(3/2),x)","\int \frac{\sqrt[6]{c + d x}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/6)/(a + b*x)**(3/2), x)","F",0
1741,0,0,0,0.000000," ","integrate((d*x+c)**(1/6)/(b*x+a)**(5/2),x)","\int \frac{\sqrt[6]{c + d x}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(1/6)/(a + b*x)**(5/2), x)","F",0
1742,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)*(d*x+c)**(5/6),x)","\int \left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{5}{6}}\, dx"," ",0,"Integral((a + b*x)**(3/2)*(c + d*x)**(5/6), x)","F",0
1743,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)*(d*x+c)**(5/6),x)","\int \sqrt{a + b x} \left(c + d x\right)^{\frac{5}{6}}\, dx"," ",0,"Integral(sqrt(a + b*x)*(c + d*x)**(5/6), x)","F",0
1744,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(1/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\sqrt{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/sqrt(a + b*x), x)","F",0
1745,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(3/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\left(a + b x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/(a + b*x)**(3/2), x)","F",0
1746,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(5/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\left(a + b x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/(a + b*x)**(5/2), x)","F",0
1747,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(7/2),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\left(a + b x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/(a + b*x)**(7/2), x)","F",0
1748,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(1/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{2}}}{\sqrt[6]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(5/2)/(c + d*x)**(1/6), x)","F",0
1749,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(1/6),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\sqrt[6]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(1/6), x)","F",0
1750,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(1/6),x)","\int \frac{\sqrt{a + b x}}{\sqrt[6]{c + d x}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(1/6), x)","F",0
1751,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(1/6),x)","\int \frac{1}{\sqrt{a + b x} \sqrt[6]{c + d x}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(1/6)), x)","F",0
1752,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(1/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \sqrt[6]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(1/6)), x)","F",0
1753,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(1/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \sqrt[6]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(1/6)), x)","F",0
1754,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(5/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{2}}}{\left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((a + b*x)**(5/2)/(c + d*x)**(5/6), x)","F",0
1755,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(5/6),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(5/6), x)","F",0
1756,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(5/6),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(5/6), x)","F",0
1757,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(5/6),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(5/6)), x)","F",0
1758,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(5/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(5/6)), x)","F",0
1759,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(5/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(5/6)), x)","F",0
1760,0,0,0,0.000000," ","integrate((b*x+a)**(5/2)/(d*x+c)**(7/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{2}}}{\left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((a + b*x)**(5/2)/(c + d*x)**(7/6), x)","F",0
1761,0,0,0,0.000000," ","integrate((b*x+a)**(3/2)/(d*x+c)**(7/6),x)","\int \frac{\left(a + b x\right)^{\frac{3}{2}}}{\left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((a + b*x)**(3/2)/(c + d*x)**(7/6), x)","F",0
1762,0,0,0,0.000000," ","integrate((b*x+a)**(1/2)/(d*x+c)**(7/6),x)","\int \frac{\sqrt{a + b x}}{\left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(sqrt(a + b*x)/(c + d*x)**(7/6), x)","F",0
1763,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/2)/(d*x+c)**(7/6),x)","\int \frac{1}{\sqrt{a + b x} \left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x)*(c + d*x)**(7/6)), x)","F",0
1764,0,0,0,0.000000," ","integrate(1/(b*x+a)**(3/2)/(d*x+c)**(7/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{3}{2}} \left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(3/2)*(c + d*x)**(7/6)), x)","F",0
1765,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/2)/(d*x+c)**(7/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{2}} \left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/2)*(c + d*x)**(7/6)), x)","F",0
1766,-1,0,0,0.000000," ","integrate((b*x+a)**(1/6)*(d*x+c)**(13/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1767,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)*(d*x+c)**(7/6),x)","\int \sqrt[6]{a + b x} \left(c + d x\right)^{\frac{7}{6}}\, dx"," ",0,"Integral((a + b*x)**(1/6)*(c + d*x)**(7/6), x)","F",0
1768,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)*(d*x+c)**(1/6),x)","\int \sqrt[6]{a + b x} \sqrt[6]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(1/6)*(c + d*x)**(1/6), x)","F",0
1769,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(5/6),x)","\int \frac{\sqrt[6]{a + b x}}{\left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((a + b*x)**(1/6)/(c + d*x)**(5/6), x)","F",0
1770,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(11/6),x)","\int \frac{\sqrt[6]{a + b x}}{\left(c + d x\right)^{\frac{11}{6}}}\, dx"," ",0,"Integral((a + b*x)**(1/6)/(c + d*x)**(11/6), x)","F",0
1771,-1,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(17/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1772,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)*(d*x+c)**(5/6),x)","\int \sqrt[6]{a + b x} \left(c + d x\right)^{\frac{5}{6}}\, dx"," ",0,"Integral((a + b*x)**(1/6)*(c + d*x)**(5/6), x)","F",0
1773,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(1/6),x)","\int \frac{\sqrt[6]{a + b x}}{\sqrt[6]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(1/6)/(c + d*x)**(1/6), x)","F",0
1774,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(7/6),x)","\int \frac{\sqrt[6]{a + b x}}{\left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((a + b*x)**(1/6)/(c + d*x)**(7/6), x)","F",0
1775,0,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(13/6),x)","\int \frac{\sqrt[6]{a + b x}}{\left(c + d x\right)^{\frac{13}{6}}}\, dx"," ",0,"Integral((a + b*x)**(1/6)/(c + d*x)**(13/6), x)","F",0
1776,-1,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(19/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1777,-1,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(25/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1778,-1,0,0,0.000000," ","integrate((b*x+a)**(1/6)/(d*x+c)**(31/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1779,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)*(d*x+c)**(1/6),x)","\int \left(a + b x\right)^{\frac{5}{6}} \sqrt[6]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(5/6)*(c + d*x)**(1/6), x)","F",0
1780,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(5/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{6}}}{\left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((a + b*x)**(5/6)/(c + d*x)**(5/6), x)","F",0
1781,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(11/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{6}}}{\left(c + d x\right)^{\frac{11}{6}}}\, dx"," ",0,"Integral((a + b*x)**(5/6)/(c + d*x)**(11/6), x)","F",0
1782,-1,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(17/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1783,-1,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(23/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1784,-1,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(29/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1785,-1,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(35/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1786,-1,0,0,0.000000," ","integrate((b*x+a)**(5/6)*(d*x+c)**(11/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1787,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)*(d*x+c)**(5/6),x)","\int \left(a + b x\right)^{\frac{5}{6}} \left(c + d x\right)^{\frac{5}{6}}\, dx"," ",0,"Integral((a + b*x)**(5/6)*(c + d*x)**(5/6), x)","F",0
1788,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(1/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{6}}}{\sqrt[6]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(5/6)/(c + d*x)**(1/6), x)","F",0
1789,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(7/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{6}}}{\left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((a + b*x)**(5/6)/(c + d*x)**(7/6), x)","F",0
1790,0,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(13/6),x)","\int \frac{\left(a + b x\right)^{\frac{5}{6}}}{\left(c + d x\right)^{\frac{13}{6}}}\, dx"," ",0,"Integral((a + b*x)**(5/6)/(c + d*x)**(13/6), x)","F",0
1791,-1,0,0,0.000000," ","integrate((b*x+a)**(5/6)/(d*x+c)**(19/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1792,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)*(d*x+c)**(13/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1793,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)*(d*x+c)**(7/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1794,0,0,0,0.000000," ","integrate((b*x+a)**(7/6)*(d*x+c)**(1/6),x)","\int \left(a + b x\right)^{\frac{7}{6}} \sqrt[6]{c + d x}\, dx"," ",0,"Integral((a + b*x)**(7/6)*(c + d*x)**(1/6), x)","F",0
1795,0,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(5/6),x)","\int \frac{\left(a + b x\right)^{\frac{7}{6}}}{\left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((a + b*x)**(7/6)/(c + d*x)**(5/6), x)","F",0
1796,0,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(11/6),x)","\int \frac{\left(a + b x\right)^{\frac{7}{6}}}{\left(c + d x\right)^{\frac{11}{6}}}\, dx"," ",0,"Integral((a + b*x)**(7/6)/(c + d*x)**(11/6), x)","F",0
1797,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(17/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1798,0,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(1/6),x)","\int \frac{\left(a + b x\right)^{\frac{7}{6}}}{\sqrt[6]{c + d x}}\, dx"," ",0,"Integral((a + b*x)**(7/6)/(c + d*x)**(1/6), x)","F",0
1799,0,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(7/6),x)","\int \frac{\left(a + b x\right)^{\frac{7}{6}}}{\left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((a + b*x)**(7/6)/(c + d*x)**(7/6), x)","F",0
1800,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(13/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1801,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(19/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1802,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(25/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1803,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(31/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1804,-1,0,0,0.000000," ","integrate((b*x+a)**(7/6)/(d*x+c)**(37/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1805,0,0,0,0.000000," ","integrate((d*x+c)**(7/6)/(b*x+a)**(1/6),x)","\int \frac{\left(c + d x\right)^{\frac{7}{6}}}{\sqrt[6]{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(7/6)/(a + b*x)**(1/6), x)","F",0
1806,0,0,0,0.000000," ","integrate((d*x+c)**(1/6)/(b*x+a)**(1/6),x)","\int \frac{\sqrt[6]{c + d x}}{\sqrt[6]{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(1/6)/(a + b*x)**(1/6), x)","F",0
1807,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(5/6),x)","\int \frac{1}{\sqrt[6]{a + b x} \left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/6)*(c + d*x)**(5/6)), x)","F",0
1808,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(11/6),x)","\int \frac{1}{\sqrt[6]{a + b x} \left(c + d x\right)^{\frac{11}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/6)*(c + d*x)**(11/6)), x)","F",0
1809,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(17/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1810,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(23/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1811,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(29/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1812,-1,0,0,0.000000," ","integrate((d*x+c)**(11/6)/(b*x+a)**(1/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1813,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(1/6),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\sqrt[6]{a + b x}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/(a + b*x)**(1/6), x)","F",0
1814,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(1/6),x)","\int \frac{1}{\sqrt[6]{a + b x} \sqrt[6]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/6)*(c + d*x)**(1/6)), x)","F",0
1815,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(7/6),x)","\int \frac{1}{\sqrt[6]{a + b x} \left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/6)*(c + d*x)**(7/6)), x)","F",0
1816,0,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(13/6),x)","\int \frac{1}{\sqrt[6]{a + b x} \left(c + d x\right)^{\frac{13}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(1/6)*(c + d*x)**(13/6)), x)","F",0
1817,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(1/6)/(d*x+c)**(19/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1818,-1,0,0,0.000000," ","integrate((d*x+c)**(13/6)/(b*x+a)**(5/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1819,0,0,0,0.000000," ","integrate((d*x+c)**(7/6)/(b*x+a)**(5/6),x)","\int \frac{\left(c + d x\right)^{\frac{7}{6}}}{\left(a + b x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((c + d*x)**(7/6)/(a + b*x)**(5/6), x)","F",0
1820,0,0,0,0.000000," ","integrate((d*x+c)**(1/6)/(b*x+a)**(5/6),x)","\int \frac{\sqrt[6]{c + d x}}{\left(a + b x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((c + d*x)**(1/6)/(a + b*x)**(5/6), x)","F",0
1821,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(5/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{6}} \left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/6)*(c + d*x)**(5/6)), x)","F",0
1822,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(11/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{6}} \left(c + d x\right)^{\frac{11}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/6)*(c + d*x)**(11/6)), x)","F",0
1823,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(17/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1824,-1,0,0,0.000000," ","integrate((d*x+c)**(11/6)/(b*x+a)**(5/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1825,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(5/6),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\left(a + b x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/(a + b*x)**(5/6), x)","F",0
1826,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(1/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{6}} \sqrt[6]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/6)*(c + d*x)**(1/6)), x)","F",0
1827,0,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(7/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{5}{6}} \left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(5/6)*(c + d*x)**(7/6)), x)","F",0
1828,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(13/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1829,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(19/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1830,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(5/6)/(d*x+c)**(25/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1831,-1,0,0,0.000000," ","integrate((d*x+c)**(13/6)/(b*x+a)**(7/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1832,0,0,0,0.000000," ","integrate((d*x+c)**(7/6)/(b*x+a)**(7/6),x)","\int \frac{\left(c + d x\right)^{\frac{7}{6}}}{\left(a + b x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((c + d*x)**(7/6)/(a + b*x)**(7/6), x)","F",0
1833,0,0,0,0.000000," ","integrate((d*x+c)**(1/6)/(b*x+a)**(7/6),x)","\int \frac{\sqrt[6]{c + d x}}{\left(a + b x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((c + d*x)**(1/6)/(a + b*x)**(7/6), x)","F",0
1834,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(5/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{6}} \left(c + d x\right)^{\frac{5}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/6)*(c + d*x)**(5/6)), x)","F",0
1835,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(11/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{6}} \left(c + d x\right)^{\frac{11}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/6)*(c + d*x)**(11/6)), x)","F",0
1836,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(17/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1837,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(23/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1838,-1,0,0,0.000000," ","integrate((d*x+c)**(11/6)/(b*x+a)**(7/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1839,0,0,0,0.000000," ","integrate((d*x+c)**(5/6)/(b*x+a)**(7/6),x)","\int \frac{\left(c + d x\right)^{\frac{5}{6}}}{\left(a + b x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral((c + d*x)**(5/6)/(a + b*x)**(7/6), x)","F",0
1840,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(1/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{6}} \sqrt[6]{c + d x}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/6)*(c + d*x)**(1/6)), x)","F",0
1841,0,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(7/6),x)","\int \frac{1}{\left(a + b x\right)^{\frac{7}{6}} \left(c + d x\right)^{\frac{7}{6}}}\, dx"," ",0,"Integral(1/((a + b*x)**(7/6)*(c + d*x)**(7/6)), x)","F",0
1842,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(13/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1843,-1,0,0,0.000000," ","integrate(1/(b*x+a)**(7/6)/(d*x+c)**(19/6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1844,1,20,0,0.268689," ","integrate((b*x+a)**m*(a+b*(2+m)*x),x)","a x \left(a + b x\right)^{m} + b x^{2} \left(a + b x\right)^{m}"," ",0,"a*x*(a + b*x)**m + b*x**2*(a + b*x)**m","B",0
1845,-2,0,0,0.000000," ","integrate((b*x+a)**m*(d*x+c)**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1846,1,4058,0,4.666409," ","integrate((b*x+a)**m*(d*x+c)**3,x)","\begin{cases} a^{m} \left(c^{3} x + \frac{3 c^{2} d x^{2}}{2} + c d^{2} x^{3} + \frac{d^{3} x^{4}}{4}\right) & \text{for}\: b = 0 \\\frac{6 a^{3} d^{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} 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{6 a^{2} b c d^{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 d^{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 d^{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} 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}} - \frac{18 a b^{2} c d^{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} d^{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} d^{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} c^{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} c^{2} d 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} c d^{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} d^{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}\: m = -4 \\- \frac{6 a^{3} d^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{9 a^{3} d^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{6 a^{2} b c d^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{9 a^{2} b c d^{2}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b d^{3} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b d^{3} x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{3 a b^{2} c^{2} d}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{12 a b^{2} c d^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{12 a b^{2} c d^{2} x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} d^{3} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{b^{3} c^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 b^{3} c^{2} d x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{6 b^{3} c d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} d^{3} x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: m = -3 \\\frac{6 a^{3} d^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3} d^{3}}{2 a b^{4} + 2 b^{5} x} - \frac{12 a^{2} b c d^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{12 a^{2} b c d^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b d^{3} x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a b^{2} c^{2} d \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a b^{2} c^{2} d}{2 a b^{4} + 2 b^{5} x} - \frac{12 a b^{2} c d^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} d^{3} x^{2}}{2 a b^{4} + 2 b^{5} x} - \frac{2 b^{3} c^{3}}{2 a b^{4} + 2 b^{5} x} + \frac{6 b^{3} c^{2} d x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 b^{3} c d^{2} x^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} d^{3} x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: m = -2 \\- \frac{a^{3} d^{3} \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{3 a^{2} c d^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} + \frac{a^{2} d^{3} x}{b^{3}} - \frac{3 a c^{2} d \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{3 a c d^{2} x}{b^{2}} - \frac{a d^{3} x^{2}}{2 b^{2}} + \frac{c^{3} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{3 c^{2} d x}{b} + \frac{3 c d^{2} x^{2}}{2 b} + \frac{d^{3} x^{3}}{3 b} & \text{for}\: m = -1 \\- \frac{6 a^{4} d^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{6 a^{3} b c d^{2} m \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{24 a^{3} b c d^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{6 a^{3} b d^{3} m x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{3 a^{2} b^{2} c^{2} d m^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{21 a^{2} b^{2} c^{2} d m \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{36 a^{2} b^{2} c^{2} d \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{6 a^{2} b^{2} c d^{2} m^{2} x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{24 a^{2} b^{2} c d^{2} m x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{3 a^{2} b^{2} d^{3} m^{2} x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} - \frac{3 a^{2} b^{2} d^{3} m x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{a b^{3} c^{3} m^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{9 a b^{3} c^{3} m^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{26 a b^{3} c^{3} m \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{24 a b^{3} c^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{3 a b^{3} c^{2} d m^{3} x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{21 a b^{3} c^{2} d m^{2} x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{36 a b^{3} c^{2} d m x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{3 a b^{3} c d^{2} m^{3} x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{15 a b^{3} c d^{2} m^{2} x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{12 a b^{3} c d^{2} m x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{a b^{3} d^{3} m^{3} x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{3 a b^{3} d^{3} m^{2} x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{2 a b^{3} d^{3} m x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{b^{4} c^{3} m^{3} x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{9 b^{4} c^{3} m^{2} x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{26 b^{4} c^{3} m x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{24 b^{4} c^{3} x \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{3 b^{4} c^{2} d m^{3} x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{24 b^{4} c^{2} d m^{2} x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{57 b^{4} c^{2} d m x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{36 b^{4} c^{2} d x^{2} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{3 b^{4} c d^{2} m^{3} x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{21 b^{4} c d^{2} m^{2} x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{42 b^{4} c d^{2} m x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{24 b^{4} c d^{2} x^{3} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{b^{4} d^{3} m^{3} x^{4} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{6 b^{4} d^{3} m^{2} x^{4} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{11 b^{4} d^{3} m x^{4} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} + \frac{6 b^{4} d^{3} x^{4} \left(a + b x\right)^{m}}{b^{4} m^{4} + 10 b^{4} m^{3} + 35 b^{4} m^{2} + 50 b^{4} m + 24 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**m*(c**3*x + 3*c**2*d*x**2/2 + c*d**2*x**3 + d**3*x**4/4), Eq(b, 0)), (6*a**3*d**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*d**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*c*d**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*d**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*d**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*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) - 18*a*b**2*c*d**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*d**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*d**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*c**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*c**2*d*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*c*d**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*d**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(m, -4)), (-6*a**3*d**3*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 9*a**3*d**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 6*a**2*b*c*d**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 9*a**2*b*c*d**2/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*d**3*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*d**3*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 3*a*b**2*c**2*d/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 12*a*b**2*c*d**2*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 12*a*b**2*c*d**2*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*d**3*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - b**3*c**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*b**3*c**2*d*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 6*b**3*c*d**2*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*d**3*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(m, -3)), (6*a**3*d**3*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3*d**3/(2*a*b**4 + 2*b**5*x) - 12*a**2*b*c*d**2*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 12*a**2*b*c*d**2/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*d**3*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a*b**2*c**2*d*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a*b**2*c**2*d/(2*a*b**4 + 2*b**5*x) - 12*a*b**2*c*d**2*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*d**3*x**2/(2*a*b**4 + 2*b**5*x) - 2*b**3*c**3/(2*a*b**4 + 2*b**5*x) + 6*b**3*c**2*d*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*b**3*c*d**2*x**2/(2*a*b**4 + 2*b**5*x) + b**3*d**3*x**3/(2*a*b**4 + 2*b**5*x), Eq(m, -2)), (-a**3*d**3*log(a/b + x)/b**4 + 3*a**2*c*d**2*log(a/b + x)/b**3 + a**2*d**3*x/b**3 - 3*a*c**2*d*log(a/b + x)/b**2 - 3*a*c*d**2*x/b**2 - a*d**3*x**2/(2*b**2) + c**3*log(a/b + x)/b + 3*c**2*d*x/b + 3*c*d**2*x**2/(2*b) + d**3*x**3/(3*b), Eq(m, -1)), (-6*a**4*d**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 6*a**3*b*c*d**2*m*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 24*a**3*b*c*d**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 6*a**3*b*d**3*m*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 3*a**2*b**2*c**2*d*m**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 21*a**2*b**2*c**2*d*m*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 36*a**2*b**2*c**2*d*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 6*a**2*b**2*c*d**2*m**2*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 24*a**2*b**2*c*d**2*m*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 3*a**2*b**2*d**3*m**2*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) - 3*a**2*b**2*d**3*m*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + a*b**3*c**3*m**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 9*a*b**3*c**3*m**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 26*a*b**3*c**3*m*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 24*a*b**3*c**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 3*a*b**3*c**2*d*m**3*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 21*a*b**3*c**2*d*m**2*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 36*a*b**3*c**2*d*m*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 3*a*b**3*c*d**2*m**3*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 15*a*b**3*c*d**2*m**2*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 12*a*b**3*c*d**2*m*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + a*b**3*d**3*m**3*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 3*a*b**3*d**3*m**2*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 2*a*b**3*d**3*m*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + b**4*c**3*m**3*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 9*b**4*c**3*m**2*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 26*b**4*c**3*m*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 24*b**4*c**3*x*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 3*b**4*c**2*d*m**3*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 24*b**4*c**2*d*m**2*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 57*b**4*c**2*d*m*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 36*b**4*c**2*d*x**2*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 3*b**4*c*d**2*m**3*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 21*b**4*c*d**2*m**2*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 42*b**4*c*d**2*m*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 24*b**4*c*d**2*x**3*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + b**4*d**3*m**3*x**4*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 6*b**4*d**3*m**2*x**4*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 11*b**4*d**3*m*x**4*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4) + 6*b**4*d**3*x**4*(a + b*x)**m/(b**4*m**4 + 10*b**4*m**3 + 35*b**4*m**2 + 50*b**4*m + 24*b**4), True))","A",0
1847,1,1506,0,2.137408," ","integrate((b*x+a)**m*(d*x+c)**2,x)","\begin{cases} a^{m} \left(c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3}\right) & \text{for}\: b = 0 \\\frac{2 a^{2} d^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2} d^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{2 a b c d}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b d^{2} x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{b^{2} c^{2}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{4 b^{2} c d x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: m = -3 \\- \frac{2 a^{2} d^{2} \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2} d^{2}}{a b^{3} + b^{4} x} + \frac{2 a b c d \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{2 a b c d}{a b^{3} + b^{4} x} - \frac{2 a b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{b^{2} c^{2}}{a b^{3} + b^{4} x} + \frac{2 b^{2} c d x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} + \frac{b^{2} d^{2} x^{2}}{a b^{3} + b^{4} x} & \text{for}\: m = -2 \\\frac{a^{2} d^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{2 a c d \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{a d^{2} x}{b^{2}} + \frac{c^{2} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{2 c d x}{b} + \frac{d^{2} x^{2}}{2 b} & \text{for}\: m = -1 \\\frac{2 a^{3} d^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} - \frac{2 a^{2} b c d m \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} - \frac{6 a^{2} b c d \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} - \frac{2 a^{2} b d^{2} m x \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{a b^{2} c^{2} m^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{5 a b^{2} c^{2} m \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{6 a b^{2} c^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{2 a b^{2} c d m^{2} x \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{6 a b^{2} c d m x \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{a b^{2} d^{2} m^{2} x^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{a b^{2} d^{2} m x^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{b^{3} c^{2} m^{2} x \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{5 b^{3} c^{2} m x \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{6 b^{3} c^{2} x \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{2 b^{3} c d m^{2} x^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{8 b^{3} c d m x^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{6 b^{3} c d x^{2} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{b^{3} d^{2} m^{2} x^{3} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{3 b^{3} d^{2} m x^{3} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} + \frac{2 b^{3} d^{2} x^{3} \left(a + b x\right)^{m}}{b^{3} m^{3} + 6 b^{3} m^{2} + 11 b^{3} m + 6 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**m*(c**2*x + c*d*x**2 + d**2*x**3/3), Eq(b, 0)), (2*a**2*d**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2*d**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - 2*a*b*c*d/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*d**2*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*d**2*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - b**2*c**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - 4*b**2*c*d*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*d**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(m, -3)), (-2*a**2*d**2*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2*d**2/(a*b**3 + b**4*x) + 2*a*b*c*d*log(a/b + x)/(a*b**3 + b**4*x) + 2*a*b*c*d/(a*b**3 + b**4*x) - 2*a*b*d**2*x*log(a/b + x)/(a*b**3 + b**4*x) - b**2*c**2/(a*b**3 + b**4*x) + 2*b**2*c*d*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*d**2*x**2/(a*b**3 + b**4*x), Eq(m, -2)), (a**2*d**2*log(a/b + x)/b**3 - 2*a*c*d*log(a/b + x)/b**2 - a*d**2*x/b**2 + c**2*log(a/b + x)/b + 2*c*d*x/b + d**2*x**2/(2*b), Eq(m, -1)), (2*a**3*d**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) - 2*a**2*b*c*d*m*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) - 6*a**2*b*c*d*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) - 2*a**2*b*d**2*m*x*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + a*b**2*c**2*m**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 5*a*b**2*c**2*m*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 6*a*b**2*c**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 2*a*b**2*c*d*m**2*x*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 6*a*b**2*c*d*m*x*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + a*b**2*d**2*m**2*x**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + a*b**2*d**2*m*x**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + b**3*c**2*m**2*x*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 5*b**3*c**2*m*x*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 6*b**3*c**2*x*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 2*b**3*c*d*m**2*x**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 8*b**3*c*d*m*x**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 6*b**3*c*d*x**2*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + b**3*d**2*m**2*x**3*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 3*b**3*d**2*m*x**3*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3) + 2*b**3*d**2*x**3*(a + b*x)**m/(b**3*m**3 + 6*b**3*m**2 + 11*b**3*m + 6*b**3), True))","A",0
1848,1,377,0,0.856251," ","integrate((b*x+a)**m*(d*x+c),x)","\begin{cases} a^{m} \left(c x + \frac{d x^{2}}{2}\right) & \text{for}\: b = 0 \\\frac{a d \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a d}{a b^{2} + b^{3} x} - \frac{b c}{a b^{2} + b^{3} x} + \frac{b d x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: m = -2 \\- \frac{a d \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{c \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{d x}{b} & \text{for}\: m = -1 \\- \frac{a^{2} d \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{a b c m \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{2 a b c \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{a b d m x \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{b^{2} c m x \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{2 b^{2} c x \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{b^{2} d m x^{2} \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} + \frac{b^{2} d x^{2} \left(a + b x\right)^{m}}{b^{2} m^{2} + 3 b^{2} m + 2 b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**m*(c*x + d*x**2/2), Eq(b, 0)), (a*d*log(a/b + x)/(a*b**2 + b**3*x) + a*d/(a*b**2 + b**3*x) - b*c/(a*b**2 + b**3*x) + b*d*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(m, -2)), (-a*d*log(a/b + x)/b**2 + c*log(a/b + x)/b + d*x/b, Eq(m, -1)), (-a**2*d*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + a*b*c*m*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + 2*a*b*c*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + a*b*d*m*x*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + b**2*c*m*x*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + 2*b**2*c*x*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + b**2*d*m*x**2*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2) + b**2*d*x**2*(a + b*x)**m/(b**2*m**2 + 3*b**2*m + 2*b**2), True))","A",0
1849,0,0,0,0.000000," ","integrate((b*x+a)**m/(d*x+c),x)","\int \frac{\left(a + b x\right)^{m}}{c + d x}\, dx"," ",0,"Integral((a + b*x)**m/(c + d*x), x)","F",0
1850,0,0,0,0.000000," ","integrate((b*x+a)**m/(d*x+c)**2,x)","\int \frac{\left(a + b x\right)^{m}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*x)**m/(c + d*x)**2, x)","F",0
1851,0,0,0,0.000000," ","integrate((b*x+a)**m/(d*x+c)**3,x)","\int \frac{\left(a + b x\right)^{m}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b*x)**m/(c + d*x)**3, x)","F",0
1852,1,4058,0,4.438758," ","integrate((b*x+a)**3*(d*x+c)**n,x)","\begin{cases} c^{n} \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}\: d = 0 \\- \frac{2 a^{3} d^{3}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{3 a^{2} b c d^{2}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{9 a^{2} b d^{3} x}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{6 a b^{2} c^{2} d}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{18 a b^{2} c d^{2} x}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{18 a b^{2} d^{3} x^{2}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{6 b^{3} c^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{11 b^{3} c^{3}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{18 b^{3} c^{2} d x \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{27 b^{3} c^{2} d x}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{18 b^{3} c d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{18 b^{3} c d^{2} x^{2}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{6 b^{3} d^{3} x^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{a^{3} d^{3}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{3 a^{2} b c d^{2}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{6 a^{2} b d^{3} x}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{6 a b^{2} c^{2} d \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{9 a b^{2} c^{2} d}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{12 a b^{2} c d^{2} x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{12 a b^{2} c d^{2} x}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{6 a b^{2} d^{3} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{6 b^{3} c^{3} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{9 b^{3} c^{3}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{12 b^{3} c^{2} d x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{12 b^{3} c^{2} d x}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{6 b^{3} c d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{2 b^{3} d^{3} x^{3}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} & \text{for}\: n = -3 \\- \frac{2 a^{3} d^{3}}{2 c d^{4} + 2 d^{5} x} + \frac{6 a^{2} b c d^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} + \frac{6 a^{2} b c d^{2}}{2 c d^{4} + 2 d^{5} x} + \frac{6 a^{2} b d^{3} x \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} - \frac{12 a b^{2} c^{2} d \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} - \frac{12 a b^{2} c^{2} d}{2 c d^{4} + 2 d^{5} x} - \frac{12 a b^{2} c d^{2} x \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} + \frac{6 a b^{2} d^{3} x^{2}}{2 c d^{4} + 2 d^{5} x} + \frac{6 b^{3} c^{3} \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} + \frac{6 b^{3} c^{3}}{2 c d^{4} + 2 d^{5} x} + \frac{6 b^{3} c^{2} d x \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} - \frac{3 b^{3} c d^{2} x^{2}}{2 c d^{4} + 2 d^{5} x} + \frac{b^{3} d^{3} x^{3}}{2 c d^{4} + 2 d^{5} x} & \text{for}\: n = -2 \\\frac{a^{3} \log{\left(\frac{c}{d} + x \right)}}{d} - \frac{3 a^{2} b c \log{\left(\frac{c}{d} + x \right)}}{d^{2}} + \frac{3 a^{2} b x}{d} + \frac{3 a b^{2} c^{2} \log{\left(\frac{c}{d} + x \right)}}{d^{3}} - \frac{3 a b^{2} c x}{d^{2}} + \frac{3 a b^{2} x^{2}}{2 d} - \frac{b^{3} c^{3} \log{\left(\frac{c}{d} + x \right)}}{d^{4}} + \frac{b^{3} c^{2} x}{d^{3}} - \frac{b^{3} c x^{2}}{2 d^{2}} + \frac{b^{3} x^{3}}{3 d} & \text{for}\: n = -1 \\\frac{a^{3} c d^{3} n^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{9 a^{3} c d^{3} n^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{26 a^{3} c d^{3} n \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 a^{3} c d^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{a^{3} d^{4} n^{3} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{9 a^{3} d^{4} n^{2} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{26 a^{3} d^{4} n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 a^{3} d^{4} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{3 a^{2} b c^{2} d^{2} n^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{21 a^{2} b c^{2} d^{2} n \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{36 a^{2} b c^{2} d^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{3 a^{2} b c d^{3} n^{3} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{21 a^{2} b c d^{3} n^{2} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{36 a^{2} b c d^{3} n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{3 a^{2} b d^{4} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 a^{2} b d^{4} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{57 a^{2} b d^{4} n x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{36 a^{2} b d^{4} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 a b^{2} c^{3} d n \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 a b^{2} c^{3} d \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{6 a b^{2} c^{2} d^{2} n^{2} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{24 a b^{2} c^{2} d^{2} n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{3 a b^{2} c d^{3} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{15 a b^{2} c d^{3} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{12 a b^{2} c d^{3} n x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{3 a b^{2} d^{4} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{21 a b^{2} d^{4} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{42 a b^{2} d^{4} n x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 a b^{2} d^{4} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{6 b^{3} c^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 b^{3} c^{3} d n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{3 b^{3} c^{2} d^{2} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{3 b^{3} c^{2} d^{2} n x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{b^{3} c d^{3} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{3 b^{3} c d^{3} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{2 b^{3} c d^{3} n x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{b^{3} d^{4} n^{3} x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 b^{3} d^{4} n^{2} x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{11 b^{3} d^{4} n x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 b^{3} d^{4} x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a**3*x + 3*a**2*b*x**2/2 + a*b**2*x**3 + b**3*x**4/4), Eq(d, 0)), (-2*a**3*d**3/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 3*a**2*b*c*d**2/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 9*a**2*b*d**3*x/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 6*a*b**2*c**2*d/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 18*a*b**2*c*d**2*x/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 18*a*b**2*d**3*x**2/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 6*b**3*c**3*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 11*b**3*c**3/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 18*b**3*c**2*d*x*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 27*b**3*c**2*d*x/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 18*b**3*c*d**2*x**2*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 18*b**3*c*d**2*x**2/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 6*b**3*d**3*x**3*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3), Eq(n, -4)), (-a**3*d**3/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 3*a**2*b*c*d**2/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 6*a**2*b*d**3*x/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 6*a*b**2*c**2*d*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 9*a*b**2*c**2*d/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 12*a*b**2*c*d**2*x*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 12*a*b**2*c*d**2*x/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 6*a*b**2*d**3*x**2*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 6*b**3*c**3*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 9*b**3*c**3/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 12*b**3*c**2*d*x*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 12*b**3*c**2*d*x/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 6*b**3*c*d**2*x**2*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 2*b**3*d**3*x**3/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2), Eq(n, -3)), (-2*a**3*d**3/(2*c*d**4 + 2*d**5*x) + 6*a**2*b*c*d**2*log(c/d + x)/(2*c*d**4 + 2*d**5*x) + 6*a**2*b*c*d**2/(2*c*d**4 + 2*d**5*x) + 6*a**2*b*d**3*x*log(c/d + x)/(2*c*d**4 + 2*d**5*x) - 12*a*b**2*c**2*d*log(c/d + x)/(2*c*d**4 + 2*d**5*x) - 12*a*b**2*c**2*d/(2*c*d**4 + 2*d**5*x) - 12*a*b**2*c*d**2*x*log(c/d + x)/(2*c*d**4 + 2*d**5*x) + 6*a*b**2*d**3*x**2/(2*c*d**4 + 2*d**5*x) + 6*b**3*c**3*log(c/d + x)/(2*c*d**4 + 2*d**5*x) + 6*b**3*c**3/(2*c*d**4 + 2*d**5*x) + 6*b**3*c**2*d*x*log(c/d + x)/(2*c*d**4 + 2*d**5*x) - 3*b**3*c*d**2*x**2/(2*c*d**4 + 2*d**5*x) + b**3*d**3*x**3/(2*c*d**4 + 2*d**5*x), Eq(n, -2)), (a**3*log(c/d + x)/d - 3*a**2*b*c*log(c/d + x)/d**2 + 3*a**2*b*x/d + 3*a*b**2*c**2*log(c/d + x)/d**3 - 3*a*b**2*c*x/d**2 + 3*a*b**2*x**2/(2*d) - b**3*c**3*log(c/d + x)/d**4 + b**3*c**2*x/d**3 - b**3*c*x**2/(2*d**2) + b**3*x**3/(3*d), Eq(n, -1)), (a**3*c*d**3*n**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 9*a**3*c*d**3*n**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 26*a**3*c*d**3*n*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*a**3*c*d**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + a**3*d**4*n**3*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 9*a**3*d**4*n**2*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 26*a**3*d**4*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*a**3*d**4*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 3*a**2*b*c**2*d**2*n**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 21*a**2*b*c**2*d**2*n*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 36*a**2*b*c**2*d**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 3*a**2*b*c*d**3*n**3*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 21*a**2*b*c*d**3*n**2*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 36*a**2*b*c*d**3*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 3*a**2*b*d**4*n**3*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*a**2*b*d**4*n**2*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 57*a**2*b*d**4*n*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 36*a**2*b*d**4*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*a*b**2*c**3*d*n*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*a*b**2*c**3*d*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 6*a*b**2*c**2*d**2*n**2*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 24*a*b**2*c**2*d**2*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 3*a*b**2*c*d**3*n**3*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 15*a*b**2*c*d**3*n**2*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 12*a*b**2*c*d**3*n*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 3*a*b**2*d**4*n**3*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 21*a*b**2*d**4*n**2*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 42*a*b**2*d**4*n*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*a*b**2*d**4*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 6*b**3*c**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*b**3*c**3*d*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 3*b**3*c**2*d**2*n**2*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 3*b**3*c**2*d**2*n*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + b**3*c*d**3*n**3*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 3*b**3*c*d**3*n**2*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 2*b**3*c*d**3*n*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + b**3*d**4*n**3*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*b**3*d**4*n**2*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 11*b**3*d**4*n*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*b**3*d**4*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4), True))","A",0
1853,1,1506,0,2.088719," ","integrate((b*x+a)**2*(d*x+c)**n,x)","\begin{cases} c^{n} \left(a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3}\right) & \text{for}\: d = 0 \\- \frac{a^{2} d^{2}}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} - \frac{2 a b c d}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} - \frac{4 a b d^{2} x}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} + \frac{2 b^{2} c^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} + \frac{3 b^{2} c^{2}}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} + \frac{4 b^{2} c d x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} + \frac{4 b^{2} c d x}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} + \frac{2 b^{2} d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{3} + 4 c d^{4} x + 2 d^{5} x^{2}} & \text{for}\: n = -3 \\- \frac{a^{2} d^{2}}{c d^{3} + d^{4} x} + \frac{2 a b c d \log{\left(\frac{c}{d} + x \right)}}{c d^{3} + d^{4} x} + \frac{2 a b c d}{c d^{3} + d^{4} x} + \frac{2 a b d^{2} x \log{\left(\frac{c}{d} + x \right)}}{c d^{3} + d^{4} x} - \frac{2 b^{2} c^{2} \log{\left(\frac{c}{d} + x \right)}}{c d^{3} + d^{4} x} - \frac{2 b^{2} c^{2}}{c d^{3} + d^{4} x} - \frac{2 b^{2} c d x \log{\left(\frac{c}{d} + x \right)}}{c d^{3} + d^{4} x} + \frac{b^{2} d^{2} x^{2}}{c d^{3} + d^{4} x} & \text{for}\: n = -2 \\\frac{a^{2} \log{\left(\frac{c}{d} + x \right)}}{d} - \frac{2 a b c \log{\left(\frac{c}{d} + x \right)}}{d^{2}} + \frac{2 a b x}{d} + \frac{b^{2} c^{2} \log{\left(\frac{c}{d} + x \right)}}{d^{3}} - \frac{b^{2} c x}{d^{2}} + \frac{b^{2} x^{2}}{2 d} & \text{for}\: n = -1 \\\frac{a^{2} c d^{2} n^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{5 a^{2} c d^{2} n \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{6 a^{2} c d^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{a^{2} d^{3} n^{2} x \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{5 a^{2} d^{3} n x \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{6 a^{2} d^{3} x \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} - \frac{2 a b c^{2} d n \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} - \frac{6 a b c^{2} d \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{2 a b c d^{2} n^{2} x \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{6 a b c d^{2} n x \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{2 a b d^{3} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{8 a b d^{3} n x^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{6 a b d^{3} x^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{2 b^{2} c^{3} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} - \frac{2 b^{2} c^{2} d n x \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{b^{2} c d^{2} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{b^{2} c d^{2} n x^{2} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{b^{2} d^{3} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{3 b^{2} d^{3} n x^{3} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} + \frac{2 b^{2} d^{3} x^{3} \left(c + d x\right)^{n}}{d^{3} n^{3} + 6 d^{3} n^{2} + 11 d^{3} n + 6 d^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a**2*x + a*b*x**2 + b**2*x**3/3), Eq(d, 0)), (-a**2*d**2/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) - 2*a*b*c*d/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) - 4*a*b*d**2*x/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) + 2*b**2*c**2*log(c/d + x)/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) + 3*b**2*c**2/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) + 4*b**2*c*d*x*log(c/d + x)/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) + 4*b**2*c*d*x/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2) + 2*b**2*d**2*x**2*log(c/d + x)/(2*c**2*d**3 + 4*c*d**4*x + 2*d**5*x**2), Eq(n, -3)), (-a**2*d**2/(c*d**3 + d**4*x) + 2*a*b*c*d*log(c/d + x)/(c*d**3 + d**4*x) + 2*a*b*c*d/(c*d**3 + d**4*x) + 2*a*b*d**2*x*log(c/d + x)/(c*d**3 + d**4*x) - 2*b**2*c**2*log(c/d + x)/(c*d**3 + d**4*x) - 2*b**2*c**2/(c*d**3 + d**4*x) - 2*b**2*c*d*x*log(c/d + x)/(c*d**3 + d**4*x) + b**2*d**2*x**2/(c*d**3 + d**4*x), Eq(n, -2)), (a**2*log(c/d + x)/d - 2*a*b*c*log(c/d + x)/d**2 + 2*a*b*x/d + b**2*c**2*log(c/d + x)/d**3 - b**2*c*x/d**2 + b**2*x**2/(2*d), Eq(n, -1)), (a**2*c*d**2*n**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 5*a**2*c*d**2*n*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 6*a**2*c*d**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + a**2*d**3*n**2*x*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 5*a**2*d**3*n*x*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 6*a**2*d**3*x*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) - 2*a*b*c**2*d*n*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) - 6*a*b*c**2*d*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 2*a*b*c*d**2*n**2*x*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 6*a*b*c*d**2*n*x*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 2*a*b*d**3*n**2*x**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 8*a*b*d**3*n*x**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 6*a*b*d**3*x**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 2*b**2*c**3*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) - 2*b**2*c**2*d*n*x*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + b**2*c*d**2*n**2*x**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + b**2*c*d**2*n*x**2*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + b**2*d**3*n**2*x**3*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 3*b**2*d**3*n*x**3*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3) + 2*b**2*d**3*x**3*(c + d*x)**n/(d**3*n**3 + 6*d**3*n**2 + 11*d**3*n + 6*d**3), True))","A",0
1854,1,377,0,0.821589," ","integrate((b*x+a)*(d*x+c)**n,x)","\begin{cases} c^{n} \left(a x + \frac{b x^{2}}{2}\right) & \text{for}\: d = 0 \\- \frac{a d}{c d^{2} + d^{3} x} + \frac{b c \log{\left(\frac{c}{d} + x \right)}}{c d^{2} + d^{3} x} + \frac{b c}{c d^{2} + d^{3} x} + \frac{b d x \log{\left(\frac{c}{d} + x \right)}}{c d^{2} + d^{3} x} & \text{for}\: n = -2 \\\frac{a \log{\left(\frac{c}{d} + x \right)}}{d} - \frac{b c \log{\left(\frac{c}{d} + x \right)}}{d^{2}} + \frac{b x}{d} & \text{for}\: n = -1 \\\frac{a c d n \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} + \frac{2 a c d \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} + \frac{a d^{2} n x \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} + \frac{2 a d^{2} x \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} - \frac{b c^{2} \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} + \frac{b c d n x \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} + \frac{b d^{2} n x^{2} \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} + \frac{b d^{2} x^{2} \left(c + d x\right)^{n}}{d^{2} n^{2} + 3 d^{2} n + 2 d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a*x + b*x**2/2), Eq(d, 0)), (-a*d/(c*d**2 + d**3*x) + b*c*log(c/d + x)/(c*d**2 + d**3*x) + b*c/(c*d**2 + d**3*x) + b*d*x*log(c/d + x)/(c*d**2 + d**3*x), Eq(n, -2)), (a*log(c/d + x)/d - b*c*log(c/d + x)/d**2 + b*x/d, Eq(n, -1)), (a*c*d*n*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) + 2*a*c*d*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) + a*d**2*n*x*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) + 2*a*d**2*x*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) - b*c**2*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) + b*c*d*n*x*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) + b*d**2*n*x**2*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2) + b*d**2*x**2*(c + d*x)**n/(d**2*n**2 + 3*d**2*n + 2*d**2), True))","A",0
1855,1,20,0,0.063462," ","integrate((d*x+c)**n,x)","\frac{\begin{cases} \frac{\left(c + d x\right)^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(c + d x \right)} & \text{otherwise} \end{cases}}{d}"," ",0,"Piecewise(((c + d*x)**(n + 1)/(n + 1), Ne(n, -1)), (log(c + d*x), True))/d","A",0
1856,0,0,0,0.000000," ","integrate((d*x+c)**n/(b*x+a),x)","\int \frac{\left(c + d x\right)^{n}}{a + b x}\, dx"," ",0,"Integral((c + d*x)**n/(a + b*x), x)","F",0
1857,0,0,0,0.000000," ","integrate((d*x+c)**n/(b*x+a)**2,x)","\int \frac{\left(c + d x\right)^{n}}{\left(a + b x\right)^{2}}\, dx"," ",0,"Integral((c + d*x)**n/(a + b*x)**2, x)","F",0
1858,0,0,0,0.000000," ","integrate((d*x+c)**n/(b*x+a)**3,x)","\int \frac{\left(c + d x\right)^{n}}{\left(a + b x\right)^{3}}\, dx"," ",0,"Integral((c + d*x)**n/(a + b*x)**3, x)","F",0
1859,-1,0,0,0.000000," ","integrate((b*x+a)**(-4+n)/((d*x+c)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1860,-1,0,0,0.000000," ","integrate((b*x+a)**(-3+n)/((d*x+c)**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1861,-2,0,0,0.000000," ","integrate((b*x+a)**(-2+n)/((d*x+c)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1862,-2,0,0,0.000000," ","integrate((b*x+a)**(-1+n)/((d*x+c)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1863,-2,0,0,0.000000," ","integrate((b*x+a)**n/((d*x+c)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1864,-2,0,0,0.000000," ","integrate((b*x+a)**(1+n)/((d*x+c)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1865,-2,0,0,0.000000," ","integrate((b*x+a)**(2+n)/((d*x+c)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1866,-2,0,0,0.000000," ","integrate((d*x+c)**n/((b*x+a)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1867,-1,0,0,0.000000," ","integrate((b*x+a)**(-1-n)*(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1868,-2,0,0,0.000000," ","integrate((b*x+a)**(-2-n)*(d*x+c)**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1869,-1,0,0,0.000000," ","integrate((b*x+a)**(-3-n)*(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1870,-1,0,0,0.000000," ","integrate((b*x+a)**(-4-n)*(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1871,-1,0,0,0.000000," ","integrate((b*x+a)**(-5-n)*(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1872,-2,0,0,0.000000," ","integrate((b*x+a)**n/((d*x+c)**n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1873,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x+c)**(-1-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1874,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x+c)**(-2-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1875,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x+c)**(-3-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1876,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x+c)**(-4-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1877,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x+c)**(-5-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1878,-2,0,0,0.000000," ","integrate((b*x+a)**(-2+n)*(d*x+c)**(1-n),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1879,-1,0,0,0.000000," ","integrate((b*x+a)**(1+n)*(d*x+c)**(-1-n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1880,0,0,0,0.000000," ","integrate((b*x+a)**m/(d*x+c),x)","\int \frac{\left(a + b x\right)^{m}}{c + d x}\, dx"," ",0,"Integral((a + b*x)**m/(c + d*x), x)","F",0
1881,1,233,0,0.694267," ","integrate(1/(b*x+a)**2/(d*x+c),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
1882,-1,0,0,0.000000," ","integrate((b*x+a)**m*(a*c*(1+m)+b*c*(2+m)*x)**(-3-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1883,-1,0,0,0.000000," ","integrate((b*x+a)**(-1-b*c/(-a*d+b*c))*(d*x+c)**(-1+a*d/(-a*d+b*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1884,-1,0,0,0.000000," ","integrate((b*x+a)**((a*d-2*b*c)/(-a*d+b*c))*(d*x+c)**((-2*a*d+b*c)/(a*d-b*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1885,1,29,0,2.107730," ","integrate((1-x)**n/(1+x)**(1/2),x)","2 \cdot 2^{n} \sqrt{x + 1} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - n \\ \frac{3}{2} \end{matrix}\middle| {\frac{\left(x + 1\right) e^{2 i \pi}}{2}} \right)}"," ",0,"2*2**n*sqrt(x + 1)*hyper((1/2, -n), (3/2,), (x + 1)*exp_polar(2*I*pi)/2)","C",0
1886,1,31,0,2.123574," ","integrate((1+x)**n/(1-x)**(1/2),x)","- 2 \cdot 2^{n} i \sqrt{x - 1} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - n \\ \frac{3}{2} \end{matrix}\middle| {\frac{\left(x - 1\right) e^{i \pi}}{2}} \right)}"," ",0,"-2*2**n*I*sqrt(x - 1)*hyper((1/2, -n), (3/2,), (x - 1)*exp_polar(I*pi)/2)","C",0
1887,1,37,0,89.943457," ","integrate((1-x)**n*(1+x)**(7/3),x)","\frac{2^{n} \left(x + 1\right)^{\frac{10}{3}} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{10}{3}, - n \\ \frac{13}{3} \end{matrix}\middle| {\frac{\left(x + 1\right) e^{2 i \pi}}{2}} \right)}}{\Gamma\left(\frac{13}{3}\right)}"," ",0,"2**n*(x + 1)**(10/3)*gamma(10/3)*hyper((10/3, -n), (13/3,), (x + 1)*exp_polar(2*I*pi)/2)/gamma(13/3)","C",0
1888,1,42,0,90.088769," ","integrate((1-x)**(7/3)*(1+x)**n,x)","\frac{\sqrt[3]{-1} \cdot 2^{n} \left(x - 1\right)^{\frac{10}{3}} \Gamma\left(\frac{10}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{10}{3}, - n \\ \frac{13}{3} \end{matrix}\middle| {\frac{\left(x - 1\right) e^{i \pi}}{2}} \right)}}{\Gamma\left(\frac{13}{3}\right)}"," ",0,"(-1)**(1/3)*2**n*(x - 1)**(10/3)*gamma(10/3)*hyper((10/3, -n), (13/3,), (x - 1)*exp_polar(I*pi)/2)/gamma(13/3)","C",0
1889,1,42,0,25.034105," ","integrate((2+3*x)**m/((1+2*x)**m),x)","\frac{3^{2 m} \left(x + \frac{2}{3}\right) \left(x + \frac{2}{3}\right)^{m} e^{- i \pi m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} m, m + 1 \\ m + 2 \end{matrix}\middle| {6 x + 4} \right)}}{\Gamma\left(m + 2\right)}"," ",0,"3**(2*m)*(x + 2/3)*(x + 2/3)**m*exp(-I*pi*m)*gamma(m + 1)*hyper((m, m + 1), (m + 2,), 6*x + 4)/gamma(m + 2)","C",0
1890,-2,0,0,0.000000," ","integrate((d*(b*x+a)/(a*d-b*c))**m*(d*x+c)**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1891,1,22,0,0.059749," ","integrate(d*x**3+c*x**2+b*x+a,x)","a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3} + \frac{d x^{4}}{4}"," ",0,"a*x + b*x**2/2 + c*x**3/3 + d*x**4/4","A",0
1892,1,8,0,0.054209," ","integrate(x**4-x**3,x)","\frac{x^{5}}{5} - \frac{x^{4}}{4}"," ",0,"x**5/5 - x**4/4","A",0
1893,1,5,0,0.053756," ","integrate(x**5-1,x)","\frac{x^{6}}{6} - x"," ",0,"x**6/6 - x","A",0
1894,1,7,0,0.052978," ","integrate(7+4*x,x)","2 x^{2} + 7 x"," ",0,"2*x**2 + 7*x","A",0
1895,1,10,0,0.055329," ","integrate(pi*x**3+4*x,x)","\frac{\pi x^{4}}{4} + 2 x^{2}"," ",0,"pi*x**4/4 + 2*x**2","A",0
1896,1,8,0,0.054284," ","integrate(5*x**2+2*x,x)","\frac{5 x^{3}}{3} + x^{2}"," ",0,"5*x**3/3 + x**2","A",0
1897,1,8,0,0.055268," ","integrate(1/2*x**2+1/3*x**3,x)","\frac{x^{4}}{12} + \frac{x^{3}}{6}"," ",0,"x**4/12 + x**3/6","A",0
1898,1,15,0,0.056638," ","integrate(2*x**2-5*x+3,x)","\frac{2 x^{3}}{3} - \frac{5 x^{2}}{2} + 3 x"," ",0,"2*x**3/3 - 5*x**2/2 + 3*x","A",0
1899,1,12,0,0.054165," ","integrate(x**3+x**2-2*x,x)","\frac{x^{4}}{4} + \frac{x^{3}}{3} - x^{2}"," ",0,"x**4/4 + x**3/3 - x**2","A",0
1900,1,10,0,0.055646," ","integrate(-3*x**5-x**2+1,x)","- \frac{x^{6}}{2} - \frac{x^{3}}{3} + x"," ",0,"-x**6/2 - x**3/3 + x","A",0
1901,1,12,0,0.057240," ","integrate(4*x**3+3*x**2+2*x+5,x)","x^{4} + x^{3} + x^{2} + 5 x"," ",0,"x**4 + x**3 + x**2 + 5*x","A",0
1902,1,20,0,0.160390," ","integrate(a+d/x**3+c/x**2+b/x,x)","a x + b \log{\left(x \right)} + \frac{- 2 c x - d}{2 x^{2}}"," ",0,"a*x + b*log(x) + (-2*c*x - d)/(2*x**2)","A",0
1903,1,15,0,0.080724," ","integrate(1/x**5+x+x**5,x)","\frac{x^{6}}{6} + \frac{x^{2}}{2} - \frac{1}{4 x^{4}}"," ",0,"x**6/6 + x**2/2 - 1/(4*x**4)","A",0
1904,1,14,0,0.085456," ","integrate(1/x**3+1/x**2+1/x,x)","\log{\left(x \right)} + \frac{- 2 x - 1}{2 x^{2}}"," ",0,"log(x) + (-2*x - 1)/(2*x**2)","A",0
1905,1,7,0,0.078130," ","integrate(-2/x**2+3/x,x)","3 \log{\left(x \right)} + \frac{2}{x}"," ",0,"3*log(x) + 2/x","A",0
1906,1,10,0,0.083098," ","integrate(-1/7/x**6+x**6,x)","\frac{x^{7}}{7} + \frac{1}{35 x^{5}}"," ",0,"x**7/7 + 1/(35*x**5)","A",0
1907,1,8,0,0.075924," ","integrate(1+1/x+x,x)","\frac{x^{2}}{2} + x + \log{\left(x \right)}"," ",0,"x**2/2 + x + log(x)","A",0
1908,1,8,0,0.076153," ","integrate(-3/x**3+4/x**2,x)","\frac{3 - 8 x}{2 x^{2}}"," ",0,"(3 - 8*x)/(2*x**2)","A",0
1909,1,10,0,0.076156," ","integrate(1/x+2*x+x**2,x)","\frac{x^{3}}{3} + x^{2} + \log{\left(x \right)}"," ",0,"x**3/3 + x**2 + log(x)","A",0
1910,1,12,0,0.058915," ","integrate(x**(5/6)-x**3,x)","\frac{6 x^{\frac{11}{6}}}{11} - \frac{x^{4}}{4}"," ",0,"6*x**(11/6)/11 - x**4/4","A",0
1911,1,10,0,0.057461," ","integrate(33+x**(1/33),x)","\frac{33 x^{\frac{34}{33}}}{34} + 33 x"," ",0,"33*x**(34/33)/34 + 33*x","A",0
1912,1,12,0,0.060698," ","integrate(1/2/x**(1/2)+2*x**(1/2),x)","\frac{4 x^{\frac{3}{2}}}{3} + \sqrt{x}"," ",0,"4*x**(3/2)/3 + sqrt(x)","A",0
1913,1,14,0,0.060906," ","integrate(-1/x**2+10/x+6*x**(1/2),x)","4 x^{\frac{3}{2}} + 10 \log{\left(x \right)} + \frac{1}{x}"," ",0,"4*x**(3/2) + 10*log(x) + 1/x","A",0
1914,1,14,0,0.059253," ","integrate(1/x**(3/2)+x**(3/2),x)","\frac{2 x^{\frac{5}{2}}}{5} - \frac{2}{\sqrt{x}}"," ",0,"2*x**(5/2)/5 - 2/sqrt(x)","A",0
1915,1,12,0,0.060516," ","integrate(-5*x**(3/2)+7*x**(5/2),x)","2 x^{\frac{7}{2}} - 2 x^{\frac{5}{2}}"," ",0,"2*x**(7/2) - 2*x**(5/2)","A",0
1916,1,19,0,0.061885," ","integrate(-1/2*x+2/x**(1/2)+x**(1/2),x)","\frac{2 x^{\frac{3}{2}}}{3} + 4 \sqrt{x} - \frac{x^{2}}{4}"," ",0,"2*x**(3/2)/3 + 4*sqrt(x) - x**2/4","A",0
1917,1,20,0,0.061780," ","integrate(-2/x+x**(3/2)+1/5*x**(1/2),x)","\frac{2 x^{\frac{5}{2}}}{5} + \frac{2 x^{\frac{3}{2}}}{15} - 2 \log{\left(x \right)}"," ",0,"2*x**(5/2)/5 + 2*x**(3/2)/15 - 2*log(x)","A",0
