1,1,14,0,0.170581," ","integrate(x**3*ln(c*x),x)","\frac{x^{4} \log{\left(c x \right)}}{4} - \frac{x^{4}}{16}"," ",0,"x**4*log(c*x)/4 - x**4/16","A",0
2,1,14,0,0.105098," ","integrate(x**2*ln(c*x),x)","\frac{x^{3} \log{\left(c x \right)}}{3} - \frac{x^{3}}{9}"," ",0,"x**3*log(c*x)/3 - x**3/9","A",0
3,1,14,0,0.100882," ","integrate(x*ln(c*x),x)","\frac{x^{2} \log{\left(c x \right)}}{2} - \frac{x^{2}}{4}"," ",0,"x**2*log(c*x)/2 - x**2/4","A",0
4,1,7,0,0.088005," ","integrate(ln(c*x),x)","x \log{\left(c x \right)} - x"," ",0,"x*log(c*x) - x","A",0
5,1,7,0,0.090245," ","integrate(ln(c*x)/x,x)","\frac{\log{\left(c x \right)}^{2}}{2}"," ",0,"log(c*x)**2/2","A",0
6,1,10,0,0.096920," ","integrate(ln(c*x)/x**2,x)","- \frac{\log{\left(c x \right)}}{x} - \frac{1}{x}"," ",0,"-log(c*x)/x - 1/x","A",0
7,1,17,0,0.104605," ","integrate(ln(c*x)/x**3,x)","- \frac{\log{\left(c x \right)}}{2 x^{2}} - \frac{1}{4 x^{2}}"," ",0,"-log(c*x)/(2*x**2) - 1/(4*x**2)","A",0
8,1,26,0,0.116842," ","integrate(x**3*ln(c*x)**2,x)","\frac{x^{4} \log{\left(c x \right)}^{2}}{4} - \frac{x^{4} \log{\left(c x \right)}}{8} + \frac{x^{4}}{32}"," ",0,"x**4*log(c*x)**2/4 - x**4*log(c*x)/8 + x**4/32","A",0
9,1,29,0,0.114193," ","integrate(x**2*ln(c*x)**2,x)","\frac{x^{3} \log{\left(c x \right)}^{2}}{3} - \frac{2 x^{3} \log{\left(c x \right)}}{9} + \frac{2 x^{3}}{27}"," ",0,"x**3*log(c*x)**2/3 - 2*x**3*log(c*x)/9 + 2*x**3/27","A",0
10,1,26,0,0.108357," ","integrate(x*ln(c*x)**2,x)","\frac{x^{2} \log{\left(c x \right)}^{2}}{2} - \frac{x^{2} \log{\left(c x \right)}}{2} + \frac{x^{2}}{4}"," ",0,"x**2*log(c*x)**2/2 - x**2*log(c*x)/2 + x**2/4","A",0
11,1,19,0,0.097522," ","integrate(ln(c*x)**2,x)","x \log{\left(c x \right)}^{2} - 2 x \log{\left(c x \right)} + 2 x"," ",0,"x*log(c*x)**2 - 2*x*log(c*x) + 2*x","A",0
12,1,7,0,0.091784," ","integrate(ln(c*x)**2/x,x)","\frac{\log{\left(c x \right)}^{3}}{3}"," ",0,"log(c*x)**3/3","A",0
13,1,20,0,0.118302," ","integrate(ln(c*x)**2/x**2,x)","- \frac{\log{\left(c x \right)}^{2}}{x} - \frac{2 \log{\left(c x \right)}}{x} - \frac{2}{x}"," ",0,"-log(c*x)**2/x - 2*log(c*x)/x - 2/x","A",0
14,1,29,0,0.125924," ","integrate(ln(c*x)**2/x**3,x)","- \frac{\log{\left(c x \right)}^{2}}{2 x^{2}} - \frac{\log{\left(c x \right)}}{2 x^{2}} - \frac{1}{4 x^{2}}"," ",0,"-log(c*x)**2/(2*x**2) - log(c*x)/(2*x**2) - 1/(4*x**2)","A",0
15,1,42,0,0.131275," ","integrate(x**3*ln(c*x)**3,x)","\frac{x^{4} \log{\left(c x \right)}^{3}}{4} - \frac{3 x^{4} \log{\left(c x \right)}^{2}}{16} + \frac{3 x^{4} \log{\left(c x \right)}}{32} - \frac{3 x^{4}}{128}"," ",0,"x**4*log(c*x)**3/4 - 3*x**4*log(c*x)**2/16 + 3*x**4*log(c*x)/32 - 3*x**4/128","A",0
16,1,41,0,0.132733," ","integrate(x**2*ln(c*x)**3,x)","\frac{x^{3} \log{\left(c x \right)}^{3}}{3} - \frac{x^{3} \log{\left(c x \right)}^{2}}{3} + \frac{2 x^{3} \log{\left(c x \right)}}{9} - \frac{2 x^{3}}{27}"," ",0,"x**3*log(c*x)**3/3 - x**3*log(c*x)**2/3 + 2*x**3*log(c*x)/9 - 2*x**3/27","A",0
17,1,42,0,0.127298," ","integrate(x*ln(c*x)**3,x)","\frac{x^{2} \log{\left(c x \right)}^{3}}{2} - \frac{3 x^{2} \log{\left(c x \right)}^{2}}{4} + \frac{3 x^{2} \log{\left(c x \right)}}{4} - \frac{3 x^{2}}{8}"," ",0,"x**2*log(c*x)**3/2 - 3*x**2*log(c*x)**2/4 + 3*x**2*log(c*x)/4 - 3*x**2/8","A",0
18,1,29,0,0.110409," ","integrate(ln(c*x)**3,x)","x \log{\left(c x \right)}^{3} - 3 x \log{\left(c x \right)}^{2} + 6 x \log{\left(c x \right)} - 6 x"," ",0,"x*log(c*x)**3 - 3*x*log(c*x)**2 + 6*x*log(c*x) - 6*x","A",0
19,1,7,0,0.091143," ","integrate(ln(c*x)**3/x,x)","\frac{\log{\left(c x \right)}^{4}}{4}"," ",0,"log(c*x)**4/4","A",0
20,1,31,0,0.133752," ","integrate(ln(c*x)**3/x**2,x)","- \frac{\log{\left(c x \right)}^{3}}{x} - \frac{3 \log{\left(c x \right)}^{2}}{x} - \frac{6 \log{\left(c x \right)}}{x} - \frac{6}{x}"," ",0,"-log(c*x)**3/x - 3*log(c*x)**2/x - 6*log(c*x)/x - 6/x","A",0
21,1,44,0,0.144132," ","integrate(ln(c*x)**3/x**3,x)","- \frac{\log{\left(c x \right)}^{3}}{2 x^{2}} - \frac{3 \log{\left(c x \right)}^{2}}{4 x^{2}} - \frac{3 \log{\left(c x \right)}}{4 x^{2}} - \frac{3}{8 x^{2}}"," ",0,"-log(c*x)**3/(2*x**2) - 3*log(c*x)**2/(4*x**2) - 3*log(c*x)/(4*x**2) - 3/(8*x**2)","A",0
22,0,0,0,0.000000," ","integrate(x**3/ln(c*x),x)","\int \frac{x^{3}}{\log{\left(c x \right)}}\, dx"," ",0,"Integral(x**3/log(c*x), x)","F",0
23,0,0,0,0.000000," ","integrate(x**2/ln(c*x),x)","\int \frac{x^{2}}{\log{\left(c x \right)}}\, dx"," ",0,"Integral(x**2/log(c*x), x)","F",0
24,0,0,0,0.000000," ","integrate(x/ln(c*x),x)","\int \frac{x}{\log{\left(c x \right)}}\, dx"," ",0,"Integral(x/log(c*x), x)","F",0
25,1,5,0,0.478589," ","integrate(1/ln(c*x),x)","\frac{\operatorname{li}{\left(c x \right)}}{c}"," ",0,"li(c*x)/c","A",0
26,1,5,0,0.104510," ","integrate(1/x/ln(c*x),x)","\log{\left(\log{\left(c x \right)} \right)}"," ",0,"log(log(c*x))","A",0
27,0,0,0,0.000000," ","integrate(1/x**2/ln(c*x),x)","\int \frac{1}{x^{2} \log{\left(c x \right)}}\, dx"," ",0,"Integral(1/(x**2*log(c*x)), x)","F",0
28,0,0,0,0.000000," ","integrate(1/x**3/ln(c*x),x)","\int \frac{1}{x^{3} \log{\left(c x \right)}}\, dx"," ",0,"Integral(1/(x**3*log(c*x)), x)","F",0
29,0,0,0,0.000000," ","integrate(x**3/ln(c*x)**2,x)","- \frac{x^{4}}{\log{\left(c x \right)}} + 4 \int \frac{x^{3}}{\log{\left(c x \right)}}\, dx"," ",0,"-x**4/log(c*x) + 4*Integral(x**3/log(c*x), x)","F",0
30,0,0,0,0.000000," ","integrate(x**2/ln(c*x)**2,x)","- \frac{x^{3}}{\log{\left(c x \right)}} + 3 \int \frac{x^{2}}{\log{\left(c x \right)}}\, dx"," ",0,"-x**3/log(c*x) + 3*Integral(x**2/log(c*x), x)","F",0
31,0,0,0,0.000000," ","integrate(x/ln(c*x)**2,x)","- \frac{x^{2}}{\log{\left(c x \right)}} + 2 \int \frac{x}{\log{\left(c x \right)}}\, dx"," ",0,"-x**2/log(c*x) + 2*Integral(x/log(c*x), x)","F",0
32,1,12,0,0.504148," ","integrate(1/ln(c*x)**2,x)","- \frac{x}{\log{\left(c x \right)}} + \frac{\operatorname{li}{\left(c x \right)}}{c}"," ",0,"-x/log(c*x) + li(c*x)/c","A",0
33,1,7,0,0.088996," ","integrate(1/x/ln(c*x)**2,x)","- \frac{1}{\log{\left(c x \right)}}"," ",0,"-1/log(c*x)","A",0
34,0,0,0,0.000000," ","integrate(1/x**2/ln(c*x)**2,x)","- \int \frac{1}{x^{2} \log{\left(c x \right)}}\, dx - \frac{1}{x \log{\left(c x \right)}}"," ",0,"-Integral(1/(x**2*log(c*x)), x) - 1/(x*log(c*x))","F",0
35,0,0,0,0.000000," ","integrate(1/x**3/ln(c*x)**2,x)","- 2 \int \frac{1}{x^{3} \log{\left(c x \right)}}\, dx - \frac{1}{x^{2} \log{\left(c x \right)}}"," ",0,"-2*Integral(1/(x**3*log(c*x)), x) - 1/(x**2*log(c*x))","F",0
36,0,0,0,0.000000," ","integrate(x**3/ln(c*x)**3,x)","\frac{- 4 x^{4} \log{\left(c x \right)} - x^{4}}{2 \log{\left(c x \right)}^{2}} + 8 \int \frac{x^{3}}{\log{\left(c x \right)}}\, dx"," ",0,"(-4*x**4*log(c*x) - x**4)/(2*log(c*x)**2) + 8*Integral(x**3/log(c*x), x)","F",0
37,0,0,0,0.000000," ","integrate(x**2/ln(c*x)**3,x)","\frac{- 3 x^{3} \log{\left(c x \right)} - x^{3}}{2 \log{\left(c x \right)}^{2}} + \frac{9 \int \frac{x^{2}}{\log{\left(c x \right)}}\, dx}{2}"," ",0,"(-3*x**3*log(c*x) - x**3)/(2*log(c*x)**2) + 9*Integral(x**2/log(c*x), x)/2","F",0
38,0,0,0,0.000000," ","integrate(x/ln(c*x)**3,x)","\frac{- 2 x^{2} \log{\left(c x \right)} - x^{2}}{2 \log{\left(c x \right)}^{2}} + 2 \int \frac{x}{\log{\left(c x \right)}}\, dx"," ",0,"(-2*x**2*log(c*x) - x**2)/(2*log(c*x)**2) + 2*Integral(x/log(c*x), x)","F",0
39,1,26,0,0.502571," ","integrate(1/ln(c*x)**3,x)","\frac{- x \log{\left(c x \right)} - x}{2 \log{\left(c x \right)}^{2}} + \frac{\operatorname{li}{\left(c x \right)}}{2 c}"," ",0,"(-x*log(c*x) - x)/(2*log(c*x)**2) + li(c*x)/(2*c)","A",0
40,1,10,0,0.092457," ","integrate(1/x/ln(c*x)**3,x)","- \frac{1}{2 \log{\left(c x \right)}^{2}}"," ",0,"-1/(2*log(c*x)**2)","A",0
41,0,0,0,0.000000," ","integrate(1/x**2/ln(c*x)**3,x)","\frac{\int \frac{1}{x^{2} \log{\left(c x \right)}}\, dx}{2} + \frac{\log{\left(c x \right)} - 1}{2 x \log{\left(c x \right)}^{2}}"," ",0,"Integral(1/(x**2*log(c*x)), x)/2 + (log(c*x) - 1)/(2*x*log(c*x)**2)","F",0
42,0,0,0,0.000000," ","integrate(1/x**3/ln(c*x)**3,x)","2 \int \frac{1}{x^{3} \log{\left(c x \right)}}\, dx + \frac{2 \log{\left(c x \right)} - 1}{2 x^{2} \log{\left(c x \right)}^{2}}"," ",0,"2*Integral(1/(x**3*log(c*x)), x) + (2*log(c*x) - 1)/(2*x**2*log(c*x)**2)","F",0
43,1,36,0,1.364791," ","integrate(x**3*(a+b*ln(c*x**n)),x)","\frac{a x^{4}}{4} + \frac{b n x^{4} \log{\left(x \right)}}{4} - \frac{b n x^{4}}{16} + \frac{b x^{4} \log{\left(c \right)}}{4}"," ",0,"a*x**4/4 + b*n*x**4*log(x)/4 - b*n*x**4/16 + b*x**4*log(c)/4","A",0
44,1,36,0,0.779682," ","integrate(x**2*(a+b*ln(c*x**n)),x)","\frac{a x^{3}}{3} + \frac{b n x^{3} \log{\left(x \right)}}{3} - \frac{b n x^{3}}{9} + \frac{b x^{3} \log{\left(c \right)}}{3}"," ",0,"a*x**3/3 + b*n*x**3*log(x)/3 - b*n*x**3/9 + b*x**3*log(c)/3","A",0
45,1,36,0,0.464514," ","integrate(x*(a+b*ln(c*x**n)),x)","\frac{a x^{2}}{2} + \frac{b n x^{2} \log{\left(x \right)}}{2} - \frac{b n x^{2}}{4} + \frac{b x^{2} \log{\left(c \right)}}{2}"," ",0,"a*x**2/2 + b*n*x**2*log(x)/2 - b*n*x**2/4 + b*x**2*log(c)/2","A",0
46,1,19,0,0.249357," ","integrate(a+b*ln(c*x**n),x)","a x + b \left(n x \log{\left(x \right)} - n x + x \log{\left(c \right)}\right)"," ",0,"a*x + b*(n*x*log(x) - n*x + x*log(c))","A",0
47,1,34,0,8.602710," ","integrate((a+b*ln(c*x**n))/x,x)","\begin{cases} a \log{\left(x \right)} & \text{for}\: b = 0 \\- \left(- a - b \log{\left(c \right)}\right) \log{\left(x \right)} & \text{for}\: n = 0 \\\frac{\left(- a - b \log{\left(c x^{n} \right)}\right)^{2}}{2 b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(x), Eq(b, 0)), (-(-a - b*log(c))*log(x), Eq(n, 0)), ((-a - b*log(c*x**n))**2/(2*b*n), True))","A",0
48,1,24,0,0.455816," ","integrate((a+b*ln(c*x**n))/x**2,x)","- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}"," ",0,"-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x","A",0
49,1,37,0,0.938315," ","integrate((a+b*ln(c*x**n))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{b n \log{\left(x \right)}}{2 x^{2}} - \frac{b n}{4 x^{2}} - \frac{b \log{\left(c \right)}}{2 x^{2}}"," ",0,"-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2)","A",0
50,1,131,0,2.402811," ","integrate(x**3*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} x^{4}}{4} + \frac{a b n x^{4} \log{\left(x \right)}}{2} - \frac{a b n x^{4}}{8} + \frac{a b x^{4} \log{\left(c \right)}}{2} + \frac{b^{2} n^{2} x^{4} \log{\left(x \right)}^{2}}{4} - \frac{b^{2} n^{2} x^{4} \log{\left(x \right)}}{8} + \frac{b^{2} n^{2} x^{4}}{32} + \frac{b^{2} n x^{4} \log{\left(c \right)} \log{\left(x \right)}}{2} - \frac{b^{2} n x^{4} \log{\left(c \right)}}{8} + \frac{b^{2} x^{4} \log{\left(c \right)}^{2}}{4}"," ",0,"a**2*x**4/4 + a*b*n*x**4*log(x)/2 - a*b*n*x**4/8 + a*b*x**4*log(c)/2 + b**2*n**2*x**4*log(x)**2/4 - b**2*n**2*x**4*log(x)/8 + b**2*n**2*x**4/32 + b**2*n*x**4*log(c)*log(x)/2 - b**2*n*x**4*log(c)/8 + b**2*x**4*log(c)**2/4","B",0
51,1,143,0,1.517677," ","integrate(x**2*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} x^{3}}{3} + \frac{2 a b n x^{3} \log{\left(x \right)}}{3} - \frac{2 a b n x^{3}}{9} + \frac{2 a b x^{3} \log{\left(c \right)}}{3} + \frac{b^{2} n^{2} x^{3} \log{\left(x \right)}^{2}}{3} - \frac{2 b^{2} n^{2} x^{3} \log{\left(x \right)}}{9} + \frac{2 b^{2} n^{2} x^{3}}{27} + \frac{2 b^{2} n x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{2 b^{2} n x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} x^{3} \log{\left(c \right)}^{2}}{3}"," ",0,"a**2*x**3/3 + 2*a*b*n*x**3*log(x)/3 - 2*a*b*n*x**3/9 + 2*a*b*x**3*log(c)/3 + b**2*n**2*x**3*log(x)**2/3 - 2*b**2*n**2*x**3*log(x)/9 + 2*b**2*n**2*x**3/27 + 2*b**2*n*x**3*log(c)*log(x)/3 - 2*b**2*n*x**3*log(c)/9 + b**2*x**3*log(c)**2/3","B",0
52,1,126,0,0.927525," ","integrate(x*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} x^{2}}{2} + a b n x^{2} \log{\left(x \right)} - \frac{a b n x^{2}}{2} + a b x^{2} \log{\left(c \right)} + \frac{b^{2} n^{2} x^{2} \log{\left(x \right)}^{2}}{2} - \frac{b^{2} n^{2} x^{2} \log{\left(x \right)}}{2} + \frac{b^{2} n^{2} x^{2}}{4} + b^{2} n x^{2} \log{\left(c \right)} \log{\left(x \right)} - \frac{b^{2} n x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} x^{2} \log{\left(c \right)}^{2}}{2}"," ",0,"a**2*x**2/2 + a*b*n*x**2*log(x) - a*b*n*x**2/2 + a*b*x**2*log(c) + b**2*n**2*x**2*log(x)**2/2 - b**2*n**2*x**2*log(x)/2 + b**2*n**2*x**2/4 + b**2*n*x**2*log(c)*log(x) - b**2*n*x**2*log(c)/2 + b**2*x**2*log(c)**2/2","B",0
53,1,109,0,0.521338," ","integrate((a+b*ln(c*x**n))**2,x)","a^{2} x + 2 a b n x \log{\left(x \right)} - 2 a b n x + 2 a b x \log{\left(c \right)} + b^{2} n^{2} x \log{\left(x \right)}^{2} - 2 b^{2} n^{2} x \log{\left(x \right)} + 2 b^{2} n^{2} x + 2 b^{2} n x \log{\left(c \right)} \log{\left(x \right)} - 2 b^{2} n x \log{\left(c \right)} + b^{2} x \log{\left(c \right)}^{2}"," ",0,"a**2*x + 2*a*b*n*x*log(x) - 2*a*b*n*x + 2*a*b*x*log(c) + b**2*n**2*x*log(x)**2 - 2*b**2*n**2*x*log(x) + 2*b**2*n**2*x + 2*b**2*n*x*log(c)*log(x) - 2*b**2*n*x*log(c) + b**2*x*log(c)**2","B",0
54,1,60,0,22.814561," ","integrate((a+b*ln(c*x**n))**2/x,x)","\begin{cases} \frac{a^{2} \log{\left(c x^{n} \right)} + a b \log{\left(c x^{n} \right)}^{2} + \frac{b^{2} \log{\left(c x^{n} \right)}^{3}}{3}}{n} & \text{for}\: n \neq 0 \\\left(a^{2} + 2 a b \log{\left(c \right)} + b^{2} \log{\left(c \right)}^{2}\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**2*log(c*x**n) + a*b*log(c*x**n)**2 + b**2*log(c*x**n)**3/3)/n, Ne(n, 0)), ((a**2 + 2*a*b*log(c) + b**2*log(c)**2)*log(x), True))","A",0
55,1,110,0,0.571882," ","integrate((a+b*ln(c*x**n))**2/x**2,x)","- \frac{a^{2}}{x} - \frac{2 a b n \log{\left(x \right)}}{x} - \frac{2 a b n}{x} - \frac{2 a b \log{\left(c \right)}}{x} - \frac{b^{2} n^{2} \log{\left(x \right)}^{2}}{x} - \frac{2 b^{2} n^{2} \log{\left(x \right)}}{x} - \frac{2 b^{2} n^{2}}{x} - \frac{2 b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{2 b^{2} n \log{\left(c \right)}}{x} - \frac{b^{2} \log{\left(c \right)}^{2}}{x}"," ",0,"-a**2/x - 2*a*b*n*log(x)/x - 2*a*b*n/x - 2*a*b*log(c)/x - b**2*n**2*log(x)**2/x - 2*b**2*n**2*log(x)/x - 2*b**2*n**2/x - 2*b**2*n*log(c)*log(x)/x - 2*b**2*n*log(c)/x - b**2*log(c)**2/x","B",0
56,1,128,0,1.123469," ","integrate((a+b*ln(c*x**n))**2/x**3,x)","- \frac{a^{2}}{2 x^{2}} - \frac{a b n \log{\left(x \right)}}{x^{2}} - \frac{a b n}{2 x^{2}} - \frac{a b \log{\left(c \right)}}{x^{2}} - \frac{b^{2} n^{2} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{b^{2} n^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{b^{2} n^{2}}{4 x^{2}} - \frac{b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} n \log{\left(c \right)}}{2 x^{2}} - \frac{b^{2} \log{\left(c \right)}^{2}}{2 x^{2}}"," ",0,"-a**2/(2*x**2) - a*b*n*log(x)/x**2 - a*b*n/(2*x**2) - a*b*log(c)/x**2 - b**2*n**2*log(x)**2/(2*x**2) - b**2*n**2*log(x)/(2*x**2) - b**2*n**2/(4*x**2) - b**2*n*log(c)*log(x)/x**2 - b**2*n*log(c)/(2*x**2) - b**2*log(c)**2/(2*x**2)","B",0
57,1,338,0,4.395910," ","integrate(x**3*(a+b*ln(c*x**n))**3,x)","\frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b n x^{4} \log{\left(x \right)}}{4} - \frac{3 a^{2} b n x^{4}}{16} + \frac{3 a^{2} b x^{4} \log{\left(c \right)}}{4} + \frac{3 a b^{2} n^{2} x^{4} \log{\left(x \right)}^{2}}{4} - \frac{3 a b^{2} n^{2} x^{4} \log{\left(x \right)}}{8} + \frac{3 a b^{2} n^{2} x^{4}}{32} + \frac{3 a b^{2} n x^{4} \log{\left(c \right)} \log{\left(x \right)}}{2} - \frac{3 a b^{2} n x^{4} \log{\left(c \right)}}{8} + \frac{3 a b^{2} x^{4} \log{\left(c \right)}^{2}}{4} + \frac{b^{3} n^{3} x^{4} \log{\left(x \right)}^{3}}{4} - \frac{3 b^{3} n^{3} x^{4} \log{\left(x \right)}^{2}}{16} + \frac{3 b^{3} n^{3} x^{4} \log{\left(x \right)}}{32} - \frac{3 b^{3} n^{3} x^{4}}{128} + \frac{3 b^{3} n^{2} x^{4} \log{\left(c \right)} \log{\left(x \right)}^{2}}{4} - \frac{3 b^{3} n^{2} x^{4} \log{\left(c \right)} \log{\left(x \right)}}{8} + \frac{3 b^{3} n^{2} x^{4} \log{\left(c \right)}}{32} + \frac{3 b^{3} n x^{4} \log{\left(c \right)}^{2} \log{\left(x \right)}}{4} - \frac{3 b^{3} n x^{4} \log{\left(c \right)}^{2}}{16} + \frac{b^{3} x^{4} \log{\left(c \right)}^{3}}{4}"," ",0,"a**3*x**4/4 + 3*a**2*b*n*x**4*log(x)/4 - 3*a**2*b*n*x**4/16 + 3*a**2*b*x**4*log(c)/4 + 3*a*b**2*n**2*x**4*log(x)**2/4 - 3*a*b**2*n**2*x**4*log(x)/8 + 3*a*b**2*n**2*x**4/32 + 3*a*b**2*n*x**4*log(c)*log(x)/2 - 3*a*b**2*n*x**4*log(c)/8 + 3*a*b**2*x**4*log(c)**2/4 + b**3*n**3*x**4*log(x)**3/4 - 3*b**3*n**3*x**4*log(x)**2/16 + 3*b**3*n**3*x**4*log(x)/32 - 3*b**3*n**3*x**4/128 + 3*b**3*n**2*x**4*log(c)*log(x)**2/4 - 3*b**3*n**2*x**4*log(c)*log(x)/8 + 3*b**3*n**2*x**4*log(c)/32 + 3*b**3*n*x**4*log(c)**2*log(x)/4 - 3*b**3*n*x**4*log(c)**2/16 + b**3*x**4*log(c)**3/4","B",0
58,1,311,0,2.889598," ","integrate(x**2*(a+b*ln(c*x**n))**3,x)","\frac{a^{3} x^{3}}{3} + a^{2} b n x^{3} \log{\left(x \right)} - \frac{a^{2} b n x^{3}}{3} + a^{2} b x^{3} \log{\left(c \right)} + a b^{2} n^{2} x^{3} \log{\left(x \right)}^{2} - \frac{2 a b^{2} n^{2} x^{3} \log{\left(x \right)}}{3} + \frac{2 a b^{2} n^{2} x^{3}}{9} + 2 a b^{2} n x^{3} \log{\left(c \right)} \log{\left(x \right)} - \frac{2 a b^{2} n x^{3} \log{\left(c \right)}}{3} + a b^{2} x^{3} \log{\left(c \right)}^{2} + \frac{b^{3} n^{3} x^{3} \log{\left(x \right)}^{3}}{3} - \frac{b^{3} n^{3} x^{3} \log{\left(x \right)}^{2}}{3} + \frac{2 b^{3} n^{3} x^{3} \log{\left(x \right)}}{9} - \frac{2 b^{3} n^{3} x^{3}}{27} + b^{3} n^{2} x^{3} \log{\left(c \right)} \log{\left(x \right)}^{2} - \frac{2 b^{3} n^{2} x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} + \frac{2 b^{3} n^{2} x^{3} \log{\left(c \right)}}{9} + b^{3} n x^{3} \log{\left(c \right)}^{2} \log{\left(x \right)} - \frac{b^{3} n x^{3} \log{\left(c \right)}^{2}}{3} + \frac{b^{3} x^{3} \log{\left(c \right)}^{3}}{3}"," ",0,"a**3*x**3/3 + a**2*b*n*x**3*log(x) - a**2*b*n*x**3/3 + a**2*b*x**3*log(c) + a*b**2*n**2*x**3*log(x)**2 - 2*a*b**2*n**2*x**3*log(x)/3 + 2*a*b**2*n**2*x**3/9 + 2*a*b**2*n*x**3*log(c)*log(x) - 2*a*b**2*n*x**3*log(c)/3 + a*b**2*x**3*log(c)**2 + b**3*n**3*x**3*log(x)**3/3 - b**3*n**3*x**3*log(x)**2/3 + 2*b**3*n**3*x**3*log(x)/9 - 2*b**3*n**3*x**3/27 + b**3*n**2*x**3*log(c)*log(x)**2 - 2*b**3*n**2*x**3*log(c)*log(x)/3 + 2*b**3*n**2*x**3*log(c)/9 + b**3*n*x**3*log(c)**2*log(x) - b**3*n*x**3*log(c)**2/3 + b**3*x**3*log(c)**3/3","B",0
59,1,337,0,1.776796," ","integrate(x*(a+b*ln(c*x**n))**3,x)","\frac{a^{3} x^{2}}{2} + \frac{3 a^{2} b n x^{2} \log{\left(x \right)}}{2} - \frac{3 a^{2} b n x^{2}}{4} + \frac{3 a^{2} b x^{2} \log{\left(c \right)}}{2} + \frac{3 a b^{2} n^{2} x^{2} \log{\left(x \right)}^{2}}{2} - \frac{3 a b^{2} n^{2} x^{2} \log{\left(x \right)}}{2} + \frac{3 a b^{2} n^{2} x^{2}}{4} + 3 a b^{2} n x^{2} \log{\left(c \right)} \log{\left(x \right)} - \frac{3 a b^{2} n x^{2} \log{\left(c \right)}}{2} + \frac{3 a b^{2} x^{2} \log{\left(c \right)}^{2}}{2} + \frac{b^{3} n^{3} x^{2} \log{\left(x \right)}^{3}}{2} - \frac{3 b^{3} n^{3} x^{2} \log{\left(x \right)}^{2}}{4} + \frac{3 b^{3} n^{3} x^{2} \log{\left(x \right)}}{4} - \frac{3 b^{3} n^{3} x^{2}}{8} + \frac{3 b^{3} n^{2} x^{2} \log{\left(c \right)} \log{\left(x \right)}^{2}}{2} - \frac{3 b^{3} n^{2} x^{2} \log{\left(c \right)} \log{\left(x \right)}}{2} + \frac{3 b^{3} n^{2} x^{2} \log{\left(c \right)}}{4} + \frac{3 b^{3} n x^{2} \log{\left(c \right)}^{2} \log{\left(x \right)}}{2} - \frac{3 b^{3} n x^{2} \log{\left(c \right)}^{2}}{4} + \frac{b^{3} x^{2} \log{\left(c \right)}^{3}}{2}"," ",0,"a**3*x**2/2 + 3*a**2*b*n*x**2*log(x)/2 - 3*a**2*b*n*x**2/4 + 3*a**2*b*x**2*log(c)/2 + 3*a*b**2*n**2*x**2*log(x)**2/2 - 3*a*b**2*n**2*x**2*log(x)/2 + 3*a*b**2*n**2*x**2/4 + 3*a*b**2*n*x**2*log(c)*log(x) - 3*a*b**2*n*x**2*log(c)/2 + 3*a*b**2*x**2*log(c)**2/2 + b**3*n**3*x**2*log(x)**3/2 - 3*b**3*n**3*x**2*log(x)**2/4 + 3*b**3*n**3*x**2*log(x)/4 - 3*b**3*n**3*x**2/8 + 3*b**3*n**2*x**2*log(c)*log(x)**2/2 - 3*b**3*n**2*x**2*log(c)*log(x)/2 + 3*b**3*n**2*x**2*log(c)/4 + 3*b**3*n*x**2*log(c)**2*log(x)/2 - 3*b**3*n*x**2*log(c)**2/4 + b**3*x**2*log(c)**3/2","B",0
60,1,270,0,1.035423," ","integrate((a+b*ln(c*x**n))**3,x)","a^{3} x + 3 a^{2} b n x \log{\left(x \right)} - 3 a^{2} b n x + 3 a^{2} b x \log{\left(c \right)} + 3 a b^{2} n^{2} x \log{\left(x \right)}^{2} - 6 a b^{2} n^{2} x \log{\left(x \right)} + 6 a b^{2} n^{2} x + 6 a b^{2} n x \log{\left(c \right)} \log{\left(x \right)} - 6 a b^{2} n x \log{\left(c \right)} + 3 a b^{2} x \log{\left(c \right)}^{2} + b^{3} n^{3} x \log{\left(x \right)}^{3} - 3 b^{3} n^{3} x \log{\left(x \right)}^{2} + 6 b^{3} n^{3} x \log{\left(x \right)} - 6 b^{3} n^{3} x + 3 b^{3} n^{2} x \log{\left(c \right)} \log{\left(x \right)}^{2} - 6 b^{3} n^{2} x \log{\left(c \right)} \log{\left(x \right)} + 6 b^{3} n^{2} x \log{\left(c \right)} + 3 b^{3} n x \log{\left(c \right)}^{2} \log{\left(x \right)} - 3 b^{3} n x \log{\left(c \right)}^{2} + b^{3} x \log{\left(c \right)}^{3}"," ",0,"a**3*x + 3*a**2*b*n*x*log(x) - 3*a**2*b*n*x + 3*a**2*b*x*log(c) + 3*a*b**2*n**2*x*log(x)**2 - 6*a*b**2*n**2*x*log(x) + 6*a*b**2*n**2*x + 6*a*b**2*n*x*log(c)*log(x) - 6*a*b**2*n*x*log(c) + 3*a*b**2*x*log(c)**2 + b**3*n**3*x*log(x)**3 - 3*b**3*n**3*x*log(x)**2 + 6*b**3*n**3*x*log(x) - 6*b**3*n**3*x + 3*b**3*n**2*x*log(c)*log(x)**2 - 6*b**3*n**2*x*log(c)*log(x) + 6*b**3*n**2*x*log(c) + 3*b**3*n*x*log(c)**2*log(x) - 3*b**3*n*x*log(c)**2 + b**3*x*log(c)**3","B",0
61,1,92,0,28.942439," ","integrate((a+b*ln(c*x**n))**3/x,x)","\begin{cases} \frac{a^{3} \log{\left(c x^{n} \right)} + \frac{3 a^{2} b \log{\left(c x^{n} \right)}^{2}}{2} + a b^{2} \log{\left(c x^{n} \right)}^{3} + \frac{b^{3} \log{\left(c x^{n} \right)}^{4}}{4}}{n} & \text{for}\: n \neq 0 \\\left(a^{3} + 3 a^{2} b \log{\left(c \right)} + 3 a b^{2} \log{\left(c \right)}^{2} + b^{3} \log{\left(c \right)}^{3}\right) \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a**3*log(c*x**n) + 3*a**2*b*log(c*x**n)**2/2 + a*b**2*log(c*x**n)**3 + b**3*log(c*x**n)**4/4)/n, Ne(n, 0)), ((a**3 + 3*a**2*b*log(c) + 3*a*b**2*log(c)**2 + b**3*log(c)**3)*log(x), True))","B",0
62,1,272,0,1.033501," ","integrate((a+b*ln(c*x**n))**3/x**2,x)","- \frac{a^{3}}{x} - \frac{3 a^{2} b n \log{\left(x \right)}}{x} - \frac{3 a^{2} b n}{x} - \frac{3 a^{2} b \log{\left(c \right)}}{x} - \frac{3 a b^{2} n^{2} \log{\left(x \right)}^{2}}{x} - \frac{6 a b^{2} n^{2} \log{\left(x \right)}}{x} - \frac{6 a b^{2} n^{2}}{x} - \frac{6 a b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{6 a b^{2} n \log{\left(c \right)}}{x} - \frac{3 a b^{2} \log{\left(c \right)}^{2}}{x} - \frac{b^{3} n^{3} \log{\left(x \right)}^{3}}{x} - \frac{3 b^{3} n^{3} \log{\left(x \right)}^{2}}{x} - \frac{6 b^{3} n^{3} \log{\left(x \right)}}{x} - \frac{6 b^{3} n^{3}}{x} - \frac{3 b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)}^{2}}{x} - \frac{6 b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{6 b^{3} n^{2} \log{\left(c \right)}}{x} - \frac{3 b^{3} n \log{\left(c \right)}^{2} \log{\left(x \right)}}{x} - \frac{3 b^{3} n \log{\left(c \right)}^{2}}{x} - \frac{b^{3} \log{\left(c \right)}^{3}}{x}"," ",0,"-a**3/x - 3*a**2*b*n*log(x)/x - 3*a**2*b*n/x - 3*a**2*b*log(c)/x - 3*a*b**2*n**2*log(x)**2/x - 6*a*b**2*n**2*log(x)/x - 6*a*b**2*n**2/x - 6*a*b**2*n*log(c)*log(x)/x - 6*a*b**2*n*log(c)/x - 3*a*b**2*log(c)**2/x - b**3*n**3*log(x)**3/x - 3*b**3*n**3*log(x)**2/x - 6*b**3*n**3*log(x)/x - 6*b**3*n**3/x - 3*b**3*n**2*log(c)*log(x)**2/x - 6*b**3*n**2*log(c)*log(x)/x - 6*b**3*n**2*log(c)/x - 3*b**3*n*log(c)**2*log(x)/x - 3*b**3*n*log(c)**2/x - b**3*log(c)**3/x","B",0
63,1,338,0,1.157486," ","integrate((a+b*ln(c*x**n))**3/x**3,x)","- \frac{a^{3}}{2 x^{2}} - \frac{3 a^{2} b n \log{\left(x \right)}}{2 x^{2}} - \frac{3 a^{2} b n}{4 x^{2}} - \frac{3 a^{2} b \log{\left(c \right)}}{2 x^{2}} - \frac{3 a b^{2} n^{2} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{3 a b^{2} n^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{3 a b^{2} n^{2}}{4 x^{2}} - \frac{3 a b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{3 a b^{2} n \log{\left(c \right)}}{2 x^{2}} - \frac{3 a b^{2} \log{\left(c \right)}^{2}}{2 x^{2}} - \frac{b^{3} n^{3} \log{\left(x \right)}^{3}}{2 x^{2}} - \frac{3 b^{3} n^{3} \log{\left(x \right)}^{2}}{4 x^{2}} - \frac{3 b^{3} n^{3} \log{\left(x \right)}}{4 x^{2}} - \frac{3 b^{3} n^{3}}{8 x^{2}} - \frac{3 b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{3 b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)}}{2 x^{2}} - \frac{3 b^{3} n^{2} \log{\left(c \right)}}{4 x^{2}} - \frac{3 b^{3} n \log{\left(c \right)}^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{3 b^{3} n \log{\left(c \right)}^{2}}{4 x^{2}} - \frac{b^{3} \log{\left(c \right)}^{3}}{2 x^{2}}"," ",0,"-a**3/(2*x**2) - 3*a**2*b*n*log(x)/(2*x**2) - 3*a**2*b*n/(4*x**2) - 3*a**2*b*log(c)/(2*x**2) - 3*a*b**2*n**2*log(x)**2/(2*x**2) - 3*a*b**2*n**2*log(x)/(2*x**2) - 3*a*b**2*n**2/(4*x**2) - 3*a*b**2*n*log(c)*log(x)/x**2 - 3*a*b**2*n*log(c)/(2*x**2) - 3*a*b**2*log(c)**2/(2*x**2) - b**3*n**3*log(x)**3/(2*x**2) - 3*b**3*n**3*log(x)**2/(4*x**2) - 3*b**3*n**3*log(x)/(4*x**2) - 3*b**3*n**3/(8*x**2) - 3*b**3*n**2*log(c)*log(x)**2/(2*x**2) - 3*b**3*n**2*log(c)*log(x)/(2*x**2) - 3*b**3*n**2*log(c)/(4*x**2) - 3*b**3*n*log(c)**2*log(x)/(2*x**2) - 3*b**3*n*log(c)**2/(4*x**2) - b**3*log(c)**3/(2*x**2)","B",0
64,1,313,0,1.811047," ","integrate((a+b*ln(c*x**n))**3/x**4,x)","- \frac{a^{3}}{3 x^{3}} - \frac{a^{2} b n \log{\left(x \right)}}{x^{3}} - \frac{a^{2} b n}{3 x^{3}} - \frac{a^{2} b \log{\left(c \right)}}{x^{3}} - \frac{a b^{2} n^{2} \log{\left(x \right)}^{2}}{x^{3}} - \frac{2 a b^{2} n^{2} \log{\left(x \right)}}{3 x^{3}} - \frac{2 a b^{2} n^{2}}{9 x^{3}} - \frac{2 a b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x^{3}} - \frac{2 a b^{2} n \log{\left(c \right)}}{3 x^{3}} - \frac{a b^{2} \log{\left(c \right)}^{2}}{x^{3}} - \frac{b^{3} n^{3} \log{\left(x \right)}^{3}}{3 x^{3}} - \frac{b^{3} n^{3} \log{\left(x \right)}^{2}}{3 x^{3}} - \frac{2 b^{3} n^{3} \log{\left(x \right)}}{9 x^{3}} - \frac{2 b^{3} n^{3}}{27 x^{3}} - \frac{b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)}^{2}}{x^{3}} - \frac{2 b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)}}{3 x^{3}} - \frac{2 b^{3} n^{2} \log{\left(c \right)}}{9 x^{3}} - \frac{b^{3} n \log{\left(c \right)}^{2} \log{\left(x \right)}}{x^{3}} - \frac{b^{3} n \log{\left(c \right)}^{2}}{3 x^{3}} - \frac{b^{3} \log{\left(c \right)}^{3}}{3 x^{3}}"," ",0,"-a**3/(3*x**3) - a**2*b*n*log(x)/x**3 - a**2*b*n/(3*x**3) - a**2*b*log(c)/x**3 - a*b**2*n**2*log(x)**2/x**3 - 2*a*b**2*n**2*log(x)/(3*x**3) - 2*a*b**2*n**2/(9*x**3) - 2*a*b**2*n*log(c)*log(x)/x**3 - 2*a*b**2*n*log(c)/(3*x**3) - a*b**2*log(c)**2/x**3 - b**3*n**3*log(x)**3/(3*x**3) - b**3*n**3*log(x)**2/(3*x**3) - 2*b**3*n**3*log(x)/(9*x**3) - 2*b**3*n**3/(27*x**3) - b**3*n**2*log(c)*log(x)**2/x**3 - 2*b**3*n**2*log(c)*log(x)/(3*x**3) - 2*b**3*n**2*log(c)/(9*x**3) - b**3*n*log(c)**2*log(x)/x**3 - b**3*n*log(c)**2/(3*x**3) - b**3*log(c)**3/(3*x**3)","B",0
65,0,0,0,0.000000," ","integrate(x**3/(a+b*ln(c*x**n)),x)","\int \frac{x^{3}}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral(x**3/(a + b*log(c*x**n)), x)","F",0
66,0,0,0,0.000000," ","integrate(x**2/(a+b*ln(c*x**n)),x)","\int \frac{x^{2}}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral(x**2/(a + b*log(c*x**n)), x)","F",0
67,0,0,0,0.000000," ","integrate(x/(a+b*ln(c*x**n)),x)","\int \frac{x}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral(x/(a + b*log(c*x**n)), x)","F",0
68,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*x**n)),x)","\int \frac{1}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral(1/(a + b*log(c*x**n)), x)","F",0
69,1,34,0,1.090055," ","integrate(1/x/(a+b*ln(c*x**n)),x)","\begin{cases} \frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \wedge n = 0 \\\frac{\log{\left(x \right)}}{a + b \log{\left(c \right)}} & \text{for}\: n = 0 \\\frac{\log{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(\frac{a}{b} + n \log{\left(x \right)} + \log{\left(c \right)} \right)}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)/a, Eq(b, 0) & Eq(n, 0)), (log(x)/(a + b*log(c)), Eq(n, 0)), (log(x)/a, Eq(b, 0)), (log(a/b + n*log(x) + log(c))/(b*n), True))","A",0
70,0,0,0,0.000000," ","integrate(1/x**2/(a+b*ln(c*x**n)),x)","\int \frac{1}{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}\, dx"," ",0,"Integral(1/(x**2*(a + b*log(c*x**n))), x)","F",0
71,0,0,0,0.000000," ","integrate(1/x**3/(a+b*ln(c*x**n)),x)","\int \frac{1}{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)}\, dx"," ",0,"Integral(1/(x**3*(a + b*log(c*x**n))), x)","F",0
72,0,0,0,0.000000," ","integrate(1/x**4/(a+b*ln(c*x**n)),x)","\int \frac{1}{x^{4} \left(a + b \log{\left(c x^{n} \right)}\right)}\, dx"," ",0,"Integral(1/(x**4*(a + b*log(c*x**n))), x)","F",0
73,0,0,0,0.000000," ","integrate(x**3/(a+b*ln(c*x**n))**2,x)","\int \frac{x^{3}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(x**3/(a + b*log(c*x**n))**2, x)","F",0
74,0,0,0,0.000000," ","integrate(x**2/(a+b*ln(c*x**n))**2,x)","\int \frac{x^{2}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(x**2/(a + b*log(c*x**n))**2, x)","F",0
75,0,0,0,0.000000," ","integrate(x/(a+b*ln(c*x**n))**2,x)","\int \frac{x}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(x/(a + b*log(c*x**n))**2, x)","F",0
76,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**(-2), x)","F",0
77,1,70,0,22.744254," ","integrate(1/x/(a+b*ln(c*x**n))**2,x)","\begin{cases} \frac{\tilde{\infty} \log{\left(x \right)}}{\log{\left(c \right)}^{2}} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\tilde{\infty} n \log{\left(x \right)} & \text{for}\: a = - b \left(n \log{\left(x \right)} + \log{\left(c \right)}\right) \\\frac{\log{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b \log{\left(c \right)}\right)^{2}} & \text{for}\: n = 0 \\- \frac{1}{a b n + b^{2} n^{2} \log{\left(x \right)} + b^{2} n \log{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x)/log(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (zoo*n*log(x), Eq(a, -b*(n*log(x) + log(c)))), (log(x)/a**2, Eq(b, 0)), (log(x)/(a + b*log(c))**2, Eq(n, 0)), (-1/(a*b*n + b**2*n**2*log(x) + b**2*n*log(c)), True))","A",0
78,0,0,0,0.000000," ","integrate(1/x**2/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(a + b*log(c*x**n))**2), x)","F",0
79,0,0,0,0.000000," ","integrate(1/x**3/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x**3*(a + b*log(c*x**n))**2), x)","F",0
80,0,0,0,0.000000," ","integrate(1/x**4/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{x^{4} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(x**4*(a + b*log(c*x**n))**2), x)","F",0
81,0,0,0,0.000000," ","integrate(x**3/(a+b*ln(c*x**n))**3,x)","\int \frac{x^{3}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral(x**3/(a + b*log(c*x**n))**3, x)","F",0
82,0,0,0,0.000000," ","integrate(x**2/(a+b*ln(c*x**n))**3,x)","\int \frac{x^{2}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral(x**2/(a + b*log(c*x**n))**3, x)","F",0
83,0,0,0,0.000000," ","integrate(x/(a+b*ln(c*x**n))**3,x)","\int \frac{x}{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral(x/(a + b*log(c*x**n))**3, x)","F",0
84,0,0,0,0.000000," ","integrate(1/(a+b*ln(c*x**n))**3,x)","\int \frac{1}{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**(-3), x)","F",0
85,1,121,0,93.787350," ","integrate(1/x/(a+b*ln(c*x**n))**3,x)","\begin{cases} \frac{\tilde{\infty} \log{\left(x \right)}}{\log{\left(c \right)}^{3}} & \text{for}\: a = 0 \wedge b = 0 \wedge n = 0 \\\tilde{\infty} n \log{\left(x \right)} & \text{for}\: a = - b \left(n \log{\left(x \right)} + \log{\left(c \right)}\right) \\\frac{\log{\left(x \right)}}{a^{3}} & \text{for}\: b = 0 \\\frac{\log{\left(x \right)}}{\left(a + b \log{\left(c \right)}\right)^{3}} & \text{for}\: n = 0 \\- \frac{1}{2 a^{2} b n + 4 a b^{2} n^{2} \log{\left(x \right)} + 4 a b^{2} n \log{\left(c \right)} + 2 b^{3} n^{3} \log{\left(x \right)}^{2} + 4 b^{3} n^{2} \log{\left(c \right)} \log{\left(x \right)} + 2 b^{3} n \log{\left(c \right)}^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x)/log(c)**3, Eq(a, 0) & Eq(b, 0) & Eq(n, 0)), (zoo*n*log(x), Eq(a, -b*(n*log(x) + log(c)))), (log(x)/a**3, Eq(b, 0)), (log(x)/(a + b*log(c))**3, Eq(n, 0)), (-1/(2*a**2*b*n + 4*a*b**2*n**2*log(x) + 4*a*b**2*n*log(c) + 2*b**3*n**3*log(x)**2 + 4*b**3*n**2*log(c)*log(x) + 2*b**3*n*log(c)**2), True))","A",0
86,0,0,0,0.000000," ","integrate(1/x**2/(a+b*ln(c*x**n))**3,x)","\int \frac{1}{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x**2*(a + b*log(c*x**n))**3), x)","F",0
87,0,0,0,0.000000," ","integrate(1/x**3/(a+b*ln(c*x**n))**3,x)","\int \frac{1}{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x**3*(a + b*log(c*x**n))**3), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x**4/(a+b*ln(c*x**n))**3,x)","\int \frac{1}{x^{4} \left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(x**4*(a + b*log(c*x**n))**3), x)","F",0
89,-1,0,0,0.000000," ","integrate((d*x)**(5/2)*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,1,70,0,25.449209," ","integrate((d*x)**(3/2)*(a+b*ln(c*x**n)),x)","\frac{2 a d^{\frac{3}{2}} x^{\frac{5}{2}}}{5} + \frac{2 b d^{\frac{3}{2}} n x^{\frac{5}{2}} \log{\left(x \right)}}{5} - \frac{4 b d^{\frac{3}{2}} n x^{\frac{5}{2}}}{25} + \frac{2 b d^{\frac{3}{2}} x^{\frac{5}{2}} \log{\left(c \right)}}{5}"," ",0,"2*a*d**(3/2)*x**(5/2)/5 + 2*b*d**(3/2)*n*x**(5/2)*log(x)/5 - 4*b*d**(3/2)*n*x**(5/2)/25 + 2*b*d**(3/2)*x**(5/2)*log(c)/5","A",0
91,1,70,0,1.064890," ","integrate((d*x)**(1/2)*(a+b*ln(c*x**n)),x)","\frac{2 a \sqrt{d} x^{\frac{3}{2}}}{3} + \frac{2 b \sqrt{d} n x^{\frac{3}{2}} \log{\left(x \right)}}{3} - \frac{4 b \sqrt{d} n x^{\frac{3}{2}}}{9} + \frac{2 b \sqrt{d} x^{\frac{3}{2}} \log{\left(c \right)}}{3}"," ",0,"2*a*sqrt(d)*x**(3/2)/3 + 2*b*sqrt(d)*n*x**(3/2)*log(x)/3 - 4*b*sqrt(d)*n*x**(3/2)/9 + 2*b*sqrt(d)*x**(3/2)*log(c)/3","A",0
92,1,63,0,0.768703," ","integrate((a+b*ln(c*x**n))/(d*x)**(1/2),x)","\frac{2 a \sqrt{x}}{\sqrt{d}} + \frac{2 b n \sqrt{x} \log{\left(x \right)}}{\sqrt{d}} - \frac{4 b n \sqrt{x}}{\sqrt{d}} + \frac{2 b \sqrt{x} \log{\left(c \right)}}{\sqrt{d}}"," ",0,"2*a*sqrt(x)/sqrt(d) + 2*b*n*sqrt(x)*log(x)/sqrt(d) - 4*b*n*sqrt(x)/sqrt(d) + 2*b*sqrt(x)*log(c)/sqrt(d)","A",0
93,1,65,0,2.860927," ","integrate((a+b*ln(c*x**n))/(d*x)**(3/2),x)","- \frac{2 a}{d^{\frac{3}{2}} \sqrt{x}} - \frac{2 b n \log{\left(x \right)}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{4 b n}{d^{\frac{3}{2}} \sqrt{x}} - \frac{2 b \log{\left(c \right)}}{d^{\frac{3}{2}} \sqrt{x}}"," ",0,"-2*a/(d**(3/2)*sqrt(x)) - 2*b*n*log(x)/(d**(3/2)*sqrt(x)) - 4*b*n/(d**(3/2)*sqrt(x)) - 2*b*log(c)/(d**(3/2)*sqrt(x))","A",0
94,1,71,0,28.214397," ","integrate((a+b*ln(c*x**n))/(d*x)**(5/2),x)","- \frac{2 a}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{2 b n \log{\left(x \right)}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{4 b n}{9 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{2 b \log{\left(c \right)}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}}"," ",0,"-2*a/(3*d**(5/2)*x**(3/2)) - 2*b*n*log(x)/(3*d**(5/2)*x**(3/2)) - 4*b*n/(9*d**(5/2)*x**(3/2)) - 2*b*log(c)/(3*d**(5/2)*x**(3/2))","A",0
95,-1,0,0,0.000000," ","integrate((d*x)**(5/2)*(a+b*ln(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,1,216,0,50.355661," ","integrate((d*x)**(3/2)*(a+b*ln(c*x**n))**2,x)","\frac{2 a^{2} d^{\frac{3}{2}} x^{\frac{5}{2}}}{5} + \frac{4 a b d^{\frac{3}{2}} n x^{\frac{5}{2}} \log{\left(x \right)}}{5} - \frac{8 a b d^{\frac{3}{2}} n x^{\frac{5}{2}}}{25} + \frac{4 a b d^{\frac{3}{2}} x^{\frac{5}{2}} \log{\left(c \right)}}{5} + \frac{2 b^{2} d^{\frac{3}{2}} n^{2} x^{\frac{5}{2}} \log{\left(x \right)}^{2}}{5} - \frac{8 b^{2} d^{\frac{3}{2}} n^{2} x^{\frac{5}{2}} \log{\left(x \right)}}{25} + \frac{16 b^{2} d^{\frac{3}{2}} n^{2} x^{\frac{5}{2}}}{125} + \frac{4 b^{2} d^{\frac{3}{2}} n x^{\frac{5}{2}} \log{\left(c \right)} \log{\left(x \right)}}{5} - \frac{8 b^{2} d^{\frac{3}{2}} n x^{\frac{5}{2}} \log{\left(c \right)}}{25} + \frac{2 b^{2} d^{\frac{3}{2}} x^{\frac{5}{2}} \log{\left(c \right)}^{2}}{5}"," ",0,"2*a**2*d**(3/2)*x**(5/2)/5 + 4*a*b*d**(3/2)*n*x**(5/2)*log(x)/5 - 8*a*b*d**(3/2)*n*x**(5/2)/25 + 4*a*b*d**(3/2)*x**(5/2)*log(c)/5 + 2*b**2*d**(3/2)*n**2*x**(5/2)*log(x)**2/5 - 8*b**2*d**(3/2)*n**2*x**(5/2)*log(x)/25 + 16*b**2*d**(3/2)*n**2*x**(5/2)/125 + 4*b**2*d**(3/2)*n*x**(5/2)*log(c)*log(x)/5 - 8*b**2*d**(3/2)*n*x**(5/2)*log(c)/25 + 2*b**2*d**(3/2)*x**(5/2)*log(c)**2/5","B",0
97,1,216,0,2.461754," ","integrate((d*x)**(1/2)*(a+b*ln(c*x**n))**2,x)","\frac{2 a^{2} \sqrt{d} x^{\frac{3}{2}}}{3} + \frac{4 a b \sqrt{d} n x^{\frac{3}{2}} \log{\left(x \right)}}{3} - \frac{8 a b \sqrt{d} n x^{\frac{3}{2}}}{9} + \frac{4 a b \sqrt{d} x^{\frac{3}{2}} \log{\left(c \right)}}{3} + \frac{2 b^{2} \sqrt{d} n^{2} x^{\frac{3}{2}} \log{\left(x \right)}^{2}}{3} - \frac{8 b^{2} \sqrt{d} n^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{9} + \frac{16 b^{2} \sqrt{d} n^{2} x^{\frac{3}{2}}}{27} + \frac{4 b^{2} \sqrt{d} n x^{\frac{3}{2}} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{8 b^{2} \sqrt{d} n x^{\frac{3}{2}} \log{\left(c \right)}}{9} + \frac{2 b^{2} \sqrt{d} x^{\frac{3}{2}} \log{\left(c \right)}^{2}}{3}"," ",0,"2*a**2*sqrt(d)*x**(3/2)/3 + 4*a*b*sqrt(d)*n*x**(3/2)*log(x)/3 - 8*a*b*sqrt(d)*n*x**(3/2)/9 + 4*a*b*sqrt(d)*x**(3/2)*log(c)/3 + 2*b**2*sqrt(d)*n**2*x**(3/2)*log(x)**2/3 - 8*b**2*sqrt(d)*n**2*x**(3/2)*log(x)/9 + 16*b**2*sqrt(d)*n**2*x**(3/2)/27 + 4*b**2*sqrt(d)*n*x**(3/2)*log(c)*log(x)/3 - 8*b**2*sqrt(d)*n*x**(3/2)*log(c)/9 + 2*b**2*sqrt(d)*x**(3/2)*log(c)**2/3","B",0
98,1,199,0,1.456700," ","integrate((a+b*ln(c*x**n))**2/(d*x)**(1/2),x)","\frac{2 a^{2} \sqrt{x}}{\sqrt{d}} + \frac{4 a b n \sqrt{x} \log{\left(x \right)}}{\sqrt{d}} - \frac{8 a b n \sqrt{x}}{\sqrt{d}} + \frac{4 a b \sqrt{x} \log{\left(c \right)}}{\sqrt{d}} + \frac{2 b^{2} n^{2} \sqrt{x} \log{\left(x \right)}^{2}}{\sqrt{d}} - \frac{8 b^{2} n^{2} \sqrt{x} \log{\left(x \right)}}{\sqrt{d}} + \frac{16 b^{2} n^{2} \sqrt{x}}{\sqrt{d}} + \frac{4 b^{2} n \sqrt{x} \log{\left(c \right)} \log{\left(x \right)}}{\sqrt{d}} - \frac{8 b^{2} n \sqrt{x} \log{\left(c \right)}}{\sqrt{d}} + \frac{2 b^{2} \sqrt{x} \log{\left(c \right)}^{2}}{\sqrt{d}}"," ",0,"2*a**2*sqrt(x)/sqrt(d) + 4*a*b*n*sqrt(x)*log(x)/sqrt(d) - 8*a*b*n*sqrt(x)/sqrt(d) + 4*a*b*sqrt(x)*log(c)/sqrt(d) + 2*b**2*n**2*sqrt(x)*log(x)**2/sqrt(d) - 8*b**2*n**2*sqrt(x)*log(x)/sqrt(d) + 16*b**2*n**2*sqrt(x)/sqrt(d) + 4*b**2*n*sqrt(x)*log(c)*log(x)/sqrt(d) - 8*b**2*n*sqrt(x)*log(c)/sqrt(d) + 2*b**2*sqrt(x)*log(c)**2/sqrt(d)","B",0
99,1,201,0,2.898663," ","integrate((a+b*ln(c*x**n))**2/(d*x)**(3/2),x)","- \frac{2 a^{2}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{4 a b n \log{\left(x \right)}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{8 a b n}{d^{\frac{3}{2}} \sqrt{x}} - \frac{4 a b \log{\left(c \right)}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{2 b^{2} n^{2} \log{\left(x \right)}^{2}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{8 b^{2} n^{2} \log{\left(x \right)}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{16 b^{2} n^{2}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{4 b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{8 b^{2} n \log{\left(c \right)}}{d^{\frac{3}{2}} \sqrt{x}} - \frac{2 b^{2} \log{\left(c \right)}^{2}}{d^{\frac{3}{2}} \sqrt{x}}"," ",0,"-2*a**2/(d**(3/2)*sqrt(x)) - 4*a*b*n*log(x)/(d**(3/2)*sqrt(x)) - 8*a*b*n/(d**(3/2)*sqrt(x)) - 4*a*b*log(c)/(d**(3/2)*sqrt(x)) - 2*b**2*n**2*log(x)**2/(d**(3/2)*sqrt(x)) - 8*b**2*n**2*log(x)/(d**(3/2)*sqrt(x)) - 16*b**2*n**2/(d**(3/2)*sqrt(x)) - 4*b**2*n*log(c)*log(x)/(d**(3/2)*sqrt(x)) - 8*b**2*n*log(c)/(d**(3/2)*sqrt(x)) - 2*b**2*log(c)**2/(d**(3/2)*sqrt(x))","B",0
100,1,218,0,26.711169," ","integrate((a+b*ln(c*x**n))**2/(d*x)**(5/2),x)","- \frac{2 a^{2}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{4 a b n \log{\left(x \right)}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{8 a b n}{9 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{4 a b \log{\left(c \right)}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{2 b^{2} n^{2} \log{\left(x \right)}^{2}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{8 b^{2} n^{2} \log{\left(x \right)}}{9 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{16 b^{2} n^{2}}{27 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{4 b^{2} n \log{\left(c \right)} \log{\left(x \right)}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{8 b^{2} n \log{\left(c \right)}}{9 d^{\frac{5}{2}} x^{\frac{3}{2}}} - \frac{2 b^{2} \log{\left(c \right)}^{2}}{3 d^{\frac{5}{2}} x^{\frac{3}{2}}}"," ",0,"-2*a**2/(3*d**(5/2)*x**(3/2)) - 4*a*b*n*log(x)/(3*d**(5/2)*x**(3/2)) - 8*a*b*n/(9*d**(5/2)*x**(3/2)) - 4*a*b*log(c)/(3*d**(5/2)*x**(3/2)) - 2*b**2*n**2*log(x)**2/(3*d**(5/2)*x**(3/2)) - 8*b**2*n**2*log(x)/(9*d**(5/2)*x**(3/2)) - 16*b**2*n**2/(27*d**(5/2)*x**(3/2)) - 4*b**2*n*log(c)*log(x)/(3*d**(5/2)*x**(3/2)) - 8*b**2*n*log(c)/(9*d**(5/2)*x**(3/2)) - 2*b**2*log(c)**2/(3*d**(5/2)*x**(3/2))","B",0
101,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(a+b*ln(c*x**n)),x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral((d*x)**(5/2)/(a + b*log(c*x**n)), x)","F",0
102,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(a+b*ln(c*x**n)),x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral((d*x)**(3/2)/(a + b*log(c*x**n)), x)","F",0
103,0,0,0,0.000000," ","integrate((d*x)**(1/2)/(a+b*ln(c*x**n)),x)","\int \frac{\sqrt{d x}}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral(sqrt(d*x)/(a + b*log(c*x**n)), x)","F",0
104,0,0,0,0.000000," ","integrate(1/(d*x)**(1/2)/(a+b*ln(c*x**n)),x)","\int \frac{1}{\sqrt{d x} \left(a + b \log{\left(c x^{n} \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(d*x)*(a + b*log(c*x**n))), x)","F",0
105,0,0,0,0.000000," ","integrate(1/(d*x)**(3/2)/(a+b*ln(c*x**n)),x)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(a + b \log{\left(c x^{n} \right)}\right)}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*(a + b*log(c*x**n))), x)","F",0
106,0,0,0,0.000000," ","integrate(1/(d*x)**(5/2)/(a+b*ln(c*x**n)),x)","\int \frac{1}{\left(d x\right)^{\frac{5}{2}} \left(a + b \log{\left(c x^{n} \right)}\right)}\, dx"," ",0,"Integral(1/((d*x)**(5/2)*(a + b*log(c*x**n))), x)","F",0
107,0,0,0,0.000000," ","integrate((d*x)**(5/2)/(a+b*ln(c*x**n))**2,x)","\int \frac{\left(d x\right)^{\frac{5}{2}}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(5/2)/(a + b*log(c*x**n))**2, x)","F",0
108,0,0,0,0.000000," ","integrate((d*x)**(3/2)/(a+b*ln(c*x**n))**2,x)","\int \frac{\left(d x\right)^{\frac{3}{2}}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((d*x)**(3/2)/(a + b*log(c*x**n))**2, x)","F",0
109,0,0,0,0.000000," ","integrate((d*x)**(1/2)/(a+b*ln(c*x**n))**2,x)","\int \frac{\sqrt{d x}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(d*x)/(a + b*log(c*x**n))**2, x)","F",0
110,0,0,0,0.000000," ","integrate(1/(d*x)**(1/2)/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{\sqrt{d x} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(d*x)*(a + b*log(c*x**n))**2), x)","F",0
111,0,0,0,0.000000," ","integrate(1/(d*x)**(3/2)/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{\left(d x\right)^{\frac{3}{2}} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(1/((d*x)**(3/2)*(a + b*log(c*x**n))**2), x)","F",0
112,0,0,0,0.000000," ","integrate(1/(d*x)**(5/2)/(a+b*ln(c*x**n))**2,x)","\int \frac{1}{\left(d x\right)^{\frac{5}{2}} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral(1/((d*x)**(5/2)*(a + b*log(c*x**n))**2), x)","F",0
113,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n)), x)","F",0
114,0,0,0,0.000000," ","integrate(x**3*ln(a*x**n)**(1/2),x)","\int x^{3} \sqrt{\log{\left(a x^{n} \right)}}\, dx"," ",0,"Integral(x**3*sqrt(log(a*x**n)), x)","F",0
115,0,0,0,0.000000," ","integrate(x**2*ln(a*x**n)**(1/2),x)","\int x^{2} \sqrt{\log{\left(a x^{n} \right)}}\, dx"," ",0,"Integral(x**2*sqrt(log(a*x**n)), x)","F",0
116,0,0,0,0.000000," ","integrate(x*ln(a*x**n)**(1/2),x)","\int x \sqrt{\log{\left(a x^{n} \right)}}\, dx"," ",0,"Integral(x*sqrt(log(a*x**n)), x)","F",0
117,0,0,0,0.000000," ","integrate(ln(a*x**n)**(1/2),x)","\int \sqrt{\log{\left(a x^{n} \right)}}\, dx"," ",0,"Integral(sqrt(log(a*x**n)), x)","F",0
118,1,29,0,1.173958," ","integrate(ln(a*x**n)**(1/2)/x,x)","- \begin{cases} - \sqrt{\log{\left(a \right)}} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{2 \log{\left(a x^{n} \right)}^{\frac{3}{2}}}{3 n} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((-sqrt(log(a))*log(x), Eq(n, 0)), (-2*log(a*x**n)**(3/2)/(3*n), True))","A",0
119,0,0,0,0.000000," ","integrate(ln(a*x**n)**(1/2)/x**2,x)","\int \frac{\sqrt{\log{\left(a x^{n} \right)}}}{x^{2}}\, dx"," ",0,"Integral(sqrt(log(a*x**n))/x**2, x)","F",0
120,0,0,0,0.000000," ","integrate(ln(a*x**n)**(1/2)/x**3,x)","\int \frac{\sqrt{\log{\left(a x^{n} \right)}}}{x^{3}}\, dx"," ",0,"Integral(sqrt(log(a*x**n))/x**3, x)","F",0
121,0,0,0,0.000000," ","integrate(x**3*ln(a*x**n)**(3/2),x)","\int x^{3} \log{\left(a x^{n} \right)}^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*log(a*x**n)**(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(x**2*ln(a*x**n)**(3/2),x)","\int x^{2} \log{\left(a x^{n} \right)}^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*log(a*x**n)**(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate(x*ln(a*x**n)**(3/2),x)","\int x \log{\left(a x^{n} \right)}^{\frac{3}{2}}\, dx"," ",0,"Integral(x*log(a*x**n)**(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate(ln(a*x**n)**(3/2),x)","\int \log{\left(a x^{n} \right)}^{\frac{3}{2}}\, dx"," ",0,"Integral(log(a*x**n)**(3/2), x)","F",0
125,1,75,0,21.924590," ","integrate(ln(a*x**n)**(3/2)/x,x)","\begin{cases} \frac{2 n \sqrt{n \log{\left(x \right)} + \log{\left(a \right)}} \log{\left(x \right)}^{2}}{5} + \frac{4 \sqrt{n \log{\left(x \right)} + \log{\left(a \right)}} \log{\left(a \right)} \log{\left(x \right)}}{5} + \frac{2 \sqrt{n \log{\left(x \right)} + \log{\left(a \right)}} \log{\left(a \right)}^{2}}{5 n} & \text{for}\: n \neq 0 \\\log{\left(a \right)}^{\frac{3}{2}} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*n*sqrt(n*log(x) + log(a))*log(x)**2/5 + 4*sqrt(n*log(x) + log(a))*log(a)*log(x)/5 + 2*sqrt(n*log(x) + log(a))*log(a)**2/(5*n), Ne(n, 0)), (log(a)**(3/2)*log(x), True))","A",0
126,0,0,0,0.000000," ","integrate(ln(a*x**n)**(3/2)/x**2,x)","\int \frac{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral(log(a*x**n)**(3/2)/x**2, x)","F",0
127,0,0,0,0.000000," ","integrate(ln(a*x**n)**(3/2)/x**3,x)","\int \frac{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral(log(a*x**n)**(3/2)/x**3, x)","F",0
128,0,0,0,0.000000," ","integrate(x**3/ln(a*x**n)**(1/2),x)","\int \frac{x^{3}}{\sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(x**3/sqrt(log(a*x**n)), x)","F",0
129,0,0,0,0.000000," ","integrate(x**2/ln(a*x**n)**(1/2),x)","\int \frac{x^{2}}{\sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(log(a*x**n)), x)","F",0
130,0,0,0,0.000000," ","integrate(x/ln(a*x**n)**(1/2),x)","\int \frac{x}{\sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(x/sqrt(log(a*x**n)), x)","F",0
131,0,0,0,0.000000," ","integrate(1/ln(a*x**n)**(1/2),x)","\int \frac{1}{\sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(1/sqrt(log(a*x**n)), x)","F",0
132,1,24,0,2.078136," ","integrate(1/x/ln(a*x**n)**(1/2),x)","\begin{cases} \frac{2 \sqrt{n \log{\left(x \right)} + \log{\left(a \right)}}}{n} & \text{for}\: n \neq 0 \\\frac{\log{\left(x \right)}}{\sqrt{\log{\left(a \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(n*log(x) + log(a))/n, Ne(n, 0)), (log(x)/sqrt(log(a)), True))","A",0
133,0,0,0,0.000000," ","integrate(1/x**2/ln(a*x**n)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(1/(x**2*sqrt(log(a*x**n))), x)","F",0
134,0,0,0,0.000000," ","integrate(1/x**3/ln(a*x**n)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(1/(x**3*sqrt(log(a*x**n))), x)","F",0
135,0,0,0,0.000000," ","integrate(x**3/ln(a*x**n)**(3/2),x)","\int \frac{x^{3}}{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/log(a*x**n)**(3/2), x)","F",0
136,0,0,0,0.000000," ","integrate(x**2/ln(a*x**n)**(3/2),x)","\int \frac{x^{2}}{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/log(a*x**n)**(3/2), x)","F",0
137,0,0,0,0.000000," ","integrate(x/ln(a*x**n)**(3/2),x)","\int \frac{x}{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/log(a*x**n)**(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate(1/ln(a*x**n)**(3/2),x)","\int \frac{1}{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(log(a*x**n)**(-3/2), x)","F",0
139,1,41,0,93.976739," ","integrate(1/x/ln(a*x**n)**(3/2),x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = 1 \wedge n = 0 \\\frac{\log{\left(x \right)}}{\log{\left(a \right)}^{\frac{3}{2}}} & \text{for}\: n = 0 \\\tilde{\infty} \log{\left(x \right)} & \text{for}\: a = e^{- n \log{\left(x \right)}} \\- \frac{2}{n \sqrt{n \log{\left(x \right)} + \log{\left(a \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, 1) & Eq(n, 0)), (log(x)/log(a)**(3/2), Eq(n, 0)), (zoo*log(x), Eq(a, exp(-n*log(x)))), (-2/(n*sqrt(n*log(x) + log(a))), True))","A",0
140,0,0,0,0.000000," ","integrate(1/x**2/ln(a*x**n)**(3/2),x)","\int \frac{1}{x^{2} \log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*log(a*x**n)**(3/2)), x)","F",0
141,0,0,0,0.000000," ","integrate(1/x**3/ln(a*x**n)**(3/2),x)","\int \frac{1}{x^{3} \log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*log(a*x**n)**(3/2)), x)","F",0
142,0,0,0,0.000000," ","integrate(x**3/ln(a*x**n)**(5/2),x)","\int \frac{x^{3}}{\log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/log(a*x**n)**(5/2), x)","F",0
143,0,0,0,0.000000," ","integrate(x**2/ln(a*x**n)**(5/2),x)","\int \frac{x^{2}}{\log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/log(a*x**n)**(5/2), x)","F",0
144,0,0,0,0.000000," ","integrate(x/ln(a*x**n)**(5/2),x)","\int \frac{x}{\log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/log(a*x**n)**(5/2), x)","F",0
145,0,0,0,0.000000," ","integrate(1/ln(a*x**n)**(5/2),x)","\int \frac{1}{\log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(log(a*x**n)**(-5/2), x)","F",0
146,-1,0,0,0.000000," ","integrate(1/x/ln(a*x**n)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,0,0,0,0.000000," ","integrate(1/x**2/ln(a*x**n)**(5/2),x)","\int \frac{1}{x^{2} \log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*log(a*x**n)**(5/2)), x)","F",0
148,0,0,0,0.000000," ","integrate(1/x**3/ln(a*x**n)**(5/2),x)","\int \frac{1}{x^{3} \log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*log(a*x**n)**(5/2)), x)","F",0
149,1,27,0,0.983941," ","integrate((d*x)**m*(a+a*(1+m)*ln(c*x**n)/n),x)","a d^{m} x x^{m} \log{\left(x \right)} + \frac{a d^{m} x x^{m} \log{\left(c \right)}}{n}"," ",0,"a*d**m*x*x**m*log(x) + a*d**m*x*x**m*log(c)/n","A",0
150,1,2778,0,43.508056," ","integrate((d*x)**m*(a+b*ln(c*x**n))**3,x)","\begin{cases} \frac{a^{3} d^{m} m^{3} x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a^{3} d^{m} m^{2} x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a^{3} d^{m} m x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{a^{3} d^{m} x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a^{2} b d^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a^{2} b d^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a^{2} b d^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{3 a^{2} b d^{m} m^{2} n x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a^{2} b d^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a^{2} b d^{m} m n x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 a^{2} b d^{m} m n x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a^{2} b d^{m} m x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a^{2} b d^{m} n x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{3 a^{2} b d^{m} n x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a^{2} b d^{m} x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a b^{2} d^{m} m^{3} n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 a b^{2} d^{m} m^{3} n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a b^{2} d^{m} m^{3} x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a b^{2} d^{m} m^{2} n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 a b^{2} d^{m} m^{2} n^{2} x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{18 a b^{2} d^{m} m^{2} n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 a b^{2} d^{m} m^{2} n x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a b^{2} d^{m} m^{2} x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a b^{2} d^{m} m n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{12 a b^{2} d^{m} m n^{2} x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 a b^{2} d^{m} m n^{2} x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{18 a b^{2} d^{m} m n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{12 a b^{2} d^{m} m n x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 a b^{2} d^{m} m x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a b^{2} d^{m} n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 a b^{2} d^{m} n^{2} x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 a b^{2} d^{m} n^{2} x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 a b^{2} d^{m} n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 a b^{2} d^{m} n x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 a b^{2} d^{m} x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{b^{3} d^{m} m^{3} n^{3} x x^{m} \log{\left(x \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} m^{3} n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} m^{3} n x x^{m} \log{\left(c \right)}^{2} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{b^{3} d^{m} m^{3} x x^{m} \log{\left(c \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} m^{2} n^{3} x x^{m} \log{\left(x \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{3 b^{3} d^{m} m^{2} n^{3} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 b^{3} d^{m} m^{2} n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 b^{3} d^{m} m^{2} n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 b^{3} d^{m} m^{2} n x x^{m} \log{\left(c \right)}^{2} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{3 b^{3} d^{m} m^{2} n x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} m^{2} x x^{m} \log{\left(c \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} m n^{3} x x^{m} \log{\left(x \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 b^{3} d^{m} m n^{3} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 b^{3} d^{m} m n^{3} x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 b^{3} d^{m} m n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{12 b^{3} d^{m} m n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 b^{3} d^{m} m n^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{9 b^{3} d^{m} m n x x^{m} \log{\left(c \right)}^{2} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 b^{3} d^{m} m n x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} m x x^{m} \log{\left(c \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{b^{3} d^{m} n^{3} x x^{m} \log{\left(x \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{3 b^{3} d^{m} n^{3} x x^{m} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 b^{3} d^{m} n^{3} x x^{m} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 b^{3} d^{m} n^{3} x x^{m}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{6 b^{3} d^{m} n^{2} x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{6 b^{3} d^{m} n^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{3 b^{3} d^{m} n x x^{m} \log{\left(c \right)}^{2} \log{\left(x \right)}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} - \frac{3 b^{3} d^{m} n x x^{m} \log{\left(c \right)}^{2}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} + \frac{b^{3} d^{m} x x^{m} \log{\left(c \right)}^{3}}{m^{4} + 4 m^{3} + 6 m^{2} + 4 m + 1} & \text{for}\: m \neq -1 \\\frac{\begin{cases} \frac{a^{3} \log{\left(c x^{n} \right)} + \frac{3 a^{2} b \log{\left(c x^{n} \right)}^{2}}{2} + a b^{2} \log{\left(c x^{n} \right)}^{3} + \frac{b^{3} \log{\left(c x^{n} \right)}^{4}}{4}}{n} & \text{for}\: n \neq 0 \\\left(a^{3} + 3 a^{2} b \log{\left(c \right)} + 3 a b^{2} \log{\left(c \right)}^{2} + b^{3} \log{\left(c \right)}^{3}\right) \log{\left(x \right)} & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*d**m*m**3*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a**3*d**m*m**2*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a**3*d**m*m*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + a**3*d**m*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a**2*b*d**m*m**3*n*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a**2*b*d**m*m**3*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a**2*b*d**m*m**2*n*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 3*a**2*b*d**m*m**2*n*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a**2*b*d**m*m**2*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a**2*b*d**m*m*n*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*a**2*b*d**m*m*n*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a**2*b*d**m*m*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a**2*b*d**m*n*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 3*a**2*b*d**m*n*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a**2*b*d**m*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a*b**2*d**m*m**3*n**2*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*a*b**2*d**m*m**3*n*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a*b**2*d**m*m**3*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a*b**2*d**m*m**2*n**2*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*a*b**2*d**m*m**2*n**2*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 18*a*b**2*d**m*m**2*n*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*a*b**2*d**m*m**2*n*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a*b**2*d**m*m**2*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a*b**2*d**m*m*n**2*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 12*a*b**2*d**m*m*n**2*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*a*b**2*d**m*m*n**2*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 18*a*b**2*d**m*m*n*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 12*a*b**2*d**m*m*n*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*a*b**2*d**m*m*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a*b**2*d**m*n**2*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*a*b**2*d**m*n**2*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*a*b**2*d**m*n**2*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*a*b**2*d**m*n*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*a*b**2*d**m*n*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*a*b**2*d**m*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + b**3*d**m*m**3*n**3*x*x**m*log(x)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*m**3*n**2*x*x**m*log(c)*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*m**3*n*x*x**m*log(c)**2*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + b**3*d**m*m**3*x*x**m*log(c)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*m**2*n**3*x*x**m*log(x)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 3*b**3*d**m*m**2*n**3*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*b**3*d**m*m**2*n**2*x*x**m*log(c)*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*b**3*d**m*m**2*n**2*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*b**3*d**m*m**2*n*x*x**m*log(c)**2*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 3*b**3*d**m*m**2*n*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*m**2*x*x**m*log(c)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*m*n**3*x*x**m*log(x)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*b**3*d**m*m*n**3*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*b**3*d**m*m*n**3*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*b**3*d**m*m*n**2*x*x**m*log(c)*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 12*b**3*d**m*m*n**2*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*b**3*d**m*m*n**2*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 9*b**3*d**m*m*n*x*x**m*log(c)**2*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*b**3*d**m*m*n*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*m*x*x**m*log(c)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + b**3*d**m*n**3*x*x**m*log(x)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 3*b**3*d**m*n**3*x*x**m*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*b**3*d**m*n**3*x*x**m*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*b**3*d**m*n**3*x*x**m/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*n**2*x*x**m*log(c)*log(x)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 6*b**3*d**m*n**2*x*x**m*log(c)*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 6*b**3*d**m*n**2*x*x**m*log(c)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + 3*b**3*d**m*n*x*x**m*log(c)**2*log(x)/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) - 3*b**3*d**m*n*x*x**m*log(c)**2/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1) + b**3*d**m*x*x**m*log(c)**3/(m**4 + 4*m**3 + 6*m**2 + 4*m + 1), Ne(m, -1)), (Piecewise(((a**3*log(c*x**n) + 3*a**2*b*log(c*x**n)**2/2 + a*b**2*log(c*x**n)**3 + b**3*log(c*x**n)**4/4)/n, Ne(n, 0)), ((a**3 + 3*a**2*b*log(c) + 3*a*b**2*log(c)**2 + b**3*log(c)**3)*log(x), True))/d, True))","A",0
151,1,891,0,27.731000," ","integrate((d*x)**m*(a+b*ln(c*x**n))**2,x)","\begin{cases} \frac{a^{2} d^{m} m^{2} x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 a^{2} d^{m} m x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{a^{2} d^{m} x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 a b d^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 a b d^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{4 a b d^{m} m n x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 a b d^{m} m n x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{4 a b d^{m} m x x^{m} \log{\left(c \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 a b d^{m} n x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 a b d^{m} n x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 a b d^{m} x x^{m} \log{\left(c \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{b^{2} d^{m} m^{2} n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 b^{2} d^{m} m^{2} n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{b^{2} d^{m} m^{2} x x^{m} \log{\left(c \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 b^{2} d^{m} m n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 b^{2} d^{m} m n^{2} x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{4 b^{2} d^{m} m n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 b^{2} d^{m} m n x x^{m} \log{\left(c \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 b^{2} d^{m} m x x^{m} \log{\left(c \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{b^{2} d^{m} n^{2} x x^{m} \log{\left(x \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 b^{2} d^{m} n^{2} x x^{m} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 b^{2} d^{m} n^{2} x x^{m}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{2 b^{2} d^{m} n x x^{m} \log{\left(c \right)} \log{\left(x \right)}}{m^{3} + 3 m^{2} + 3 m + 1} - \frac{2 b^{2} d^{m} n x x^{m} \log{\left(c \right)}}{m^{3} + 3 m^{2} + 3 m + 1} + \frac{b^{2} d^{m} x x^{m} \log{\left(c \right)}^{2}}{m^{3} + 3 m^{2} + 3 m + 1} & \text{for}\: m \neq -1 \\\frac{\begin{cases} \frac{a^{2} \log{\left(c x^{n} \right)} + a b \log{\left(c x^{n} \right)}^{2} + \frac{b^{2} \log{\left(c x^{n} \right)}^{3}}{3}}{n} & \text{for}\: n \neq 0 \\\left(a^{2} + 2 a b \log{\left(c \right)} + b^{2} \log{\left(c \right)}^{2}\right) \log{\left(x \right)} & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**m*m**2*x*x**m/(m**3 + 3*m**2 + 3*m + 1) + 2*a**2*d**m*m*x*x**m/(m**3 + 3*m**2 + 3*m + 1) + a**2*d**m*x*x**m/(m**3 + 3*m**2 + 3*m + 1) + 2*a*b*d**m*m**2*n*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) + 2*a*b*d**m*m**2*x*x**m*log(c)/(m**3 + 3*m**2 + 3*m + 1) + 4*a*b*d**m*m*n*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) - 2*a*b*d**m*m*n*x*x**m/(m**3 + 3*m**2 + 3*m + 1) + 4*a*b*d**m*m*x*x**m*log(c)/(m**3 + 3*m**2 + 3*m + 1) + 2*a*b*d**m*n*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) - 2*a*b*d**m*n*x*x**m/(m**3 + 3*m**2 + 3*m + 1) + 2*a*b*d**m*x*x**m*log(c)/(m**3 + 3*m**2 + 3*m + 1) + b**2*d**m*m**2*n**2*x*x**m*log(x)**2/(m**3 + 3*m**2 + 3*m + 1) + 2*b**2*d**m*m**2*n*x*x**m*log(c)*log(x)/(m**3 + 3*m**2 + 3*m + 1) + b**2*d**m*m**2*x*x**m*log(c)**2/(m**3 + 3*m**2 + 3*m + 1) + 2*b**2*d**m*m*n**2*x*x**m*log(x)**2/(m**3 + 3*m**2 + 3*m + 1) - 2*b**2*d**m*m*n**2*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) + 4*b**2*d**m*m*n*x*x**m*log(c)*log(x)/(m**3 + 3*m**2 + 3*m + 1) - 2*b**2*d**m*m*n*x*x**m*log(c)/(m**3 + 3*m**2 + 3*m + 1) + 2*b**2*d**m*m*x*x**m*log(c)**2/(m**3 + 3*m**2 + 3*m + 1) + b**2*d**m*n**2*x*x**m*log(x)**2/(m**3 + 3*m**2 + 3*m + 1) - 2*b**2*d**m*n**2*x*x**m*log(x)/(m**3 + 3*m**2 + 3*m + 1) + 2*b**2*d**m*n**2*x*x**m/(m**3 + 3*m**2 + 3*m + 1) + 2*b**2*d**m*n*x*x**m*log(c)*log(x)/(m**3 + 3*m**2 + 3*m + 1) - 2*b**2*d**m*n*x*x**m*log(c)/(m**3 + 3*m**2 + 3*m + 1) + b**2*d**m*x*x**m*log(c)**2/(m**3 + 3*m**2 + 3*m + 1), Ne(m, -1)), (Piecewise(((a**2*log(c*x**n) + a*b*log(c*x**n)**2 + b**2*log(c*x**n)**3/3)/n, Ne(n, 0)), ((a**2 + 2*a*b*log(c) + b**2*log(c)**2)*log(x), True))/d, True))","A",0
152,1,192,0,10.453295," ","integrate((d*x)**m*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a d^{m} m x x^{m}}{m^{2} + 2 m + 1} + \frac{a d^{m} x x^{m}}{m^{2} + 2 m + 1} + \frac{b d^{m} m n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} + \frac{b d^{m} m x x^{m} \log{\left(c \right)}}{m^{2} + 2 m + 1} + \frac{b d^{m} n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} - \frac{b d^{m} n x x^{m}}{m^{2} + 2 m + 1} + \frac{b d^{m} x x^{m} \log{\left(c \right)}}{m^{2} + 2 m + 1} & \text{for}\: m \neq -1 \\\frac{\begin{cases} a \log{\left(x \right)} & \text{for}\: b = 0 \\- \left(- a - b \log{\left(c \right)}\right) \log{\left(x \right)} & \text{for}\: n = 0 \\\frac{\left(- a - b \log{\left(c x^{n} \right)}\right)^{2}}{2 b n} & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**m*m*x*x**m/(m**2 + 2*m + 1) + a*d**m*x*x**m/(m**2 + 2*m + 1) + b*d**m*m*n*x*x**m*log(x)/(m**2 + 2*m + 1) + b*d**m*m*x*x**m*log(c)/(m**2 + 2*m + 1) + b*d**m*n*x*x**m*log(x)/(m**2 + 2*m + 1) - b*d**m*n*x*x**m/(m**2 + 2*m + 1) + b*d**m*x*x**m*log(c)/(m**2 + 2*m + 1), Ne(m, -1)), (Piecewise((a*log(x), Eq(b, 0)), (-(-a - b*log(c))*log(x), Eq(n, 0)), ((-a - b*log(c*x**n))**2/(2*b*n), True))/d, True))","A",0
153,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*ln(c*x**n)),x)","\int \frac{\left(d x\right)^{m}}{a + b \log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*log(c*x**n)), x)","F",0
154,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*ln(c*x**n))**2,x)","\int \frac{\left(d x\right)^{m}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m/(a + b*log(c*x**n))**2, x)","F",0
155,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*ln(c*x**n))**3,x)","\int \frac{\left(d x\right)^{m}}{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}\, dx"," ",0,"Integral((d*x)**m/(a + b*log(c*x**n))**3, x)","F",0
156,1,292,0,123.180897," ","integrate((d*x)**(-1+n)*ln(c*x**n)**3,x)","\begin{cases} \tilde{\infty} x \log{\left(c \right)}^{3} & \text{for}\: d = 0 \wedge n = 0 \\\frac{\log{\left(c \right)}^{3} \log{\left(x \right)}}{d} & \text{for}\: n = 0 \\0^{n - 1} \left(n^{3} x \log{\left(x \right)}^{3} - 3 n^{3} x \log{\left(x \right)}^{2} + 6 n^{3} x \log{\left(x \right)} - 6 n^{3} x + 3 n^{2} x \log{\left(c \right)} \log{\left(x \right)}^{2} - 6 n^{2} x \log{\left(c \right)} \log{\left(x \right)} + 6 n^{2} x \log{\left(c \right)} + 3 n x \log{\left(c \right)}^{2} \log{\left(x \right)} - 3 n x \log{\left(c \right)}^{2} + x \log{\left(c \right)}^{3}\right) & \text{for}\: d = 0 \\\frac{d^{n} n^{2} x^{n} \log{\left(x \right)}^{3}}{d} + \frac{3 d^{n} n x^{n} \log{\left(c \right)} \log{\left(x \right)}^{2}}{d} - \frac{3 d^{n} n x^{n} \log{\left(x \right)}^{2}}{d} + \frac{3 d^{n} x^{n} \log{\left(c \right)}^{2} \log{\left(x \right)}}{d} - \frac{6 d^{n} x^{n} \log{\left(c \right)} \log{\left(x \right)}}{d} + \frac{6 d^{n} x^{n} \log{\left(x \right)}}{d} + \frac{d^{n} x^{n} \log{\left(c \right)}^{3}}{d n} - \frac{3 d^{n} x^{n} \log{\left(c \right)}^{2}}{d n} + \frac{6 d^{n} x^{n} \log{\left(c \right)}}{d n} - \frac{6 d^{n} x^{n}}{d n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*log(c)**3, Eq(d, 0) & Eq(n, 0)), (log(c)**3*log(x)/d, Eq(n, 0)), (0**(n - 1)*(n**3*x*log(x)**3 - 3*n**3*x*log(x)**2 + 6*n**3*x*log(x) - 6*n**3*x + 3*n**2*x*log(c)*log(x)**2 - 6*n**2*x*log(c)*log(x) + 6*n**2*x*log(c) + 3*n*x*log(c)**2*log(x) - 3*n*x*log(c)**2 + x*log(c)**3), Eq(d, 0)), (d**n*n**2*x**n*log(x)**3/d + 3*d**n*n*x**n*log(c)*log(x)**2/d - 3*d**n*n*x**n*log(x)**2/d + 3*d**n*x**n*log(c)**2*log(x)/d - 6*d**n*x**n*log(c)*log(x)/d + 6*d**n*x**n*log(x)/d + d**n*x**n*log(c)**3/(d*n) - 3*d**n*x**n*log(c)**2/(d*n) + 6*d**n*x**n*log(c)/(d*n) - 6*d**n*x**n/(d*n), True))","A",0
157,1,163,0,43.863029," ","integrate((d*x)**(-1+n)*ln(c*x**n)**2,x)","\begin{cases} \tilde{\infty} x \log{\left(c \right)}^{2} & \text{for}\: d = 0 \wedge n = 0 \\\frac{\log{\left(c \right)}^{2} \log{\left(x \right)}}{d} & \text{for}\: n = 0 \\0^{n - 1} \left(n^{2} x \log{\left(x \right)}^{2} - 2 n^{2} x \log{\left(x \right)} + 2 n^{2} x + 2 n x \log{\left(c \right)} \log{\left(x \right)} - 2 n x \log{\left(c \right)} + x \log{\left(c \right)}^{2}\right) & \text{for}\: d = 0 \\\frac{d^{n} n x^{n} \log{\left(x \right)}^{2}}{d} + \frac{2 d^{n} x^{n} \log{\left(c \right)} \log{\left(x \right)}}{d} - \frac{2 d^{n} x^{n} \log{\left(x \right)}}{d} + \frac{d^{n} x^{n} \log{\left(c \right)}^{2}}{d n} - \frac{2 d^{n} x^{n} \log{\left(c \right)}}{d n} + \frac{2 d^{n} x^{n}}{d n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*log(c)**2, Eq(d, 0) & Eq(n, 0)), (log(c)**2*log(x)/d, Eq(n, 0)), (0**(n - 1)*(n**2*x*log(x)**2 - 2*n**2*x*log(x) + 2*n**2*x + 2*n*x*log(c)*log(x) - 2*n*x*log(c) + x*log(c)**2), Eq(d, 0)), (d**n*n*x**n*log(x)**2/d + 2*d**n*x**n*log(c)*log(x)/d - 2*d**n*x**n*log(x)/d + d**n*x**n*log(c)**2/(d*n) - 2*d**n*x**n*log(c)/(d*n) + 2*d**n*x**n/(d*n), True))","A",0
158,1,68,0,13.721019," ","integrate((d*x)**(-1+n)*ln(c*x**n),x)","\begin{cases} \tilde{\infty} x \log{\left(c \right)} & \text{for}\: d = 0 \wedge n = 0 \\\frac{\log{\left(c \right)} \log{\left(x \right)}}{d} & \text{for}\: n = 0 \\0^{n - 1} \left(n x \log{\left(x \right)} - n x + x \log{\left(c \right)}\right) & \text{for}\: d = 0 \\\frac{d^{n} x^{n} \log{\left(x \right)}}{d} + \frac{d^{n} x^{n} \log{\left(c \right)}}{d n} - \frac{d^{n} x^{n}}{d n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*log(c), Eq(d, 0) & Eq(n, 0)), (log(c)*log(x)/d, Eq(n, 0)), (0**(n - 1)*(n*x*log(x) - n*x + x*log(c)), Eq(d, 0)), (d**n*x**n*log(x)/d + d**n*x**n*log(c)/(d*n) - d**n*x**n/(d*n), True))","A",0
159,0,0,0,0.000000," ","integrate((d*x)**(-1+n)/ln(c*x**n),x)","\int \frac{\left(d x\right)^{n - 1}}{\log{\left(c x^{n} \right)}}\, dx"," ",0,"Integral((d*x)**(n - 1)/log(c*x**n), x)","F",0
160,0,0,0,0.000000," ","integrate((d*x)**(-1+n)/ln(c*x**n)**2,x)","\int \frac{\left(d x\right)^{n - 1}}{\log{\left(c x^{n} \right)}^{2}}\, dx"," ",0,"Integral((d*x)**(n - 1)/log(c*x**n)**2, x)","F",0
161,0,0,0,0.000000," ","integrate((d*x)**(-1+n)/ln(c*x**n)**3,x)","\int \frac{\left(d x\right)^{n - 1}}{\log{\left(c x^{n} \right)}^{3}}\, dx"," ",0,"Integral((d*x)**(n - 1)/log(c*x**n)**3, x)","F",0
162,0,0,0,0.000000," ","integrate(x**m*ln(a*x**n)**(3/2),x)","\int x^{m} \log{\left(a x^{n} \right)}^{\frac{3}{2}}\, dx"," ",0,"Integral(x**m*log(a*x**n)**(3/2), x)","F",0
163,0,0,0,0.000000," ","integrate(x**m*ln(a*x**n)**(1/2),x)","\int x^{m} \sqrt{\log{\left(a x^{n} \right)}}\, dx"," ",0,"Integral(x**m*sqrt(log(a*x**n)), x)","F",0
164,0,0,0,0.000000," ","integrate(x**m/ln(a*x**n)**(1/2),x)","\int \frac{x^{m}}{\sqrt{\log{\left(a x^{n} \right)}}}\, dx"," ",0,"Integral(x**m/sqrt(log(a*x**n)), x)","F",0
165,0,0,0,0.000000," ","integrate(x**m/ln(a*x**n)**(3/2),x)","\int \frac{x^{m}}{\log{\left(a x^{n} \right)}^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m/log(a*x**n)**(3/2), x)","F",0
166,0,0,0,0.000000," ","integrate(x**m/ln(a*x**n)**(5/2),x)","\int \frac{x^{m}}{\log{\left(a x^{n} \right)}^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**m/log(a*x**n)**(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*ln(c*x**n))**p,x)","\int \left(d x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral((d*x)**m*(a + b*log(c*x**n))**p, x)","F",0
168,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))**p,x)","\int x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))**p, x)","F",0
169,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))**p,x)","\int x \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))**p, x)","F",0
170,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**p,x)","\int \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*x**n))**p, x)","F",0
171,1,56,0,1.864964," ","integrate((a+b*ln(c*x**n))**p/x,x)","- \begin{cases} - a^{p} \log{\left(x \right)} & \text{for}\: b = 0 \\- \left(a + b \log{\left(c \right)}\right)^{p} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b \log{\left(c x^{n} \right)} \right)} & \text{otherwise} \end{cases}}{b n} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((-a**p*log(x), Eq(b, 0)), (-(a + b*log(c))**p*log(x), Eq(n, 0)), (-Piecewise(((a + b*log(c*x**n))**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*log(c*x**n)), True))/(b*n), True))","A",0
172,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**p/x**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**p/x**2, x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**p/x**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**p/x**3, x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**p/x**4,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{p}}{x^{4}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**p/x**4, x)","F",0
175,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*ln(c*x))**p,x)","\int \left(d x\right)^{m} \left(a + b \log{\left(c x \right)}\right)^{p}\, dx"," ",0,"Integral((d*x)**m*(a + b*log(c*x))**p, x)","F",0
176,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x))**p,x)","\int x^{2} \left(a + b \log{\left(c x \right)}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x))**p, x)","F",0
177,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x))**p,x)","\int x \left(a + b \log{\left(c x \right)}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*log(c*x))**p, x)","F",0
178,0,0,0,0.000000," ","integrate((a+b*ln(c*x))**p,x)","\int \left(a + b \log{\left(c x \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*x))**p, x)","F",0
179,1,39,0,1.307413," ","integrate((a+b*ln(c*x))**p/x,x)","- \begin{cases} - a^{p} \log{\left(x \right)} & \text{for}\: b = 0 \\- \frac{\begin{cases} \frac{\left(a + b \log{\left(c x \right)}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b \log{\left(c x \right)} \right)} & \text{otherwise} \end{cases}}{b} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((-a**p*log(x), Eq(b, 0)), (-Piecewise(((a + b*log(c*x))**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*log(c*x)), True))/b, True))","A",0
180,0,0,0,0.000000," ","integrate((a+b*ln(c*x))**p/x**2,x)","\int \frac{\left(a + b \log{\left(c x \right)}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x))**p/x**2, x)","F",0
181,0,0,0,0.000000," ","integrate((a+b*ln(c*x))**p/x**3,x)","\int \frac{\left(a + b \log{\left(c x \right)}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*x))**p/x**3, x)","F",0
182,0,0,0,0.000000," ","integrate((a+b*ln(c*x))**p/x**4,x)","\int \frac{\left(a + b \log{\left(c x \right)}\right)^{p}}{x^{4}}\, dx"," ",0,"Integral((a + b*log(c*x))**p/x**4, x)","F",0
183,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*ln(c*x**(1/2)))**p,x)","\int \left(d x\right)^{m} \left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p}\, dx"," ",0,"Integral((d*x)**m*(a + b*log(c*sqrt(x)))**p, x)","F",0
184,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**(1/2)))**p,x)","\int x^{2} \left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p}\, dx"," ",0,"Integral(x**2*(a + b*log(c*sqrt(x)))**p, x)","F",0
185,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**(1/2)))**p,x)","\int x \left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p}\, dx"," ",0,"Integral(x*(a + b*log(c*sqrt(x)))**p, x)","F",0
186,0,0,0,0.000000," ","integrate((a+b*ln(c*x**(1/2)))**p,x)","\int \left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*log(c*sqrt(x)))**p, x)","F",0
187,1,48,0,4.758217," ","integrate((a+b*ln(c*x**(1/2)))**p/x,x)","- \begin{cases} - a^{p} \log{\left(x \right)} & \text{for}\: b = 0 \\- \frac{2 \left(\begin{cases} \frac{\left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b \log{\left(c \sqrt{x} \right)} \right)} & \text{otherwise} \end{cases}\right)}{b} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((-a**p*log(x), Eq(b, 0)), (-2*Piecewise(((a + b*log(c*sqrt(x)))**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*log(c*sqrt(x))), True))/b, True))","A",0
188,0,0,0,0.000000," ","integrate((a+b*ln(c*x**(1/2)))**p/x**2,x)","\int \frac{\left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*sqrt(x)))**p/x**2, x)","F",0
189,0,0,0,0.000000," ","integrate((a+b*ln(c*x**(1/2)))**p/x**3,x)","\int \frac{\left(a + b \log{\left(c \sqrt{x} \right)}\right)^{p}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*sqrt(x)))**p/x**3, x)","F",0
190,-2,0,0,0.000000," ","integrate((a+b*ln(c*x**(1/2)))**p/x**4,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
191,0,0,0,0.000000," ","integrate(x**(-1+n)*(a+b*ln(c*x**n))**p,x)","\int x^{n - 1} \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral(x**(n - 1)*(a + b*log(c*x**n))**p, x)","F",0
192,0,0,0,0.000000," ","integrate((d*x**q)**m*(a+b*ln(c*x**n))**p,x)","\int \left(d x^{q}\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral((d*x**q)**m*(a + b*log(c*x**n))**p, x)","F",0
193,-1,0,0,0.000000," ","integrate((d1*x**q1)**m1*(d2*x**q2)**m2*(a+b*ln(c*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
