1,1,87,0,2.291083," ","integrate(x**3*(e*x+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{4}}{4} + \frac{a e x^{5}}{5} + \frac{b d n x^{4} \log{\left(x \right)}}{4} - \frac{b d n x^{4}}{16} + \frac{b d x^{4} \log{\left(c \right)}}{4} + \frac{b e n x^{5} \log{\left(x \right)}}{5} - \frac{b e n x^{5}}{25} + \frac{b e x^{5} \log{\left(c \right)}}{5}"," ",0,"a*d*x**4/4 + a*e*x**5/5 + b*d*n*x**4*log(x)/4 - b*d*n*x**4/16 + b*d*x**4*log(c)/4 + b*e*n*x**5*log(x)/5 - b*e*n*x**5/25 + b*e*x**5*log(c)/5","B",0
2,1,87,0,1.462635," ","integrate(x**2*(e*x+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b d n x^{3} \log{\left(x \right)}}{3} - \frac{b d n x^{3}}{9} + \frac{b d x^{3} \log{\left(c \right)}}{3} + \frac{b e n x^{4} \log{\left(x \right)}}{4} - \frac{b e n x^{4}}{16} + \frac{b e x^{4} \log{\left(c \right)}}{4}"," ",0,"a*d*x**3/3 + a*e*x**4/4 + b*d*n*x**3*log(x)/3 - b*d*n*x**3/9 + b*d*x**3*log(c)/3 + b*e*n*x**4*log(x)/4 - b*e*n*x**4/16 + b*e*x**4*log(c)/4","B",0
3,1,87,0,0.874683," ","integrate(x*(e*x+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{2}}{2} + \frac{a e x^{3}}{3} + \frac{b d n x^{2} \log{\left(x \right)}}{2} - \frac{b d n x^{2}}{4} + \frac{b d x^{2} \log{\left(c \right)}}{2} + \frac{b e n x^{3} \log{\left(x \right)}}{3} - \frac{b e n x^{3}}{9} + \frac{b e x^{3} \log{\left(c \right)}}{3}"," ",0,"a*d*x**2/2 + a*e*x**3/3 + b*d*n*x**2*log(x)/2 - b*d*n*x**2/4 + b*d*x**2*log(c)/2 + b*e*n*x**3*log(x)/3 - b*e*n*x**3/9 + b*e*x**3*log(c)/3","B",0
4,1,73,0,0.509413," ","integrate((e*x+d)*(a+b*ln(c*x**n)),x)","a d x + \frac{a e x^{2}}{2} + b d n x \log{\left(x \right)} - b d n x + b d x \log{\left(c \right)} + \frac{b e n x^{2} \log{\left(x \right)}}{2} - \frac{b e n x^{2}}{4} + \frac{b e x^{2} \log{\left(c \right)}}{2}"," ",0,"a*d*x + a*e*x**2/2 + b*d*n*x*log(x) - b*d*n*x + b*d*x*log(c) + b*e*n*x**2*log(x)/2 - b*e*n*x**2/4 + b*e*x**2*log(c)/2","A",0
5,1,58,0,0.513489," ","integrate((e*x+d)*(a+b*ln(c*x**n))/x,x)","a d \log{\left(x \right)} + a e x + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + b e n x \log{\left(x \right)} - b e n x + b e x \log{\left(c \right)}"," ",0,"a*d*log(x) + a*e*x + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x*log(x) - b*e*n*x + b*e*x*log(c)","A",0
6,1,53,0,4.977404," ","integrate((e*x+d)*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d}{x} + a e \log{\left(x \right)} + b d \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a*d/x + a*e*log(x) + b*d*(-n/x - log(c*x**n)/x) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True))","A",0
7,1,75,0,1.038834," ","integrate((e*x+d)*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d}{2 x^{2}} - \frac{a e}{x} - \frac{b d n \log{\left(x \right)}}{2 x^{2}} - \frac{b d n}{4 x^{2}} - \frac{b d \log{\left(c \right)}}{2 x^{2}} - \frac{b e n \log{\left(x \right)}}{x} - \frac{b e n}{x} - \frac{b e \log{\left(c \right)}}{x}"," ",0,"-a*d/(2*x**2) - a*e/x - b*d*n*log(x)/(2*x**2) - b*d*n/(4*x**2) - b*d*log(c)/(2*x**2) - b*e*n*log(x)/x - b*e*n/x - b*e*log(c)/x","A",0
8,1,88,0,1.643550," ","integrate((e*x+d)*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d}{3 x^{3}} - \frac{a e}{2 x^{2}} - \frac{b d n \log{\left(x \right)}}{3 x^{3}} - \frac{b d n}{9 x^{3}} - \frac{b d \log{\left(c \right)}}{3 x^{3}} - \frac{b e n \log{\left(x \right)}}{2 x^{2}} - \frac{b e n}{4 x^{2}} - \frac{b e \log{\left(c \right)}}{2 x^{2}}"," ",0,"-a*d/(3*x**3) - a*e/(2*x**2) - b*d*n*log(x)/(3*x**3) - b*d*n/(9*x**3) - b*d*log(c)/(3*x**3) - b*e*n*log(x)/(2*x**2) - b*e*n/(4*x**2) - b*e*log(c)/(2*x**2)","A",0
9,1,158,0,3.916841," ","integrate(x**3*(e*x+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{4}}{4} + \frac{2 a d e x^{5}}{5} + \frac{a e^{2} x^{6}}{6} + \frac{b d^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b d^{2} n x^{4}}{16} + \frac{b d^{2} x^{4} \log{\left(c \right)}}{4} + \frac{2 b d e n x^{5} \log{\left(x \right)}}{5} - \frac{2 b d e n x^{5}}{25} + \frac{2 b d e x^{5} \log{\left(c \right)}}{5} + \frac{b e^{2} n x^{6} \log{\left(x \right)}}{6} - \frac{b e^{2} n x^{6}}{36} + \frac{b e^{2} x^{6} \log{\left(c \right)}}{6}"," ",0,"a*d**2*x**4/4 + 2*a*d*e*x**5/5 + a*e**2*x**6/6 + b*d**2*n*x**4*log(x)/4 - b*d**2*n*x**4/16 + b*d**2*x**4*log(c)/4 + 2*b*d*e*n*x**5*log(x)/5 - 2*b*d*e*n*x**5/25 + 2*b*d*e*x**5*log(c)/5 + b*e**2*n*x**6*log(x)/6 - b*e**2*n*x**6/36 + b*e**2*x**6*log(c)/6","B",0
10,1,151,0,2.543462," ","integrate(x**2*(e*x+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{3}}{3} + \frac{a d e x^{4}}{2} + \frac{a e^{2} x^{5}}{5} + \frac{b d^{2} n x^{3} \log{\left(x \right)}}{3} - \frac{b d^{2} n x^{3}}{9} + \frac{b d^{2} x^{3} \log{\left(c \right)}}{3} + \frac{b d e n x^{4} \log{\left(x \right)}}{2} - \frac{b d e n x^{4}}{8} + \frac{b d e x^{4} \log{\left(c \right)}}{2} + \frac{b e^{2} n x^{5} \log{\left(x \right)}}{5} - \frac{b e^{2} n x^{5}}{25} + \frac{b e^{2} x^{5} \log{\left(c \right)}}{5}"," ",0,"a*d**2*x**3/3 + a*d*e*x**4/2 + a*e**2*x**5/5 + b*d**2*n*x**3*log(x)/3 - b*d**2*n*x**3/9 + b*d**2*x**3*log(c)/3 + b*d*e*n*x**4*log(x)/2 - b*d*e*n*x**4/8 + b*d*e*x**4*log(c)/2 + b*e**2*n*x**5*log(x)/5 - b*e**2*n*x**5/25 + b*e**2*x**5*log(c)/5","B",0
11,1,158,0,1.622574," ","integrate(x*(e*x+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{2}}{2} + \frac{2 a d e x^{3}}{3} + \frac{a e^{2} x^{4}}{4} + \frac{b d^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b d^{2} n x^{2}}{4} + \frac{b d^{2} x^{2} \log{\left(c \right)}}{2} + \frac{2 b d e n x^{3} \log{\left(x \right)}}{3} - \frac{2 b d e n x^{3}}{9} + \frac{2 b d e x^{3} \log{\left(c \right)}}{3} + \frac{b e^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b e^{2} n x^{4}}{16} + \frac{b e^{2} x^{4} \log{\left(c \right)}}{4}"," ",0,"a*d**2*x**2/2 + 2*a*d*e*x**3/3 + a*e**2*x**4/4 + b*d**2*n*x**2*log(x)/2 - b*d**2*n*x**2/4 + b*d**2*x**2*log(c)/2 + 2*b*d*e*n*x**3*log(x)/3 - 2*b*d*e*n*x**3/9 + 2*b*d*e*x**3*log(c)/3 + b*e**2*n*x**4*log(x)/4 - b*e**2*n*x**4/16 + b*e**2*x**4*log(c)/4","B",0
12,1,133,0,0.984199," ","integrate((e*x+d)**2*(a+b*ln(c*x**n)),x)","a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + b d^{2} n x \log{\left(x \right)} - b d^{2} n x + b d^{2} x \log{\left(c \right)} + b d e n x^{2} \log{\left(x \right)} - \frac{b d e n x^{2}}{2} + b d e x^{2} \log{\left(c \right)} + \frac{b e^{2} n x^{3} \log{\left(x \right)}}{3} - \frac{b e^{2} n x^{3}}{9} + \frac{b e^{2} x^{3} \log{\left(c \right)}}{3}"," ",0,"a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 + b*d**2*n*x*log(x) - b*d**2*n*x + b*d**2*x*log(c) + b*d*e*n*x**2*log(x) - b*d*e*n*x**2/2 + b*d*e*x**2*log(c) + b*e**2*n*x**3*log(x)/3 - b*e**2*n*x**3/9 + b*e**2*x**3*log(c)/3","B",0
13,1,128,0,0.995952," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))/x,x)","a d^{2} \log{\left(x \right)} + 2 a d e x + \frac{a e^{2} x^{2}}{2} + \frac{b d^{2} n \log{\left(x \right)}^{2}}{2} + b d^{2} \log{\left(c \right)} \log{\left(x \right)} + 2 b d e n x \log{\left(x \right)} - 2 b d e n x + 2 b d e x \log{\left(c \right)} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{2} n x^{2}}{4} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2}"," ",0,"a*d**2*log(x) + 2*a*d*e*x + a*e**2*x**2/2 + b*d**2*n*log(x)**2/2 + b*d**2*log(c)*log(x) + 2*b*d*e*n*x*log(x) - 2*b*d*e*n*x + 2*b*d*e*x*log(c) + b*e**2*n*x**2*log(x)/2 - b*e**2*n*x**2/4 + b*e**2*x**2*log(c)/2","A",0
14,1,109,0,1.008569," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d^{2}}{x} + 2 a d e \log{\left(x \right)} + a e^{2} x - \frac{b d^{2} n \log{\left(x \right)}}{x} - \frac{b d^{2} n}{x} - \frac{b d^{2} \log{\left(c \right)}}{x} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} + b e^{2} n x \log{\left(x \right)} - b e^{2} n x + b e^{2} x \log{\left(c \right)}"," ",0,"-a*d**2/x + 2*a*d*e*log(x) + a*e**2*x - b*d**2*n*log(x)/x - b*d**2*n/x - b*d**2*log(c)/x + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) + b*e**2*n*x*log(x) - b*e**2*n*x + b*e**2*x*log(c)","A",0
15,1,99,0,6.465446," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d^{2}}{2 x^{2}} - \frac{2 a d e}{x} + a e^{2} \log{\left(x \right)} + b d^{2} \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) + 2 b d e \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a*d**2/(2*x**2) - 2*a*d*e/x + a*e**2*log(x) + b*d**2*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) + 2*b*d*e*(-n/x - log(c*x**n)/x) - b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True))","A",0
16,1,134,0,1.817793," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d^{2}}{3 x^{3}} - \frac{a d e}{x^{2}} - \frac{a e^{2}}{x} - \frac{b d^{2} n \log{\left(x \right)}}{3 x^{3}} - \frac{b d^{2} n}{9 x^{3}} - \frac{b d^{2} \log{\left(c \right)}}{3 x^{3}} - \frac{b d e n \log{\left(x \right)}}{x^{2}} - \frac{b d e n}{2 x^{2}} - \frac{b d e \log{\left(c \right)}}{x^{2}} - \frac{b e^{2} n \log{\left(x \right)}}{x} - \frac{b e^{2} n}{x} - \frac{b e^{2} \log{\left(c \right)}}{x}"," ",0,"-a*d**2/(3*x**3) - a*d*e/x**2 - a*e**2/x - b*d**2*n*log(x)/(3*x**3) - b*d**2*n/(9*x**3) - b*d**2*log(c)/(3*x**3) - b*d*e*n*log(x)/x**2 - b*d*e*n/(2*x**2) - b*d*e*log(c)/x**2 - b*e**2*n*log(x)/x - b*e**2*n/x - b*e**2*log(c)/x","A",0
17,1,160,0,2.752961," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))/x**5,x)","- \frac{a d^{2}}{4 x^{4}} - \frac{2 a d e}{3 x^{3}} - \frac{a e^{2}}{2 x^{2}} - \frac{b d^{2} n \log{\left(x \right)}}{4 x^{4}} - \frac{b d^{2} n}{16 x^{4}} - \frac{b d^{2} \log{\left(c \right)}}{4 x^{4}} - \frac{2 b d e n \log{\left(x \right)}}{3 x^{3}} - \frac{2 b d e n}{9 x^{3}} - \frac{2 b d e \log{\left(c \right)}}{3 x^{3}} - \frac{b e^{2} n \log{\left(x \right)}}{2 x^{2}} - \frac{b e^{2} n}{4 x^{2}} - \frac{b e^{2} \log{\left(c \right)}}{2 x^{2}}"," ",0,"-a*d**2/(4*x**4) - 2*a*d*e/(3*x**3) - a*e**2/(2*x**2) - b*d**2*n*log(x)/(4*x**4) - b*d**2*n/(16*x**4) - b*d**2*log(c)/(4*x**4) - 2*b*d*e*n*log(x)/(3*x**3) - 2*b*d*e*n/(9*x**3) - 2*b*d*e*log(c)/(3*x**3) - b*e**2*n*log(x)/(2*x**2) - b*e**2*n/(4*x**2) - b*e**2*log(c)/(2*x**2)","A",0
18,1,153,0,4.200809," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))/x**6,x)","- \frac{a d^{2}}{5 x^{5}} - \frac{a d e}{2 x^{4}} - \frac{a e^{2}}{3 x^{3}} - \frac{b d^{2} n \log{\left(x \right)}}{5 x^{5}} - \frac{b d^{2} n}{25 x^{5}} - \frac{b d^{2} \log{\left(c \right)}}{5 x^{5}} - \frac{b d e n \log{\left(x \right)}}{2 x^{4}} - \frac{b d e n}{8 x^{4}} - \frac{b d e \log{\left(c \right)}}{2 x^{4}} - \frac{b e^{2} n \log{\left(x \right)}}{3 x^{3}} - \frac{b e^{2} n}{9 x^{3}} - \frac{b e^{2} \log{\left(c \right)}}{3 x^{3}}"," ",0,"-a*d**2/(5*x**5) - a*d*e/(2*x**4) - a*e**2/(3*x**3) - b*d**2*n*log(x)/(5*x**5) - b*d**2*n/(25*x**5) - b*d**2*log(c)/(5*x**5) - b*d*e*n*log(x)/(2*x**4) - b*d*e*n/(8*x**4) - b*d*e*log(c)/(2*x**4) - b*e**2*n*log(x)/(3*x**3) - b*e**2*n/(9*x**3) - b*e**2*log(c)/(3*x**3)","A",0
19,1,223,0,6.490108," ","integrate(x**3*(e*x+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{4}}{4} + \frac{3 a d^{2} e x^{5}}{5} + \frac{a d e^{2} x^{6}}{2} + \frac{a e^{3} x^{7}}{7} + \frac{b d^{3} n x^{4} \log{\left(x \right)}}{4} - \frac{b d^{3} n x^{4}}{16} + \frac{b d^{3} x^{4} \log{\left(c \right)}}{4} + \frac{3 b d^{2} e n x^{5} \log{\left(x \right)}}{5} - \frac{3 b d^{2} e n x^{5}}{25} + \frac{3 b d^{2} e x^{5} \log{\left(c \right)}}{5} + \frac{b d e^{2} n x^{6} \log{\left(x \right)}}{2} - \frac{b d e^{2} n x^{6}}{12} + \frac{b d e^{2} x^{6} \log{\left(c \right)}}{2} + \frac{b e^{3} n x^{7} \log{\left(x \right)}}{7} - \frac{b e^{3} n x^{7}}{49} + \frac{b e^{3} x^{7} \log{\left(c \right)}}{7}"," ",0,"a*d**3*x**4/4 + 3*a*d**2*e*x**5/5 + a*d*e**2*x**6/2 + a*e**3*x**7/7 + b*d**3*n*x**4*log(x)/4 - b*d**3*n*x**4/16 + b*d**3*x**4*log(c)/4 + 3*b*d**2*e*n*x**5*log(x)/5 - 3*b*d**2*e*n*x**5/25 + 3*b*d**2*e*x**5*log(c)/5 + b*d*e**2*n*x**6*log(x)/2 - b*d*e**2*n*x**6/12 + b*d*e**2*x**6*log(c)/2 + b*e**3*n*x**7*log(x)/7 - b*e**3*n*x**7/49 + b*e**3*x**7*log(c)/7","B",0
20,1,230,0,4.311198," ","integrate(x**2*(e*x+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{3}}{3} + \frac{3 a d^{2} e x^{4}}{4} + \frac{3 a d e^{2} x^{5}}{5} + \frac{a e^{3} x^{6}}{6} + \frac{b d^{3} n x^{3} \log{\left(x \right)}}{3} - \frac{b d^{3} n x^{3}}{9} + \frac{b d^{3} x^{3} \log{\left(c \right)}}{3} + \frac{3 b d^{2} e n x^{4} \log{\left(x \right)}}{4} - \frac{3 b d^{2} e n x^{4}}{16} + \frac{3 b d^{2} e x^{4} \log{\left(c \right)}}{4} + \frac{3 b d e^{2} n x^{5} \log{\left(x \right)}}{5} - \frac{3 b d e^{2} n x^{5}}{25} + \frac{3 b d e^{2} x^{5} \log{\left(c \right)}}{5} + \frac{b e^{3} n x^{6} \log{\left(x \right)}}{6} - \frac{b e^{3} n x^{6}}{36} + \frac{b e^{3} x^{6} \log{\left(c \right)}}{6}"," ",0,"a*d**3*x**3/3 + 3*a*d**2*e*x**4/4 + 3*a*d*e**2*x**5/5 + a*e**3*x**6/6 + b*d**3*n*x**3*log(x)/3 - b*d**3*n*x**3/9 + b*d**3*x**3*log(c)/3 + 3*b*d**2*e*n*x**4*log(x)/4 - 3*b*d**2*e*n*x**4/16 + 3*b*d**2*e*x**4*log(c)/4 + 3*b*d*e**2*n*x**5*log(x)/5 - 3*b*d*e**2*n*x**5/25 + 3*b*d*e**2*x**5*log(c)/5 + b*e**3*n*x**6*log(x)/6 - b*e**3*n*x**6/36 + b*e**3*x**6*log(c)/6","B",0
21,1,218,0,2.828790," ","integrate(x*(e*x+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{2}}{2} + a d^{2} e x^{3} + \frac{3 a d e^{2} x^{4}}{4} + \frac{a e^{3} x^{5}}{5} + \frac{b d^{3} n x^{2} \log{\left(x \right)}}{2} - \frac{b d^{3} n x^{2}}{4} + \frac{b d^{3} x^{2} \log{\left(c \right)}}{2} + b d^{2} e n x^{3} \log{\left(x \right)} - \frac{b d^{2} e n x^{3}}{3} + b d^{2} e x^{3} \log{\left(c \right)} + \frac{3 b d e^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{3 b d e^{2} n x^{4}}{16} + \frac{3 b d e^{2} x^{4} \log{\left(c \right)}}{4} + \frac{b e^{3} n x^{5} \log{\left(x \right)}}{5} - \frac{b e^{3} n x^{5}}{25} + \frac{b e^{3} x^{5} \log{\left(c \right)}}{5}"," ",0,"a*d**3*x**2/2 + a*d**2*e*x**3 + 3*a*d*e**2*x**4/4 + a*e**3*x**5/5 + b*d**3*n*x**2*log(x)/2 - b*d**3*n*x**2/4 + b*d**3*x**2*log(c)/2 + b*d**2*e*n*x**3*log(x) - b*d**2*e*n*x**3/3 + b*d**2*e*x**3*log(c) + 3*b*d*e**2*n*x**4*log(x)/4 - 3*b*d*e**2*n*x**4/16 + 3*b*d*e**2*x**4*log(c)/4 + b*e**3*n*x**5*log(x)/5 - b*e**3*n*x**5/25 + b*e**3*x**5*log(c)/5","A",0
22,1,204,0,1.804785," ","integrate((e*x+d)**3*(a+b*ln(c*x**n)),x)","a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + a d e^{2} x^{3} + \frac{a e^{3} x^{4}}{4} + b d^{3} n x \log{\left(x \right)} - b d^{3} n x + b d^{3} x \log{\left(c \right)} + \frac{3 b d^{2} e n x^{2} \log{\left(x \right)}}{2} - \frac{3 b d^{2} e n x^{2}}{4} + \frac{3 b d^{2} e x^{2} \log{\left(c \right)}}{2} + b d e^{2} n x^{3} \log{\left(x \right)} - \frac{b d e^{2} n x^{3}}{3} + b d e^{2} x^{3} \log{\left(c \right)} + \frac{b e^{3} n x^{4} \log{\left(x \right)}}{4} - \frac{b e^{3} n x^{4}}{16} + \frac{b e^{3} x^{4} \log{\left(c \right)}}{4}"," ",0,"a*d**3*x + 3*a*d**2*e*x**2/2 + a*d*e**2*x**3 + a*e**3*x**4/4 + b*d**3*n*x*log(x) - b*d**3*n*x + b*d**3*x*log(c) + 3*b*d**2*e*n*x**2*log(x)/2 - 3*b*d**2*e*n*x**2/4 + 3*b*d**2*e*x**2*log(c)/2 + b*d*e**2*n*x**3*log(x) - b*d*e**2*n*x**3/3 + b*d*e**2*x**3*log(c) + b*e**3*n*x**4*log(x)/4 - b*e**3*n*x**4/16 + b*e**3*x**4*log(c)/4","B",0
23,1,199,0,1.862869," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x,x)","a d^{3} \log{\left(x \right)} + 3 a d^{2} e x + \frac{3 a d e^{2} x^{2}}{2} + \frac{a e^{3} x^{3}}{3} + \frac{b d^{3} n \log{\left(x \right)}^{2}}{2} + b d^{3} \log{\left(c \right)} \log{\left(x \right)} + 3 b d^{2} e n x \log{\left(x \right)} - 3 b d^{2} e n x + 3 b d^{2} e x \log{\left(c \right)} + \frac{3 b d e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{3 b d e^{2} n x^{2}}{4} + \frac{3 b d e^{2} x^{2} \log{\left(c \right)}}{2} + \frac{b e^{3} n x^{3} \log{\left(x \right)}}{3} - \frac{b e^{3} n x^{3}}{9} + \frac{b e^{3} x^{3} \log{\left(c \right)}}{3}"," ",0,"a*d**3*log(x) + 3*a*d**2*e*x + 3*a*d*e**2*x**2/2 + a*e**3*x**3/3 + b*d**3*n*log(x)**2/2 + b*d**3*log(c)*log(x) + 3*b*d**2*e*n*x*log(x) - 3*b*d**2*e*n*x + 3*b*d**2*e*x*log(c) + 3*b*d*e**2*n*x**2*log(x)/2 - 3*b*d*e**2*n*x**2/4 + 3*b*d*e**2*x**2*log(c)/2 + b*e**3*n*x**3*log(x)/3 - b*e**3*n*x**3/9 + b*e**3*x**3*log(c)/3","A",0
24,1,182,0,1.868958," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d^{3}}{x} + 3 a d^{2} e \log{\left(x \right)} + 3 a d e^{2} x + \frac{a e^{3} x^{2}}{2} - \frac{b d^{3} n \log{\left(x \right)}}{x} - \frac{b d^{3} n}{x} - \frac{b d^{3} \log{\left(c \right)}}{x} + \frac{3 b d^{2} e n \log{\left(x \right)}^{2}}{2} + 3 b d^{2} e \log{\left(c \right)} \log{\left(x \right)} + 3 b d e^{2} n x \log{\left(x \right)} - 3 b d e^{2} n x + 3 b d e^{2} x \log{\left(c \right)} + \frac{b e^{3} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{3} n x^{2}}{4} + \frac{b e^{3} x^{2} \log{\left(c \right)}}{2}"," ",0,"-a*d**3/x + 3*a*d**2*e*log(x) + 3*a*d*e**2*x + a*e**3*x**2/2 - b*d**3*n*log(x)/x - b*d**3*n/x - b*d**3*log(c)/x + 3*b*d**2*e*n*log(x)**2/2 + 3*b*d**2*e*log(c)*log(x) + 3*b*d*e**2*n*x*log(x) - 3*b*d*e**2*n*x + 3*b*d*e**2*x*log(c) + b*e**3*n*x**2*log(x)/2 - b*e**3*n*x**2/4 + b*e**3*x**2*log(c)/2","A",0
25,1,182,0,1.970389," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d^{3}}{2 x^{2}} - \frac{3 a d^{2} e}{x} + 3 a d e^{2} \log{\left(x \right)} + a e^{3} x - \frac{b d^{3} n \log{\left(x \right)}}{2 x^{2}} - \frac{b d^{3} n}{4 x^{2}} - \frac{b d^{3} \log{\left(c \right)}}{2 x^{2}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{x} - \frac{3 b d^{2} e n}{x} - \frac{3 b d^{2} e \log{\left(c \right)}}{x} + \frac{3 b d e^{2} n \log{\left(x \right)}^{2}}{2} + 3 b d e^{2} \log{\left(c \right)} \log{\left(x \right)} + b e^{3} n x \log{\left(x \right)} - b e^{3} n x + b e^{3} x \log{\left(c \right)}"," ",0,"-a*d**3/(2*x**2) - 3*a*d**2*e/x + 3*a*d*e**2*log(x) + a*e**3*x - b*d**3*n*log(x)/(2*x**2) - b*d**3*n/(4*x**2) - b*d**3*log(c)/(2*x**2) - 3*b*d**2*e*n*log(x)/x - 3*b*d**2*e*n/x - 3*b*d**2*e*log(c)/x + 3*b*d*e**2*n*log(x)**2/2 + 3*b*d*e**2*log(c)*log(x) + b*e**3*n*x*log(x) - b*e**3*n*x + b*e**3*x*log(c)","A",0
26,1,144,0,8.053969," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d^{3}}{3 x^{3}} - \frac{3 a d^{2} e}{2 x^{2}} - \frac{3 a d e^{2}}{x} + a e^{3} \log{\left(x \right)} + b d^{3} \left(- \frac{n}{9 x^{3}} - \frac{\log{\left(c x^{n} \right)}}{3 x^{3}}\right) + 3 b d^{2} e \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) + 3 b d e^{2} \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e^{3} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a*d**3/(3*x**3) - 3*a*d**2*e/(2*x**2) - 3*a*d*e**2/x + a*e**3*log(x) + b*d**3*(-n/(9*x**3) - log(c*x**n)/(3*x**3)) + 3*b*d**2*e*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) + 3*b*d*e**2*(-n/x - log(c*x**n)/x) - b*e**3*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True))","A",0
27,1,206,0,2.989556," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**5,x)","- \frac{a d^{3}}{4 x^{4}} - \frac{a d^{2} e}{x^{3}} - \frac{3 a d e^{2}}{2 x^{2}} - \frac{a e^{3}}{x} - \frac{b d^{3} n \log{\left(x \right)}}{4 x^{4}} - \frac{b d^{3} n}{16 x^{4}} - \frac{b d^{3} \log{\left(c \right)}}{4 x^{4}} - \frac{b d^{2} e n \log{\left(x \right)}}{x^{3}} - \frac{b d^{2} e n}{3 x^{3}} - \frac{b d^{2} e \log{\left(c \right)}}{x^{3}} - \frac{3 b d e^{2} n \log{\left(x \right)}}{2 x^{2}} - \frac{3 b d e^{2} n}{4 x^{2}} - \frac{3 b d e^{2} \log{\left(c \right)}}{2 x^{2}} - \frac{b e^{3} n \log{\left(x \right)}}{x} - \frac{b e^{3} n}{x} - \frac{b e^{3} \log{\left(c \right)}}{x}"," ",0,"-a*d**3/(4*x**4) - a*d**2*e/x**3 - 3*a*d*e**2/(2*x**2) - a*e**3/x - b*d**3*n*log(x)/(4*x**4) - b*d**3*n/(16*x**4) - b*d**3*log(c)/(4*x**4) - b*d**2*e*n*log(x)/x**3 - b*d**2*e*n/(3*x**3) - b*d**2*e*log(c)/x**3 - 3*b*d*e**2*n*log(x)/(2*x**2) - 3*b*d*e**2*n/(4*x**2) - 3*b*d*e**2*log(c)/(2*x**2) - b*e**3*n*log(x)/x - b*e**3*n/x - b*e**3*log(c)/x","B",0
28,1,219,0,4.654131," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**6,x)","- \frac{a d^{3}}{5 x^{5}} - \frac{3 a d^{2} e}{4 x^{4}} - \frac{a d e^{2}}{x^{3}} - \frac{a e^{3}}{2 x^{2}} - \frac{b d^{3} n \log{\left(x \right)}}{5 x^{5}} - \frac{b d^{3} n}{25 x^{5}} - \frac{b d^{3} \log{\left(c \right)}}{5 x^{5}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{4 x^{4}} - \frac{3 b d^{2} e n}{16 x^{4}} - \frac{3 b d^{2} e \log{\left(c \right)}}{4 x^{4}} - \frac{b d e^{2} n \log{\left(x \right)}}{x^{3}} - \frac{b d e^{2} n}{3 x^{3}} - \frac{b d e^{2} \log{\left(c \right)}}{x^{3}} - \frac{b e^{3} n \log{\left(x \right)}}{2 x^{2}} - \frac{b e^{3} n}{4 x^{2}} - \frac{b e^{3} \log{\left(c \right)}}{2 x^{2}}"," ",0,"-a*d**3/(5*x**5) - 3*a*d**2*e/(4*x**4) - a*d*e**2/x**3 - a*e**3/(2*x**2) - b*d**3*n*log(x)/(5*x**5) - b*d**3*n/(25*x**5) - b*d**3*log(c)/(5*x**5) - 3*b*d**2*e*n*log(x)/(4*x**4) - 3*b*d**2*e*n/(16*x**4) - 3*b*d**2*e*log(c)/(4*x**4) - b*d*e**2*n*log(x)/x**3 - b*d*e**2*n/(3*x**3) - b*d*e**2*log(c)/x**3 - b*e**3*n*log(x)/(2*x**2) - b*e**3*n/(4*x**2) - b*e**3*log(c)/(2*x**2)","A",0
29,1,231,0,7.116367," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**7,x)","- \frac{a d^{3}}{6 x^{6}} - \frac{3 a d^{2} e}{5 x^{5}} - \frac{3 a d e^{2}}{4 x^{4}} - \frac{a e^{3}}{3 x^{3}} - \frac{b d^{3} n \log{\left(x \right)}}{6 x^{6}} - \frac{b d^{3} n}{36 x^{6}} - \frac{b d^{3} \log{\left(c \right)}}{6 x^{6}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{5 x^{5}} - \frac{3 b d^{2} e n}{25 x^{5}} - \frac{3 b d^{2} e \log{\left(c \right)}}{5 x^{5}} - \frac{3 b d e^{2} n \log{\left(x \right)}}{4 x^{4}} - \frac{3 b d e^{2} n}{16 x^{4}} - \frac{3 b d e^{2} \log{\left(c \right)}}{4 x^{4}} - \frac{b e^{3} n \log{\left(x \right)}}{3 x^{3}} - \frac{b e^{3} n}{9 x^{3}} - \frac{b e^{3} \log{\left(c \right)}}{3 x^{3}}"," ",0,"-a*d**3/(6*x**6) - 3*a*d**2*e/(5*x**5) - 3*a*d*e**2/(4*x**4) - a*e**3/(3*x**3) - b*d**3*n*log(x)/(6*x**6) - b*d**3*n/(36*x**6) - b*d**3*log(c)/(6*x**6) - 3*b*d**2*e*n*log(x)/(5*x**5) - 3*b*d**2*e*n/(25*x**5) - 3*b*d**2*e*log(c)/(5*x**5) - 3*b*d*e**2*n*log(x)/(4*x**4) - 3*b*d*e**2*n/(16*x**4) - 3*b*d*e**2*log(c)/(4*x**4) - b*e**3*n*log(x)/(3*x**3) - b*e**3*n/(9*x**3) - b*e**3*log(c)/(3*x**3)","A",0
30,1,224,0,10.561058," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))/x**8,x)","- \frac{a d^{3}}{7 x^{7}} - \frac{a d^{2} e}{2 x^{6}} - \frac{3 a d e^{2}}{5 x^{5}} - \frac{a e^{3}}{4 x^{4}} - \frac{b d^{3} n \log{\left(x \right)}}{7 x^{7}} - \frac{b d^{3} n}{49 x^{7}} - \frac{b d^{3} \log{\left(c \right)}}{7 x^{7}} - \frac{b d^{2} e n \log{\left(x \right)}}{2 x^{6}} - \frac{b d^{2} e n}{12 x^{6}} - \frac{b d^{2} e \log{\left(c \right)}}{2 x^{6}} - \frac{3 b d e^{2} n \log{\left(x \right)}}{5 x^{5}} - \frac{3 b d e^{2} n}{25 x^{5}} - \frac{3 b d e^{2} \log{\left(c \right)}}{5 x^{5}} - \frac{b e^{3} n \log{\left(x \right)}}{4 x^{4}} - \frac{b e^{3} n}{16 x^{4}} - \frac{b e^{3} \log{\left(c \right)}}{4 x^{4}}"," ",0,"-a*d**3/(7*x**7) - a*d**2*e/(2*x**6) - 3*a*d*e**2/(5*x**5) - a*e**3/(4*x**4) - b*d**3*n*log(x)/(7*x**7) - b*d**3*n/(49*x**7) - b*d**3*log(c)/(7*x**7) - b*d**2*e*n*log(x)/(2*x**6) - b*d**2*e*n/(12*x**6) - b*d**2*e*log(c)/(2*x**6) - 3*b*d*e**2*n*log(x)/(5*x**5) - 3*b*d*e**2*n/(25*x**5) - 3*b*d*e**2*log(c)/(5*x**5) - b*e**3*n*log(x)/(4*x**4) - b*e**3*n/(16*x**4) - b*e**3*log(c)/(4*x**4)","A",0
31,1,248,0,38.895149," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d),x)","- \frac{a d^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{a d^{2} x}{e^{3}} - \frac{a d x^{2}}{2 e^{2}} + \frac{a x^{3}}{3 e} + \frac{b d^{3} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{b d^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{b d^{2} n x}{e^{3}} + \frac{b d^{2} x \log{\left(c x^{n} \right)}}{e^{3}} + \frac{b d n x^{2}}{4 e^{2}} - \frac{b d x^{2} \log{\left(c x^{n} \right)}}{2 e^{2}} - \frac{b n x^{3}}{9 e} + \frac{b x^{3} \log{\left(c x^{n} \right)}}{3 e}"," ",0,"-a*d**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**3 + a*d**2*x/e**3 - a*d*x**2/(2*e**2) + a*x**3/(3*e) + b*d**3*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**3 - b*d**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**3 - b*d**2*n*x/e**3 + b*d**2*x*log(c*x**n)/e**3 + b*d*n*x**2/(4*e**2) - b*d*x**2*log(c*x**n)/(2*e**2) - b*n*x**3/(9*e) + b*x**3*log(c*x**n)/(3*e)","A",0
32,1,199,0,32.810939," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d),x)","\frac{a d^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{a d x}{e^{2}} + \frac{a x^{2}}{2 e} - \frac{b d^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} + \frac{b d n x}{e^{2}} - \frac{b d x \log{\left(c x^{n} \right)}}{e^{2}} - \frac{b n x^{2}}{4 e} + \frac{b x^{2} \log{\left(c x^{n} \right)}}{2 e}"," ",0,"a*d**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**2 - a*d*x/e**2 + a*x**2/(2*e) - b*d**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**2 + b*d**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**2 + b*d*n*x/e**2 - b*d*x*log(c*x**n)/e**2 - b*n*x**2/(4*e) + b*x**2*log(c*x**n)/(2*e)","A",0
33,1,144,0,13.683467," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d),x)","- \frac{a d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e} + \frac{a x}{e} + \frac{b d n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e} - \frac{b d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e} - \frac{b n x}{e} + \frac{b x \log{\left(c x^{n} \right)}}{e}"," ",0,"-a*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e + a*x/e + b*d*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e - b*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e - b*n*x/e + b*x*log(c*x**n)/e","A",0
34,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x+d),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d + e*x), x)","F",0
35,1,158,0,14.873036," ","integrate((a+b*ln(c*x**n))/x/(e*x+d),x)","- \frac{2 a e \left(\begin{cases} \frac{1}{2 e} + \frac{x}{d} & \text{for}\: e = 0 \\- \frac{\log{\left(- 2 e x \right)}}{2 e} & \text{otherwise} \end{cases}\right)}{d} - \frac{2 a e \left(\begin{cases} \frac{1}{2 e} + \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(2 d + 2 e x \right)}}{2 e} & \text{otherwise} \end{cases}\right)}{d} + b n \left(\begin{cases} - \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right) - b \left(\begin{cases} \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\log{\left(\frac{d}{x} + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-2*a*e*Piecewise((1/(2*e) + x/d, Eq(e, 0)), (-log(-2*e*x)/(2*e), True))/d - 2*a*e*Piecewise((1/(2*e) + x/d, Eq(e, 0)), (log(2*d + 2*e*x)/(2*e), True))/d + b*n*Piecewise((-1/(e*x), Eq(d, 0)), (Piecewise((log(e)*log(x) + polylog(2, d*exp_polar(I*pi)/(e*x)), Abs(x) < 1), (-log(e)*log(1/x) + polylog(2, d*exp_polar(I*pi)/(e*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) + polylog(2, d*exp_polar(I*pi)/(e*x)), True))/d, True)) - b*Piecewise((1/(e*x), Eq(d, 0)), (log(d/x + e)/d, True))*log(c*x**n)","C",0
36,1,197,0,61.192485," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d),x)","- \frac{a}{d x} + \frac{a e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{a e \log{\left(x \right)}}{d^{2}} - \frac{b n}{d x} - \frac{b \log{\left(c x^{n} \right)}}{d x} - \frac{b e^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{b e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} + \frac{b e n \log{\left(x \right)}^{2}}{2 d^{2}} - \frac{b e \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{2}}"," ",0,"-a/(d*x) + a*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**2 - a*e*log(x)/d**2 - b*n/(d*x) - b*log(c*x**n)/(d*x) - b*e**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**2 + b*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**2 + b*e*n*log(x)**2/(2*d**2) - b*e*log(x)*log(c*x**n)/d**2","A",0
37,1,246,0,77.201601," ","integrate((a+b*ln(c*x**n))/x**3/(e*x+d),x)","- \frac{a}{2 d x^{2}} + \frac{a e}{d^{2} x} - \frac{a e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{a e^{2} \log{\left(x \right)}}{d^{3}} - \frac{b n}{4 d x^{2}} - \frac{b \log{\left(c x^{n} \right)}}{2 d x^{2}} + \frac{b e n}{d^{2} x} + \frac{b e \log{\left(c x^{n} \right)}}{d^{2} x} + \frac{b e^{3} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} - \frac{b e^{2} n \log{\left(x \right)}^{2}}{2 d^{3}} + \frac{b e^{2} \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{3}}"," ",0,"-a/(2*d*x**2) + a*e/(d**2*x) - a*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**3 + a*e**2*log(x)/d**3 - b*n/(4*d*x**2) - b*log(c*x**n)/(2*d*x**2) + b*e*n/(d**2*x) + b*e*log(c*x**n)/(d**2*x) + b*e**3*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**3 - b*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**3 - b*e**2*n*log(x)**2/(2*d**3) + b*e**2*log(x)*log(c*x**n)/d**3","A",0
38,1,296,0,91.862442," ","integrate((a+b*ln(c*x**n))/x**4/(e*x+d),x)","- \frac{a}{3 d x^{3}} + \frac{a e}{2 d^{2} x^{2}} - \frac{a e^{2}}{d^{3} x} + \frac{a e^{4} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{a e^{3} \log{\left(x \right)}}{d^{4}} - \frac{b n}{9 d x^{3}} - \frac{b \log{\left(c x^{n} \right)}}{3 d x^{3}} + \frac{b e n}{4 d^{2} x^{2}} + \frac{b e \log{\left(c x^{n} \right)}}{2 d^{2} x^{2}} - \frac{b e^{2} n}{d^{3} x} - \frac{b e^{2} \log{\left(c x^{n} \right)}}{d^{3} x} - \frac{b e^{4} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{b e^{4} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} + \frac{b e^{3} n \log{\left(x \right)}^{2}}{2 d^{4}} - \frac{b e^{3} \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{4}}"," ",0,"-a/(3*d*x**3) + a*e/(2*d**2*x**2) - a*e**2/(d**3*x) + a*e**4*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**4 - a*e**3*log(x)/d**4 - b*n/(9*d*x**3) - b*log(c*x**n)/(3*d*x**3) + b*e*n/(4*d**2*x**2) + b*e*log(c*x**n)/(2*d**2*x**2) - b*e**2*n/(d**3*x) - b*e**2*log(c*x**n)/(d**3*x) - b*e**4*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**4 + b*e**4*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**4 + b*e**3*n*log(x)**2/(2*d**4) - b*e**3*log(x)*log(c*x**n)/d**4","A",0
39,1,304,0,58.729631," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d)**2,x)","- \frac{a d^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 a d^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{2 a d x}{e^{3}} + \frac{a x^{2}}{2 e^{2}} + \frac{b d^{3} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{b d^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{3 b d^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 b d^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} + \frac{2 b d n x}{e^{3}} - \frac{2 b d x \log{\left(c x^{n} \right)}}{e^{3}} - \frac{b n x^{2}}{4 e^{2}} + \frac{b x^{2} \log{\left(c x^{n} \right)}}{2 e^{2}}"," ",0,"-a*d**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**3 + 3*a*d**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**3 - 2*a*d*x/e**3 + a*x**2/(2*e**2) + b*d**3*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**3 - b*d**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**3 - 3*b*d**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**3 + 3*b*d**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**3 + 2*b*d*n*x/e**3 - 2*b*d*x*log(c*x**n)/e**3 - b*n*x**2/(4*e**2) + b*x**2*log(c*x**n)/(2*e**2)","A",0
40,1,250,0,30.047274," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d)**2,x)","\frac{a d^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{2 a d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{a x}{e^{2}} - \frac{b d^{2} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} + \frac{2 b d n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{2 b d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} - \frac{b n x}{e^{2}} + \frac{b x \log{\left(c x^{n} \right)}}{e^{2}}"," ",0,"a*d**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**2 - 2*a*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**2 + a*x/e**2 - b*d**2*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**2 + b*d**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**2 + 2*b*d*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**2 - 2*b*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**2 - b*n*x/e**2 + b*x*log(c*x**n)/e**2","A",0
41,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d)**2,x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))/(d + e*x)**2, x)","F",0
42,1,187,0,2.348995," ","integrate((a+b*ln(c*x**n))/(e*x+d)**2,x)","\begin{cases} \tilde{\infty} \left(- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{a x + b n x \log{\left(x \right)} - b n x + b x \log{\left(c \right)}}{d^{2}} & \text{for}\: e = 0 \\\frac{- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}}{e^{2}} & \text{for}\: d = 0 \\- \frac{a d}{d^{2} e + d e^{2} x} - \frac{b d n \log{\left(\frac{d}{e} + x \right)}}{d^{2} e + d e^{2} x} + \frac{b e n x \log{\left(x \right)}}{d^{2} e + d e^{2} x} - \frac{b e n x \log{\left(\frac{d}{e} + x \right)}}{d^{2} e + d e^{2} x} + \frac{b e x \log{\left(c \right)}}{d^{2} e + d e^{2} x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x), Eq(d, 0) & Eq(e, 0)), ((a*x + b*n*x*log(x) - b*n*x + b*x*log(c))/d**2, Eq(e, 0)), ((-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x)/e**2, Eq(d, 0)), (-a*d/(d**2*e + d*e**2*x) - b*d*n*log(d/e + x)/(d**2*e + d*e**2*x) + b*e*n*x*log(x)/(d**2*e + d*e**2*x) - b*e*n*x*log(d/e + x)/(d**2*e + d*e**2*x) + b*e*x*log(c)/(d**2*e + d*e**2*x), True))","A",0
43,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x+d)**2,x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x*(d + e*x)**2), x)","F",0
44,1,299,0,65.879533," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d)**2,x)","\frac{a e^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{a}{d^{2} x} + \frac{2 a e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{2 a e \log{\left(x \right)}}{d^{3}} - \frac{b e^{2} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{b e^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} - \frac{b n}{d^{2} x} - \frac{b \log{\left(c x^{n} \right)}}{d^{2} x} - \frac{2 b e^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{2 b e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} + \frac{b e n \log{\left(x \right)}^{2}}{d^{3}} - \frac{2 b e \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{3}}"," ",0,"a*e**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**2 - a/(d**2*x) + 2*a*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**3 - 2*a*e*log(x)/d**3 - b*e**2*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/d**2 + b*e**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/d**2 - b*n/(d**2*x) - b*log(c*x**n)/(d**2*x) - 2*b*e**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**3 + 2*b*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**3 + b*e*n*log(x)**2/d**3 - 2*b*e*log(x)*log(c*x**n)/d**3","A",0
45,1,357,0,124.814610," ","integrate((a+b*ln(c*x**n))/x**3/(e*x+d)**2,x)","- \frac{a}{2 d^{2} x^{2}} - \frac{a e^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{2 a e}{d^{3} x} - \frac{3 a e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{3 a e^{2} \log{\left(x \right)}}{d^{4}} - \frac{b n}{4 d^{2} x^{2}} - \frac{b \log{\left(c x^{n} \right)}}{2 d^{2} x^{2}} + \frac{b e^{3} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b e^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} + \frac{2 b e n}{d^{3} x} + \frac{2 b e \log{\left(c x^{n} \right)}}{d^{3} x} + \frac{3 b e^{3} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{3 b e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} - \frac{3 b e^{2} n \log{\left(x \right)}^{2}}{2 d^{4}} + \frac{3 b e^{2} \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{4}}"," ",0,"-a/(2*d**2*x**2) - a*e**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**3 + 2*a*e/(d**3*x) - 3*a*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**4 + 3*a*e**2*log(x)/d**4 - b*n/(4*d**2*x**2) - b*log(c*x**n)/(2*d**2*x**2) + b*e**3*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/d**3 - b*e**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/d**3 + 2*b*e*n/(d**3*x) + 2*b*e*log(c*x**n)/(d**3*x) + 3*b*e**3*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**4 - 3*b*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**4 - 3*b*e**2*n*log(x)**2/(2*d**4) + 3*b*e**2*log(x)*log(c*x**n)/d**4","A",0
46,1,372,0,48.373876," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d)**3,x)","- \frac{a d^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 a d^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{3 a d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{a x}{e^{3}} + \frac{b d^{3} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{b d^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{3 b d^{2} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 b d^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} + \frac{3 b d n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{3 b d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{b n x}{e^{3}} + \frac{b x \log{\left(c x^{n} \right)}}{e^{3}}"," ",0,"-a*d**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/e**3 + 3*a*d**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**3 - 3*a*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**3 + a*x/e**3 + b*d**3*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/e**3 - b*d**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/e**3 - 3*b*d**2*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**3 + 3*b*d**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**3 + 3*b*d*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**3 - 3*b*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**3 - b*n*x/e**3 + b*x*log(c*x**n)/e**3","A",0
47,1,328,0,45.233908," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d)**3,x)","\frac{a d^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{2 a d \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{a \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{b d^{2} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} + \frac{2 b d n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{2 b d \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} - \frac{b n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{b \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}}"," ",0,"a*d**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/e**2 - 2*a*d*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**2 + a*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**2 - b*d**2*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/e**2 + b*d**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/e**2 + 2*b*d*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**2 - 2*b*d*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**2 - b*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**2 + b*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**2","A",0
48,1,456,0,6.043757," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d)**3,x)","\begin{cases} \tilde{\infty} \left(- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}}{e^{3}} & \text{for}\: d = 0 \\\frac{\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}}{d^{3}} & \text{for}\: e = 0 \\- \frac{a d^{2}}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} - \frac{2 a d e x}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} - \frac{b d^{2} n \log{\left(\frac{d}{e} + x \right)}}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} - \frac{b d^{2} n}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} - \frac{2 b d e n x \log{\left(\frac{d}{e} + x \right)}}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} - \frac{b d e n x}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} - \frac{b e^{2} n x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2 d^{3} e^{2} + 4 d^{2} e^{3} x + 2 d e^{4} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x), Eq(d, 0) & Eq(e, 0)), ((-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x)/e**3, Eq(d, 0)), ((a*x**2/2 + b*n*x**2*log(x)/2 - b*n*x**2/4 + b*x**2*log(c)/2)/d**3, Eq(e, 0)), (-a*d**2/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) - 2*a*d*e*x/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) - b*d**2*n*log(d/e + x)/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) - b*d**2*n/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) - 2*b*d*e*n*x*log(d/e + x)/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) - b*d*e*n*x/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) + b*e**2*n*x**2*log(x)/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) - b*e**2*n*x**2*log(d/e + x)/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2) + b*e**2*x**2*log(c)/(2*d**3*e**2 + 4*d**2*e**3*x + 2*d*e**4*x**2), True))","A",0
49,1,515,0,6.632443," ","integrate((a+b*ln(c*x**n))/(e*x+d)**3,x)","\begin{cases} \tilde{\infty} \left(- \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}}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{- \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}}}{e^{3}} & \text{for}\: d = 0 \\\frac{a x + b n x \log{\left(x \right)} - b n x + b x \log{\left(c \right)}}{d^{3}} & \text{for}\: e = 0 \\- \frac{a d^{2}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{b d^{2} n \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{b d^{2} n}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{2 b d e n x \log{\left(x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{2 b d e n x \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{b d e n x}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{2 b d e x \log{\left(c \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} - \frac{b e^{2} n x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2 d^{4} e + 4 d^{3} e^{2} x + 2 d^{2} e^{3} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2)), Eq(d, 0) & Eq(e, 0)), ((-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2))/e**3, Eq(d, 0)), ((a*x + b*n*x*log(x) - b*n*x + b*x*log(c))/d**3, Eq(e, 0)), (-a*d**2/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - b*d**2*n*log(d/e + x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + b*d**2*n/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + 2*b*d*e*n*x*log(x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - 2*b*d*e*n*x*log(d/e + x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + b*d*e*n*x/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + 2*b*d*e*x*log(c)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + b*e**2*n*x**2*log(x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) - b*e**2*n*x**2*log(d/e + x)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2) + b*e**2*x**2*log(c)/(2*d**4*e + 4*d**3*e**2*x + 2*d**2*e**3*x**2), True))","A",0
50,1,335,0,98.138829," ","integrate((a+b*ln(c*x**n))/x/(e*x+d)**3,x)","- \frac{a e \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{d} - \frac{a e \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{a e \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{a \log{\left(x \right)}}{d^{3}} + \frac{b e^{2} n \left(\begin{cases} - \frac{1}{e^{3} x} & \text{for}\: d = 0 \\- \frac{1}{2 d e^{2} + 2 e^{3} x} - \frac{\log{\left(d + e x \right)}}{2 d e^{2}} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{b e^{2} \left(\begin{cases} \frac{1}{e^{3} x} & \text{for}\: d = 0 \\- \frac{1}{2 d \left(\frac{d}{x} + e\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} - \frac{2 b e n \left(\begin{cases} - \frac{1}{e^{2} x} & \text{for}\: d = 0 \\- \frac{\log{\left(d^{2} + d e x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{2 b e \left(\begin{cases} \frac{1}{e^{2} x} & \text{for}\: d = 0 \\- \frac{1}{\frac{d^{2}}{x} + d e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} + \frac{b n \left(\begin{cases} - \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{b \left(\begin{cases} \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\log{\left(\frac{d}{x} + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}}"," ",0,"-a*e*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/d - a*e*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**2 - a*e*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**3 + a*log(x)/d**3 + b*e**2*n*Piecewise((-1/(e**3*x), Eq(d, 0)), (-1/(2*d*e**2 + 2*e**3*x) - log(d + e*x)/(2*d*e**2), True))/d**2 - b*e**2*Piecewise((1/(e**3*x), Eq(d, 0)), (-1/(2*d*(d/x + e)**2), True))*log(c*x**n)/d**2 - 2*b*e*n*Piecewise((-1/(e**2*x), Eq(d, 0)), (-log(d**2 + d*e*x)/(d*e), True))/d**2 + 2*b*e*Piecewise((1/(e**2*x), Eq(d, 0)), (-1/(d**2/x + d*e), True))*log(c*x**n)/d**2 + b*n*Piecewise((-1/(e*x), Eq(d, 0)), (Piecewise((log(e)*log(x) + polylog(2, d*exp_polar(I*pi)/(e*x)), Abs(x) < 1), (-log(e)*log(1/x) + polylog(2, d*exp_polar(I*pi)/(e*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) + polylog(2, d*exp_polar(I*pi)/(e*x)), True))/d, True))/d**2 - b*Piecewise((1/(e*x), Eq(d, 0)), (log(d/x + e)/d, True))*log(c*x**n)/d**2","A",0
51,1,425,0,104.143188," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d)**3,x)","\frac{a e^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{2 a e^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{a}{d^{3} x} + \frac{3 a e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{3 a e \log{\left(x \right)}}{d^{4}} - \frac{b e^{2} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{b e^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} - \frac{2 b e^{2} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{2 b e^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} - \frac{b n}{d^{3} x} - \frac{b \log{\left(c x^{n} \right)}}{d^{3} x} - \frac{3 b e^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{3 b e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} + \frac{3 b e n \log{\left(x \right)}^{2}}{2 d^{4}} - \frac{3 b e \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{4}}"," ",0,"a*e**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/d**2 + 2*a*e**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**3 - a/(d**3*x) + 3*a*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**4 - 3*a*e*log(x)/d**4 - b*e**2*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/d**2 + b*e**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/d**2 - 2*b*e**2*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/d**3 + 2*b*e**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/d**3 - b*n/(d**3*x) - b*log(c*x**n)/(d**3*x) - 3*b*e**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**4 + 3*b*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**4 + 3*b*e*n*log(x)**2/(2*d**4) - 3*b*e*log(x)*log(c*x**n)/d**4","A",0
52,1,478,0,110.201102," ","integrate((a+b*ln(c*x**n))/x**3/(e*x+d)**3,x)","- \frac{a e^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{a}{2 d^{3} x^{2}} - \frac{3 a e^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{3 a e}{d^{4} x} - \frac{6 a e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{5}} + \frac{6 a e^{2} \log{\left(x \right)}}{d^{5}} + \frac{b e^{3} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b e^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} - \frac{b n}{4 d^{3} x^{2}} - \frac{b \log{\left(c x^{n} \right)}}{2 d^{3} x^{2}} + \frac{3 b e^{3} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{3 b e^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} + \frac{3 b e n}{d^{4} x} + \frac{3 b e \log{\left(c x^{n} \right)}}{d^{4} x} + \frac{6 b e^{3} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{5}} - \frac{6 b e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{5}} - \frac{3 b e^{2} n \log{\left(x \right)}^{2}}{d^{5}} + \frac{6 b e^{2} \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{5}}"," ",0,"-a*e**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/d**3 - a/(2*d**3*x**2) - 3*a*e**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**4 + 3*a*e/(d**4*x) - 6*a*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**5 + 6*a*e**2*log(x)/d**5 + b*e**3*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/d**3 - b*e**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/d**3 - b*n/(4*d**3*x**2) - b*log(c*x**n)/(2*d**3*x**2) + 3*b*e**3*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/d**4 - 3*b*e**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/d**4 + 3*b*e*n/(d**4*x) + 3*b*e*log(c*x**n)/(d**4*x) + 6*b*e**3*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**5 - 6*b*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**5 - 3*b*e**2*n*log(x)**2/d**5 + 6*b*e**2*log(x)*log(c*x**n)/d**5","A",0
53,1,598,0,133.882872," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x+d)**4,x)","- \frac{a d^{5} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right)}{e^{5}} + \frac{5 a d^{4} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{e^{5}} - \frac{10 a d^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{5}} + \frac{10 a d^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{5}} - \frac{4 a d x}{e^{5}} + \frac{a x^{2}}{2 e^{4}} + \frac{b d^{5} n \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{3 d}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{2 e x}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{\log{\left(x \right)}}{3 d^{3} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e} & \text{otherwise} \end{cases}\right)}{e^{5}} - \frac{b d^{5} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{5}} - \frac{5 b d^{4} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{e^{5}} + \frac{5 b d^{4} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{5}} + \frac{10 b d^{3} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{5}} - \frac{10 b d^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{5}} - \frac{10 b d^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{5}} + \frac{10 b d^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{5}} + \frac{4 b d n x}{e^{5}} - \frac{4 b d x \log{\left(c x^{n} \right)}}{e^{5}} - \frac{b n x^{2}}{4 e^{4}} + \frac{b x^{2} \log{\left(c x^{n} \right)}}{2 e^{4}}"," ",0,"-a*d**5*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))/e**5 + 5*a*d**4*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/e**5 - 10*a*d**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**5 + 10*a*d**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**5 - 4*a*d*x/e**5 + a*x**2/(2*e**4) + b*d**5*n*Piecewise((x/d**4, Eq(e, 0)), (-3*d/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - 2*e*x/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - log(x)/(3*d**3*e) + log(d/e + x)/(3*d**3*e), True))/e**5 - b*d**5*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))*log(c*x**n)/e**5 - 5*b*d**4*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/e**5 + 5*b*d**4*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/e**5 + 10*b*d**3*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**5 - 10*b*d**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**5 - 10*b*d**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**5 + 10*b*d**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**5 + 4*b*d*n*x/e**5 - 4*b*d*x*log(c*x**n)/e**5 - b*n*x**2/(4*e**4) + b*x**2*log(c*x**n)/(2*e**4)","A",0
54,1,544,0,71.888713," ","integrate(x**4*(a+b*ln(c*x**n))/(e*x+d)**4,x)","\frac{a d^{4} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right)}{e^{4}} - \frac{4 a d^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{e^{4}} + \frac{6 a d^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{4}} - \frac{4 a d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{4}} + \frac{a x}{e^{4}} - \frac{b d^{4} n \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{3 d}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{2 e x}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{\log{\left(x \right)}}{3 d^{3} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e} & \text{otherwise} \end{cases}\right)}{e^{4}} + \frac{b d^{4} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{4}} + \frac{4 b d^{3} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{e^{4}} - \frac{4 b d^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{4}} - \frac{6 b d^{2} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{4}} + \frac{6 b d^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{4}} + \frac{4 b d n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{4}} - \frac{4 b d \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{4}} - \frac{b n x}{e^{4}} + \frac{b x \log{\left(c x^{n} \right)}}{e^{4}}"," ",0,"a*d**4*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))/e**4 - 4*a*d**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/e**4 + 6*a*d**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**4 - 4*a*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**4 + a*x/e**4 - b*d**4*n*Piecewise((x/d**4, Eq(e, 0)), (-3*d/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - 2*e*x/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - log(x)/(3*d**3*e) + log(d/e + x)/(3*d**3*e), True))/e**4 + b*d**4*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))*log(c*x**n)/e**4 + 4*b*d**3*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/e**4 - 4*b*d**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/e**4 - 6*b*d**2*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**4 + 6*b*d**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**4 + 4*b*d*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**4 - 4*b*d*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**4 - b*n*x/e**4 + b*x*log(c*x**n)/e**4","A",0
55,1,500,0,70.468570," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d)**4,x)","- \frac{a d^{3} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 a d^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{3 a d \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{a \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{b d^{3} n \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{3 d}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{2 e x}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{\log{\left(x \right)}}{3 d^{3} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{b d^{3} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{3 b d^{2} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{3 b d^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} + \frac{3 b d n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{3 b d \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{b n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{b \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}}"," ",0,"-a*d**3*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))/e**3 + 3*a*d**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/e**3 - 3*a*d*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/e**3 + a*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/e**3 + b*d**3*n*Piecewise((x/d**4, Eq(e, 0)), (-3*d/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - 2*e*x/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - log(x)/(3*d**3*e) + log(d/e + x)/(3*d**3*e), True))/e**3 - b*d**3*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))*log(c*x**n)/e**3 - 3*b*d**2*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/e**3 + 3*b*d**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/e**3 + 3*b*d*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/e**3 - 3*b*d*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/e**3 - b*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/e**3 + b*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/e**3","A",0
56,1,748,0,15.670233," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d)**4,x)","\begin{cases} \tilde{\infty} \left(- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{\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}}{d^{4}} & \text{for}\: e = 0 \\\frac{- \frac{a}{x} - \frac{b n \log{\left(x \right)}}{x} - \frac{b n}{x} - \frac{b \log{\left(c \right)}}{x}}{e^{4}} & \text{for}\: d = 0 \\- \frac{2 a d^{3}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{6 a d^{2} e x}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{6 a d e^{2} x^{2}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{2 b d^{3} n \log{\left(\frac{d}{e} + x \right)}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{3 b d^{3} n}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{6 b d^{2} e n x \log{\left(\frac{d}{e} + x \right)}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{7 b d^{2} e n x}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{6 b d e^{2} n x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{4 b d e^{2} n x^{2}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} + \frac{2 b e^{3} n x^{3} \log{\left(x \right)}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} - \frac{2 b e^{3} n x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} + \frac{2 b e^{3} x^{3} \log{\left(c \right)}}{6 d^{4} e^{3} + 18 d^{3} e^{4} x + 18 d^{2} e^{5} x^{2} + 6 d e^{6} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x), Eq(d, 0) & Eq(e, 0)), ((a*x**3/3 + b*n*x**3*log(x)/3 - b*n*x**3/9 + b*x**3*log(c)/3)/d**4, Eq(e, 0)), ((-a/x - b*n*log(x)/x - b*n/x - b*log(c)/x)/e**4, Eq(d, 0)), (-2*a*d**3/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 6*a*d**2*e*x/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 6*a*d*e**2*x**2/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 2*b*d**3*n*log(d/e + x)/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 3*b*d**3*n/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 6*b*d**2*e*n*x*log(d/e + x)/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 7*b*d**2*e*n*x/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 6*b*d*e**2*n*x**2*log(d/e + x)/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 4*b*d*e**2*n*x**2/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) + 2*b*e**3*n*x**3*log(x)/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) - 2*b*e**3*n*x**3*log(d/e + x)/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3) + 2*b*e**3*x**3*log(c)/(6*d**4*e**3 + 18*d**3*e**4*x + 18*d**2*e**5*x**2 + 6*d*e**6*x**3), True))","A",0
57,1,796,0,15.686994," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d)**4,x)","\begin{cases} \tilde{\infty} \left(- \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}}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{- \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}}}{e^{4}} & \text{for}\: d = 0 \\\frac{\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}}{d^{4}} & \text{for}\: e = 0 \\- \frac{a d^{3}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} - \frac{3 a d^{2} e x}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} - \frac{b d^{3} n \log{\left(\frac{d}{e} + x \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} - \frac{3 b d^{2} e n x \log{\left(\frac{d}{e} + x \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} + \frac{b d^{2} e n x}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} + \frac{3 b d e^{2} n x^{2} \log{\left(x \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} - \frac{3 b d e^{2} n x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} + \frac{b d e^{2} n x^{2}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} + \frac{3 b d e^{2} x^{2} \log{\left(c \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} + \frac{b e^{3} n x^{3} \log{\left(x \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} - \frac{b e^{3} n x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} + \frac{b e^{3} x^{3} \log{\left(c \right)}}{6 d^{5} e^{2} + 18 d^{4} e^{3} x + 18 d^{3} e^{4} x^{2} + 6 d^{2} e^{5} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2)), Eq(d, 0) & Eq(e, 0)), ((-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2))/e**4, Eq(d, 0)), ((a*x**2/2 + b*n*x**2*log(x)/2 - b*n*x**2/4 + b*x**2*log(c)/2)/d**4, Eq(e, 0)), (-a*d**3/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) - 3*a*d**2*e*x/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) - b*d**3*n*log(d/e + x)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) - 3*b*d**2*e*n*x*log(d/e + x)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) + b*d**2*e*n*x/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) + 3*b*d*e**2*n*x**2*log(x)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) - 3*b*d*e**2*n*x**2*log(d/e + x)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) + b*d*e**2*n*x**2/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) + 3*b*d*e**2*x**2*log(c)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) + b*e**3*n*x**3*log(x)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) - b*e**3*n*x**3*log(d/e + x)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3) + b*e**3*x**3*log(c)/(6*d**5*e**2 + 18*d**4*e**3*x + 18*d**3*e**4*x**2 + 6*d**2*e**5*x**3), True))","A",0
58,1,882,0,16.079914," ","integrate((a+b*ln(c*x**n))/(e*x+d)**4,x)","\begin{cases} \tilde{\infty} \left(- \frac{a}{3 x^{3}} - \frac{b n \log{\left(x \right)}}{3 x^{3}} - \frac{b n}{9 x^{3}} - \frac{b \log{\left(c \right)}}{3 x^{3}}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{- \frac{a}{3 x^{3}} - \frac{b n \log{\left(x \right)}}{3 x^{3}} - \frac{b n}{9 x^{3}} - \frac{b \log{\left(c \right)}}{3 x^{3}}}{e^{4}} & \text{for}\: d = 0 \\\frac{a x + b n x \log{\left(x \right)} - b n x + b x \log{\left(c \right)}}{d^{4}} & \text{for}\: e = 0 \\- \frac{2 a d^{3}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} - \frac{2 b d^{3} n \log{\left(\frac{d}{e} + x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{3 b d^{3} n}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{6 b d^{2} e n x \log{\left(x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} - \frac{6 b d^{2} e n x \log{\left(\frac{d}{e} + x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{5 b d^{2} e n x}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{6 b d^{2} e x \log{\left(c \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{6 b d e^{2} n x^{2} \log{\left(x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} - \frac{6 b d e^{2} n x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{2 b d e^{2} n x^{2}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{6 b d e^{2} x^{2} \log{\left(c \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{2 b e^{3} n x^{3} \log{\left(x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} - \frac{2 b e^{3} n x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} + \frac{2 b e^{3} x^{3} \log{\left(c \right)}}{6 d^{6} e + 18 d^{5} e^{2} x + 18 d^{4} e^{3} x^{2} + 6 d^{3} e^{4} x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/(3*x**3) - b*n*log(x)/(3*x**3) - b*n/(9*x**3) - b*log(c)/(3*x**3)), Eq(d, 0) & Eq(e, 0)), ((-a/(3*x**3) - b*n*log(x)/(3*x**3) - b*n/(9*x**3) - b*log(c)/(3*x**3))/e**4, Eq(d, 0)), ((a*x + b*n*x*log(x) - b*n*x + b*x*log(c))/d**4, Eq(e, 0)), (-2*a*d**3/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) - 2*b*d**3*n*log(d/e + x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 3*b*d**3*n/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 6*b*d**2*e*n*x*log(x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) - 6*b*d**2*e*n*x*log(d/e + x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 5*b*d**2*e*n*x/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 6*b*d**2*e*x*log(c)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 6*b*d*e**2*n*x**2*log(x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) - 6*b*d*e**2*n*x**2*log(d/e + x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 2*b*d*e**2*n*x**2/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 6*b*d*e**2*x**2*log(c)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 2*b*e**3*n*x**3*log(x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) - 2*b*e**3*n*x**3*log(d/e + x)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3) + 2*b*e**3*x**3*log(c)/(6*d**6*e + 18*d**5*e**2*x + 18*d**4*e**3*x**2 + 6*d**3*e**4*x**3), True))","A",0
59,1,493,0,147.343841," ","integrate((a+b*ln(c*x**n))/x/(e*x+d)**4,x)","- \frac{a e \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right)}{d} - \frac{a e \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{a e \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{a e \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{a \log{\left(x \right)}}{d^{4}} - \frac{b e^{3} n \left(\begin{cases} - \frac{1}{e^{4} x} & \text{for}\: d = 0 \\- \frac{3 d}{6 d^{2} e^{3} + 12 d e^{4} x + 6 e^{5} x^{2}} - \frac{4 e x}{6 d^{2} e^{3} + 12 d e^{4} x + 6 e^{5} x^{2}} - \frac{\log{\left(d + e x \right)}}{3 d e^{3}} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{b e^{3} \left(\begin{cases} \frac{1}{e^{4} x} & \text{for}\: d = 0 \\- \frac{1}{3 d \left(\frac{d}{x} + e\right)^{3}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} + \frac{3 b e^{2} n \left(\begin{cases} - \frac{1}{e^{3} x} & \text{for}\: d = 0 \\- \frac{1}{2 d e^{2} + 2 e^{3} x} - \frac{\log{\left(d + e x \right)}}{2 d e^{2}} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{3 b e^{2} \left(\begin{cases} \frac{1}{e^{3} x} & \text{for}\: d = 0 \\- \frac{1}{2 d \left(\frac{d}{x} + e\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} - \frac{3 b e n \left(\begin{cases} - \frac{1}{e^{2} x} & \text{for}\: d = 0 \\- \frac{\log{\left(d^{2} + d e x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{3 b e \left(\begin{cases} \frac{1}{e^{2} x} & \text{for}\: d = 0 \\- \frac{1}{\frac{d^{2}}{x} + d e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} + \frac{b n \left(\begin{cases} - \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b \left(\begin{cases} \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\log{\left(\frac{d}{x} + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}}"," ",0,"-a*e*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))/d - a*e*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/d**2 - a*e*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**3 - a*e*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**4 + a*log(x)/d**4 - b*e**3*n*Piecewise((-1/(e**4*x), Eq(d, 0)), (-3*d/(6*d**2*e**3 + 12*d*e**4*x + 6*e**5*x**2) - 4*e*x/(6*d**2*e**3 + 12*d*e**4*x + 6*e**5*x**2) - log(d + e*x)/(3*d*e**3), True))/d**3 + b*e**3*Piecewise((1/(e**4*x), Eq(d, 0)), (-1/(3*d*(d/x + e)**3), True))*log(c*x**n)/d**3 + 3*b*e**2*n*Piecewise((-1/(e**3*x), Eq(d, 0)), (-1/(2*d*e**2 + 2*e**3*x) - log(d + e*x)/(2*d*e**2), True))/d**3 - 3*b*e**2*Piecewise((1/(e**3*x), Eq(d, 0)), (-1/(2*d*(d/x + e)**2), True))*log(c*x**n)/d**3 - 3*b*e*n*Piecewise((-1/(e**2*x), Eq(d, 0)), (-log(d**2 + d*e*x)/(d*e), True))/d**3 + 3*b*e*Piecewise((1/(e**2*x), Eq(d, 0)), (-1/(d**2/x + d*e), True))*log(c*x**n)/d**3 + b*n*Piecewise((-1/(e*x), Eq(d, 0)), (Piecewise((log(e)*log(x) + polylog(2, d*exp_polar(I*pi)/(e*x)), Abs(x) < 1), (-log(e)*log(1/x) + polylog(2, d*exp_polar(I*pi)/(e*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) + polylog(2, d*exp_polar(I*pi)/(e*x)), True))/d, True))/d**3 - b*Piecewise((1/(e*x), Eq(d, 0)), (log(d/x + e)/d, True))*log(c*x**n)/d**3","A",0
60,1,595,0,141.374976," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d)**4,x)","\frac{a e^{2} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{2 a e^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{3 a e^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{a}{d^{4} x} + \frac{4 a e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{5}} - \frac{4 a e \log{\left(x \right)}}{d^{5}} - \frac{b e^{2} n \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{3 d}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{2 e x}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{\log{\left(x \right)}}{3 d^{3} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{b e^{2} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} - \frac{2 b e^{2} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{2 b e^{2} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} - \frac{3 b e^{2} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{3 b e^{2} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} - \frac{b n}{d^{4} x} - \frac{b \log{\left(c x^{n} \right)}}{d^{4} x} - \frac{4 b e^{2} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{5}} + \frac{4 b e^{2} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{5}} + \frac{2 b e n \log{\left(x \right)}^{2}}{d^{5}} - \frac{4 b e \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{5}}"," ",0,"a*e**2*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))/d**2 + 2*a*e**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/d**3 + 3*a*e**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**4 - a/(d**4*x) + 4*a*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**5 - 4*a*e*log(x)/d**5 - b*e**2*n*Piecewise((x/d**4, Eq(e, 0)), (-3*d/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - 2*e*x/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - log(x)/(3*d**3*e) + log(d/e + x)/(3*d**3*e), True))/d**2 + b*e**2*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))*log(c*x**n)/d**2 - 2*b*e**2*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/d**3 + 2*b*e**2*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/d**3 - 3*b*e**2*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/d**4 + 3*b*e**2*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/d**4 - b*n/(d**4*x) - b*log(c*x**n)/(d**4*x) - 4*b*e**2*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**5 + 4*b*e**2*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**5 + 2*b*e*n*log(x)**2/d**5 - 4*b*e*log(x)*log(c*x**n)/d**5","A",0
61,1,649,0,148.347329," ","integrate((a+b*ln(c*x**n))/x**3/(e*x+d)**4,x)","- \frac{a e^{3} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{3 a e^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{a}{2 d^{4} x^{2}} - \frac{6 a e^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right)}{d^{5}} + \frac{4 a e}{d^{5} x} - \frac{10 a e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right)}{d^{6}} + \frac{10 a e^{2} \log{\left(x \right)}}{d^{6}} + \frac{b e^{3} n \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{3 d}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{2 e x}{6 d^{4} e + 12 d^{3} e^{2} x + 6 d^{2} e^{3} x^{2}} - \frac{\log{\left(x \right)}}{3 d^{3} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{3 d^{3} e} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b e^{3} \left(\begin{cases} \frac{x}{d^{4}} & \text{for}\: e = 0 \\- \frac{1}{3 e \left(d + e x\right)^{3}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} + \frac{3 b e^{3} n \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{3 b e^{3} \left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} - \frac{b n}{4 d^{4} x^{2}} - \frac{b \log{\left(c x^{n} \right)}}{2 d^{4} x^{2}} + \frac{6 b e^{3} n \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{d^{5}} - \frac{6 b e^{3} \left(\begin{cases} \frac{x}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{5}} + \frac{4 b e n}{d^{5} x} + \frac{4 b e \log{\left(c x^{n} \right)}}{d^{5} x} + \frac{10 b e^{3} n \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \operatorname{Li}_{2}\left(\frac{e x e^{i \pi}}{d}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{d^{6}} - \frac{10 b e^{3} \left(\begin{cases} \frac{x}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{6}} - \frac{5 b e^{2} n \log{\left(x \right)}^{2}}{d^{6}} + \frac{10 b e^{2} \log{\left(x \right)} \log{\left(c x^{n} \right)}}{d^{6}}"," ",0,"-a*e**3*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))/d**3 - 3*a*e**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))/d**4 - a/(2*d**4*x**2) - 6*a*e**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))/d**5 + 4*a*e/(d**5*x) - 10*a*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))/d**6 + 10*a*e**2*log(x)/d**6 + b*e**3*n*Piecewise((x/d**4, Eq(e, 0)), (-3*d/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - 2*e*x/(6*d**4*e + 12*d**3*e**2*x + 6*d**2*e**3*x**2) - log(x)/(3*d**3*e) + log(d/e + x)/(3*d**3*e), True))/d**3 - b*e**3*Piecewise((x/d**4, Eq(e, 0)), (-1/(3*e*(d + e*x)**3), True))*log(c*x**n)/d**3 + 3*b*e**3*n*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/d**4 - 3*b*e**3*Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(c*x**n)/d**4 - b*n/(4*d**4*x**2) - b*log(c*x**n)/(2*d**4*x**2) + 6*b*e**3*n*Piecewise((x/d**2, Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x)/(d*e), True))/d**5 - 6*b*e**3*Piecewise((x/d**2, Eq(e, 0)), (-1/(d*e + e**2*x), True))*log(c*x**n)/d**5 + 4*b*e*n/(d**5*x) + 4*b*e*log(c*x**n)/(d**5*x) + 10*b*e**3*n*Piecewise((x/d, Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x*exp_polar(I*pi)/d), Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x*exp_polar(I*pi)/d), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x*exp_polar(I*pi)/d), True))/e, True))/d**6 - 10*b*e**3*Piecewise((x/d, Eq(e, 0)), (log(d + e*x)/e, True))*log(c*x**n)/d**6 - 5*b*e**2*n*log(x)**2/d**6 + 10*b*e**2*log(x)*log(c*x**n)/d**6","A",0
62,-1,0,0,0.000000," ","integrate(x**8*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate(x**7*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate(x**6*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x+d)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,0,0,0,0.000000," ","integrate(ln(c*x)/(-c*x+1),x)","- \int \frac{\log{\left(c x \right)}}{c x - 1}\, dx"," ",0,"-Integral(log(c*x)/(c*x - 1), x)","F",0
75,0,0,0,0.000000," ","integrate(ln(x/c)/(c-x),x)","- \int \frac{\log{\left(\frac{x}{c} \right)}}{- c + x}\, dx"," ",0,"-Integral(log(x/c)/(-c + x), x)","F",0
76,1,309,0,2.748081," ","integrate(x**2*(e*x+d)*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} d x^{3}}{3} + \frac{a^{2} e x^{4}}{4} + \frac{2 a b d n x^{3} \log{\left(x \right)}}{3} - \frac{2 a b d n x^{3}}{9} + \frac{2 a b d x^{3} \log{\left(c \right)}}{3} + \frac{a b e n x^{4} \log{\left(x \right)}}{2} - \frac{a b e n x^{4}}{8} + \frac{a b e x^{4} \log{\left(c \right)}}{2} + \frac{b^{2} d n^{2} x^{3} \log{\left(x \right)}^{2}}{3} - \frac{2 b^{2} d n^{2} x^{3} \log{\left(x \right)}}{9} + \frac{2 b^{2} d n^{2} x^{3}}{27} + \frac{2 b^{2} d n x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{2 b^{2} d n x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} d x^{3} \log{\left(c \right)}^{2}}{3} + \frac{b^{2} e n^{2} x^{4} \log{\left(x \right)}^{2}}{4} - \frac{b^{2} e n^{2} x^{4} \log{\left(x \right)}}{8} + \frac{b^{2} e n^{2} x^{4}}{32} + \frac{b^{2} e n x^{4} \log{\left(c \right)} \log{\left(x \right)}}{2} - \frac{b^{2} e n x^{4} \log{\left(c \right)}}{8} + \frac{b^{2} e x^{4} \log{\left(c \right)}^{2}}{4}"," ",0,"a**2*d*x**3/3 + a**2*e*x**4/4 + 2*a*b*d*n*x**3*log(x)/3 - 2*a*b*d*n*x**3/9 + 2*a*b*d*x**3*log(c)/3 + a*b*e*n*x**4*log(x)/2 - a*b*e*n*x**4/8 + a*b*e*x**4*log(c)/2 + b**2*d*n**2*x**3*log(x)**2/3 - 2*b**2*d*n**2*x**3*log(x)/9 + 2*b**2*d*n**2*x**3/27 + 2*b**2*d*n*x**3*log(c)*log(x)/3 - 2*b**2*d*n*x**3*log(c)/9 + b**2*d*x**3*log(c)**2/3 + b**2*e*n**2*x**4*log(x)**2/4 - b**2*e*n**2*x**4*log(x)/8 + b**2*e*n**2*x**4/32 + b**2*e*n*x**4*log(c)*log(x)/2 - b**2*e*n*x**4*log(c)/8 + b**2*e*x**4*log(c)**2/4","B",0
77,1,304,0,1.799299," ","integrate(x*(e*x+d)*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} d x^{2}}{2} + \frac{a^{2} e x^{3}}{3} + a b d n x^{2} \log{\left(x \right)} - \frac{a b d n x^{2}}{2} + a b d x^{2} \log{\left(c \right)} + \frac{2 a b e n x^{3} \log{\left(x \right)}}{3} - \frac{2 a b e n x^{3}}{9} + \frac{2 a b e x^{3} \log{\left(c \right)}}{3} + \frac{b^{2} d n^{2} x^{2} \log{\left(x \right)}^{2}}{2} - \frac{b^{2} d n^{2} x^{2} \log{\left(x \right)}}{2} + \frac{b^{2} d n^{2} x^{2}}{4} + b^{2} d n x^{2} \log{\left(c \right)} \log{\left(x \right)} - \frac{b^{2} d n x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} d x^{2} \log{\left(c \right)}^{2}}{2} + \frac{b^{2} e n^{2} x^{3} \log{\left(x \right)}^{2}}{3} - \frac{2 b^{2} e n^{2} x^{3} \log{\left(x \right)}}{9} + \frac{2 b^{2} e n^{2} x^{3}}{27} + \frac{2 b^{2} e n x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{2 b^{2} e n x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} e x^{3} \log{\left(c \right)}^{2}}{3}"," ",0,"a**2*d*x**2/2 + a**2*e*x**3/3 + a*b*d*n*x**2*log(x) - a*b*d*n*x**2/2 + a*b*d*x**2*log(c) + 2*a*b*e*n*x**3*log(x)/3 - 2*a*b*e*n*x**3/9 + 2*a*b*e*x**3*log(c)/3 + b**2*d*n**2*x**2*log(x)**2/2 - b**2*d*n**2*x**2*log(x)/2 + b**2*d*n**2*x**2/4 + b**2*d*n*x**2*log(c)*log(x) - b**2*d*n*x**2*log(c)/2 + b**2*d*x**2*log(c)**2/2 + b**2*e*n**2*x**3*log(x)**2/3 - 2*b**2*e*n**2*x**3*log(x)/9 + 2*b**2*e*n**2*x**3/27 + 2*b**2*e*n*x**3*log(c)*log(x)/3 - 2*b**2*e*n*x**3*log(c)/9 + b**2*e*x**3*log(c)**2/3","B",0
78,1,270,0,1.101608," ","integrate((e*x+d)*(a+b*ln(c*x**n))**2,x)","a^{2} d x + \frac{a^{2} e x^{2}}{2} + 2 a b d n x \log{\left(x \right)} - 2 a b d n x + 2 a b d x \log{\left(c \right)} + a b e n x^{2} \log{\left(x \right)} - \frac{a b e n x^{2}}{2} + a b e x^{2} \log{\left(c \right)} + b^{2} d n^{2} x \log{\left(x \right)}^{2} - 2 b^{2} d n^{2} x \log{\left(x \right)} + 2 b^{2} d n^{2} x + 2 b^{2} d n x \log{\left(c \right)} \log{\left(x \right)} - 2 b^{2} d n x \log{\left(c \right)} + b^{2} d x \log{\left(c \right)}^{2} + \frac{b^{2} e n^{2} x^{2} \log{\left(x \right)}^{2}}{2} - \frac{b^{2} e n^{2} x^{2} \log{\left(x \right)}}{2} + \frac{b^{2} e n^{2} x^{2}}{4} + b^{2} e n x^{2} \log{\left(c \right)} \log{\left(x \right)} - \frac{b^{2} e n x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} e x^{2} \log{\left(c \right)}^{2}}{2}"," ",0,"a**2*d*x + a**2*e*x**2/2 + 2*a*b*d*n*x*log(x) - 2*a*b*d*n*x + 2*a*b*d*x*log(c) + a*b*e*n*x**2*log(x) - a*b*e*n*x**2/2 + a*b*e*x**2*log(c) + b**2*d*n**2*x*log(x)**2 - 2*b**2*d*n**2*x*log(x) + 2*b**2*d*n**2*x + 2*b**2*d*n*x*log(c)*log(x) - 2*b**2*d*n*x*log(c) + b**2*d*x*log(c)**2 + b**2*e*n**2*x**2*log(x)**2/2 - b**2*e*n**2*x**2*log(x)/2 + b**2*e*n**2*x**2/4 + b**2*e*n*x**2*log(c)*log(x) - b**2*e*n*x**2*log(c)/2 + b**2*e*x**2*log(c)**2/2","B",0
79,1,204,0,1.048366," ","integrate((e*x+d)*(a+b*ln(c*x**n))**2/x,x)","a^{2} d \log{\left(x \right)} + a^{2} e x + a b d n \log{\left(x \right)}^{2} + 2 a b d \log{\left(c \right)} \log{\left(x \right)} + 2 a b e n x \log{\left(x \right)} - 2 a b e n x + 2 a b e x \log{\left(c \right)} + \frac{b^{2} d n^{2} \log{\left(x \right)}^{3}}{3} + b^{2} d n \log{\left(c \right)} \log{\left(x \right)}^{2} + b^{2} d \log{\left(c \right)}^{2} \log{\left(x \right)} + b^{2} e n^{2} x \log{\left(x \right)}^{2} - 2 b^{2} e n^{2} x \log{\left(x \right)} + 2 b^{2} e n^{2} x + 2 b^{2} e n x \log{\left(c \right)} \log{\left(x \right)} - 2 b^{2} e n x \log{\left(c \right)} + b^{2} e x \log{\left(c \right)}^{2}"," ",0,"a**2*d*log(x) + a**2*e*x + a*b*d*n*log(x)**2 + 2*a*b*d*log(c)*log(x) + 2*a*b*e*n*x*log(x) - 2*a*b*e*n*x + 2*a*b*e*x*log(c) + b**2*d*n**2*log(x)**3/3 + b**2*d*n*log(c)*log(x)**2 + b**2*d*log(c)**2*log(x) + b**2*e*n**2*x*log(x)**2 - 2*b**2*e*n**2*x*log(x) + 2*b**2*e*n**2*x + 2*b**2*e*n*x*log(c)*log(x) - 2*b**2*e*n*x*log(c) + b**2*e*x*log(c)**2","B",0
80,1,182,0,6.634051," ","integrate((e*x+d)*(a+b*ln(c*x**n))**2/x**2,x)","- \frac{a^{2} d}{x} + a^{2} e \log{\left(x \right)} - \frac{2 a b d n}{x} - \frac{2 a b d \log{\left(c x^{n} \right)}}{x} - 2 a b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) - \frac{b^{2} d n^{2} \log{\left(x \right)}^{2}}{x} - \frac{2 b^{2} d n^{2} \log{\left(x \right)}}{x} - \frac{2 b^{2} d n^{2}}{x} - \frac{2 b^{2} d n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{2 b^{2} d n \log{\left(c \right)}}{x} - \frac{b^{2} d \log{\left(c \right)}^{2}}{x} - b^{2} e \left(\begin{cases} - \log{\left(c \right)}^{2} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{3}}{3 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a**2*d/x + a**2*e*log(x) - 2*a*b*d*n/x - 2*a*b*d*log(c*x**n)/x - 2*a*b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)) - b**2*d*n**2*log(x)**2/x - 2*b**2*d*n**2*log(x)/x - 2*b**2*d*n**2/x - 2*b**2*d*n*log(c)*log(x)/x - 2*b**2*d*n*log(c)/x - b**2*d*log(c)**2/x - b**2*e*Piecewise((-log(c)**2*log(x), Eq(n, 0)), (-log(c*x**n)**3/(3*n), True))","A",0
81,1,272,0,1.283644," ","integrate((e*x+d)*(a+b*ln(c*x**n))**2/x**3,x)","- \frac{a^{2} d}{2 x^{2}} - \frac{a^{2} e}{x} - \frac{a b d n \log{\left(x \right)}}{x^{2}} - \frac{a b d n}{2 x^{2}} - \frac{a b d \log{\left(c \right)}}{x^{2}} - \frac{2 a b e n \log{\left(x \right)}}{x} - \frac{2 a b e n}{x} - \frac{2 a b e \log{\left(c \right)}}{x} - \frac{b^{2} d n^{2} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{b^{2} d n^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{b^{2} d n^{2}}{4 x^{2}} - \frac{b^{2} d n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} d n \log{\left(c \right)}}{2 x^{2}} - \frac{b^{2} d \log{\left(c \right)}^{2}}{2 x^{2}} - \frac{b^{2} e n^{2} \log{\left(x \right)}^{2}}{x} - \frac{2 b^{2} e n^{2} \log{\left(x \right)}}{x} - \frac{2 b^{2} e n^{2}}{x} - \frac{2 b^{2} e n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{2 b^{2} e n \log{\left(c \right)}}{x} - \frac{b^{2} e \log{\left(c \right)}^{2}}{x}"," ",0,"-a**2*d/(2*x**2) - a**2*e/x - a*b*d*n*log(x)/x**2 - a*b*d*n/(2*x**2) - a*b*d*log(c)/x**2 - 2*a*b*e*n*log(x)/x - 2*a*b*e*n/x - 2*a*b*e*log(c)/x - b**2*d*n**2*log(x)**2/(2*x**2) - b**2*d*n**2*log(x)/(2*x**2) - b**2*d*n**2/(4*x**2) - b**2*d*n*log(c)*log(x)/x**2 - b**2*d*n*log(c)/(2*x**2) - b**2*d*log(c)**2/(2*x**2) - b**2*e*n**2*log(x)**2/x - 2*b**2*e*n**2*log(x)/x - 2*b**2*e*n**2/x - 2*b**2*e*n*log(c)*log(x)/x - 2*b**2*e*n*log(c)/x - b**2*e*log(c)**2/x","B",0
82,1,306,0,2.028410," ","integrate((e*x+d)*(a+b*ln(c*x**n))**2/x**4,x)","- \frac{a^{2} d}{3 x^{3}} - \frac{a^{2} e}{2 x^{2}} - \frac{2 a b d n \log{\left(x \right)}}{3 x^{3}} - \frac{2 a b d n}{9 x^{3}} - \frac{2 a b d \log{\left(c \right)}}{3 x^{3}} - \frac{a b e n \log{\left(x \right)}}{x^{2}} - \frac{a b e n}{2 x^{2}} - \frac{a b e \log{\left(c \right)}}{x^{2}} - \frac{b^{2} d n^{2} \log{\left(x \right)}^{2}}{3 x^{3}} - \frac{2 b^{2} d n^{2} \log{\left(x \right)}}{9 x^{3}} - \frac{2 b^{2} d n^{2}}{27 x^{3}} - \frac{2 b^{2} d n \log{\left(c \right)} \log{\left(x \right)}}{3 x^{3}} - \frac{2 b^{2} d n \log{\left(c \right)}}{9 x^{3}} - \frac{b^{2} d \log{\left(c \right)}^{2}}{3 x^{3}} - \frac{b^{2} e n^{2} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{b^{2} e n^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{b^{2} e n^{2}}{4 x^{2}} - \frac{b^{2} e n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} e n \log{\left(c \right)}}{2 x^{2}} - \frac{b^{2} e \log{\left(c \right)}^{2}}{2 x^{2}}"," ",0,"-a**2*d/(3*x**3) - a**2*e/(2*x**2) - 2*a*b*d*n*log(x)/(3*x**3) - 2*a*b*d*n/(9*x**3) - 2*a*b*d*log(c)/(3*x**3) - a*b*e*n*log(x)/x**2 - a*b*e*n/(2*x**2) - a*b*e*log(c)/x**2 - b**2*d*n**2*log(x)**2/(3*x**3) - 2*b**2*d*n**2*log(x)/(9*x**3) - 2*b**2*d*n**2/(27*x**3) - 2*b**2*d*n*log(c)*log(x)/(3*x**3) - 2*b**2*d*n*log(c)/(9*x**3) - b**2*d*log(c)**2/(3*x**3) - b**2*e*n**2*log(x)**2/(2*x**2) - b**2*e*n**2*log(x)/(2*x**2) - b**2*e*n**2/(4*x**2) - b**2*e*n*log(c)*log(x)/x**2 - b**2*e*n*log(c)/(2*x**2) - b**2*e*log(c)**2/(2*x**2)","B",0
83,1,311,0,3.067681," ","integrate((e*x+d)*(a+b*ln(c*x**n))**2/x**5,x)","- \frac{a^{2} d}{4 x^{4}} - \frac{a^{2} e}{3 x^{3}} - \frac{a b d n \log{\left(x \right)}}{2 x^{4}} - \frac{a b d n}{8 x^{4}} - \frac{a b d \log{\left(c \right)}}{2 x^{4}} - \frac{2 a b e n \log{\left(x \right)}}{3 x^{3}} - \frac{2 a b e n}{9 x^{3}} - \frac{2 a b e \log{\left(c \right)}}{3 x^{3}} - \frac{b^{2} d n^{2} \log{\left(x \right)}^{2}}{4 x^{4}} - \frac{b^{2} d n^{2} \log{\left(x \right)}}{8 x^{4}} - \frac{b^{2} d n^{2}}{32 x^{4}} - \frac{b^{2} d n \log{\left(c \right)} \log{\left(x \right)}}{2 x^{4}} - \frac{b^{2} d n \log{\left(c \right)}}{8 x^{4}} - \frac{b^{2} d \log{\left(c \right)}^{2}}{4 x^{4}} - \frac{b^{2} e n^{2} \log{\left(x \right)}^{2}}{3 x^{3}} - \frac{2 b^{2} e n^{2} \log{\left(x \right)}}{9 x^{3}} - \frac{2 b^{2} e n^{2}}{27 x^{3}} - \frac{2 b^{2} e n \log{\left(c \right)} \log{\left(x \right)}}{3 x^{3}} - \frac{2 b^{2} e n \log{\left(c \right)}}{9 x^{3}} - \frac{b^{2} e \log{\left(c \right)}^{2}}{3 x^{3}}"," ",0,"-a**2*d/(4*x**4) - a**2*e/(3*x**3) - a*b*d*n*log(x)/(2*x**4) - a*b*d*n/(8*x**4) - a*b*d*log(c)/(2*x**4) - 2*a*b*e*n*log(x)/(3*x**3) - 2*a*b*e*n/(9*x**3) - 2*a*b*e*log(c)/(3*x**3) - b**2*d*n**2*log(x)**2/(4*x**4) - b**2*d*n**2*log(x)/(8*x**4) - b**2*d*n**2/(32*x**4) - b**2*d*n*log(c)*log(x)/(2*x**4) - b**2*d*n*log(c)/(8*x**4) - b**2*d*log(c)**2/(4*x**4) - b**2*e*n**2*log(x)**2/(3*x**3) - 2*b**2*e*n**2*log(x)/(9*x**3) - 2*b**2*e*n**2/(27*x**3) - 2*b**2*e*n*log(c)*log(x)/(3*x**3) - 2*b**2*e*n*log(c)/(9*x**3) - b**2*e*log(c)**2/(3*x**3)","B",0
84,1,517,0,4.824706," ","integrate(x**2*(e*x+d)**2*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} d^{2} x^{3}}{3} + \frac{a^{2} d e x^{4}}{2} + \frac{a^{2} e^{2} x^{5}}{5} + \frac{2 a b d^{2} n x^{3} \log{\left(x \right)}}{3} - \frac{2 a b d^{2} n x^{3}}{9} + \frac{2 a b d^{2} x^{3} \log{\left(c \right)}}{3} + a b d e n x^{4} \log{\left(x \right)} - \frac{a b d e n x^{4}}{4} + a b d e x^{4} \log{\left(c \right)} + \frac{2 a b e^{2} n x^{5} \log{\left(x \right)}}{5} - \frac{2 a b e^{2} n x^{5}}{25} + \frac{2 a b e^{2} x^{5} \log{\left(c \right)}}{5} + \frac{b^{2} d^{2} n^{2} x^{3} \log{\left(x \right)}^{2}}{3} - \frac{2 b^{2} d^{2} n^{2} x^{3} \log{\left(x \right)}}{9} + \frac{2 b^{2} d^{2} n^{2} x^{3}}{27} + \frac{2 b^{2} d^{2} n x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{2 b^{2} d^{2} n x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} d^{2} x^{3} \log{\left(c \right)}^{2}}{3} + \frac{b^{2} d e n^{2} x^{4} \log{\left(x \right)}^{2}}{2} - \frac{b^{2} d e n^{2} x^{4} \log{\left(x \right)}}{4} + \frac{b^{2} d e n^{2} x^{4}}{16} + b^{2} d e n x^{4} \log{\left(c \right)} \log{\left(x \right)} - \frac{b^{2} d e n x^{4} \log{\left(c \right)}}{4} + \frac{b^{2} d e x^{4} \log{\left(c \right)}^{2}}{2} + \frac{b^{2} e^{2} n^{2} x^{5} \log{\left(x \right)}^{2}}{5} - \frac{2 b^{2} e^{2} n^{2} x^{5} \log{\left(x \right)}}{25} + \frac{2 b^{2} e^{2} n^{2} x^{5}}{125} + \frac{2 b^{2} e^{2} n x^{5} \log{\left(c \right)} \log{\left(x \right)}}{5} - \frac{2 b^{2} e^{2} n x^{5} \log{\left(c \right)}}{25} + \frac{b^{2} e^{2} x^{5} \log{\left(c \right)}^{2}}{5}"," ",0,"a**2*d**2*x**3/3 + a**2*d*e*x**4/2 + a**2*e**2*x**5/5 + 2*a*b*d**2*n*x**3*log(x)/3 - 2*a*b*d**2*n*x**3/9 + 2*a*b*d**2*x**3*log(c)/3 + a*b*d*e*n*x**4*log(x) - a*b*d*e*n*x**4/4 + a*b*d*e*x**4*log(c) + 2*a*b*e**2*n*x**5*log(x)/5 - 2*a*b*e**2*n*x**5/25 + 2*a*b*e**2*x**5*log(c)/5 + b**2*d**2*n**2*x**3*log(x)**2/3 - 2*b**2*d**2*n**2*x**3*log(x)/9 + 2*b**2*d**2*n**2*x**3/27 + 2*b**2*d**2*n*x**3*log(c)*log(x)/3 - 2*b**2*d**2*n*x**3*log(c)/9 + b**2*d**2*x**3*log(c)**2/3 + b**2*d*e*n**2*x**4*log(x)**2/2 - b**2*d*e*n**2*x**4*log(x)/4 + b**2*d*e*n**2*x**4/16 + b**2*d*e*n*x**4*log(c)*log(x) - b**2*d*e*n*x**4*log(c)/4 + b**2*d*e*x**4*log(c)**2/2 + b**2*e**2*n**2*x**5*log(x)**2/5 - 2*b**2*e**2*n**2*x**5*log(x)/25 + 2*b**2*e**2*n**2*x**5/125 + 2*b**2*e**2*n*x**5*log(c)*log(x)/5 - 2*b**2*e**2*n*x**5*log(c)/25 + b**2*e**2*x**5*log(c)**2/5","B",0
85,1,510,0,3.268976," ","integrate(x*(e*x+d)**2*(a+b*ln(c*x**n))**2,x)","\frac{a^{2} d^{2} x^{2}}{2} + \frac{2 a^{2} d e x^{3}}{3} + \frac{a^{2} e^{2} x^{4}}{4} + a b d^{2} n x^{2} \log{\left(x \right)} - \frac{a b d^{2} n x^{2}}{2} + a b d^{2} x^{2} \log{\left(c \right)} + \frac{4 a b d e n x^{3} \log{\left(x \right)}}{3} - \frac{4 a b d e n x^{3}}{9} + \frac{4 a b d e x^{3} \log{\left(c \right)}}{3} + \frac{a b e^{2} n x^{4} \log{\left(x \right)}}{2} - \frac{a b e^{2} n x^{4}}{8} + \frac{a b e^{2} x^{4} \log{\left(c \right)}}{2} + \frac{b^{2} d^{2} n^{2} x^{2} \log{\left(x \right)}^{2}}{2} - \frac{b^{2} d^{2} n^{2} x^{2} \log{\left(x \right)}}{2} + \frac{b^{2} d^{2} n^{2} x^{2}}{4} + b^{2} d^{2} n x^{2} \log{\left(c \right)} \log{\left(x \right)} - \frac{b^{2} d^{2} n x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} d^{2} x^{2} \log{\left(c \right)}^{2}}{2} + \frac{2 b^{2} d e n^{2} x^{3} \log{\left(x \right)}^{2}}{3} - \frac{4 b^{2} d e n^{2} x^{3} \log{\left(x \right)}}{9} + \frac{4 b^{2} d e n^{2} x^{3}}{27} + \frac{4 b^{2} d e n x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{4 b^{2} d e n x^{3} \log{\left(c \right)}}{9} + \frac{2 b^{2} d e x^{3} \log{\left(c \right)}^{2}}{3} + \frac{b^{2} e^{2} n^{2} x^{4} \log{\left(x \right)}^{2}}{4} - \frac{b^{2} e^{2} n^{2} x^{4} \log{\left(x \right)}}{8} + \frac{b^{2} e^{2} n^{2} x^{4}}{32} + \frac{b^{2} e^{2} n x^{4} \log{\left(c \right)} \log{\left(x \right)}}{2} - \frac{b^{2} e^{2} n x^{4} \log{\left(c \right)}}{8} + \frac{b^{2} e^{2} x^{4} \log{\left(c \right)}^{2}}{4}"," ",0,"a**2*d**2*x**2/2 + 2*a**2*d*e*x**3/3 + a**2*e**2*x**4/4 + a*b*d**2*n*x**2*log(x) - a*b*d**2*n*x**2/2 + a*b*d**2*x**2*log(c) + 4*a*b*d*e*n*x**3*log(x)/3 - 4*a*b*d*e*n*x**3/9 + 4*a*b*d*e*x**3*log(c)/3 + a*b*e**2*n*x**4*log(x)/2 - a*b*e**2*n*x**4/8 + a*b*e**2*x**4*log(c)/2 + b**2*d**2*n**2*x**2*log(x)**2/2 - b**2*d**2*n**2*x**2*log(x)/2 + b**2*d**2*n**2*x**2/4 + b**2*d**2*n*x**2*log(c)*log(x) - b**2*d**2*n*x**2*log(c)/2 + b**2*d**2*x**2*log(c)**2/2 + 2*b**2*d*e*n**2*x**3*log(x)**2/3 - 4*b**2*d*e*n**2*x**3*log(x)/9 + 4*b**2*d*e*n**2*x**3/27 + 4*b**2*d*e*n*x**3*log(c)*log(x)/3 - 4*b**2*d*e*n*x**3*log(c)/9 + 2*b**2*d*e*x**3*log(c)**2/3 + b**2*e**2*n**2*x**4*log(x)**2/4 - b**2*e**2*n**2*x**4*log(x)/8 + b**2*e**2*n**2*x**4/32 + b**2*e**2*n*x**4*log(c)*log(x)/2 - b**2*e**2*n*x**4*log(c)/8 + b**2*e**2*x**4*log(c)**2/4","B",0
86,1,478,0,2.184953," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**2,x)","a^{2} d^{2} x + a^{2} d e x^{2} + \frac{a^{2} e^{2} x^{3}}{3} + 2 a b d^{2} n x \log{\left(x \right)} - 2 a b d^{2} n x + 2 a b d^{2} x \log{\left(c \right)} + 2 a b d e n x^{2} \log{\left(x \right)} - a b d e n x^{2} + 2 a b d e x^{2} \log{\left(c \right)} + \frac{2 a b e^{2} n x^{3} \log{\left(x \right)}}{3} - \frac{2 a b e^{2} n x^{3}}{9} + \frac{2 a b e^{2} x^{3} \log{\left(c \right)}}{3} + b^{2} d^{2} n^{2} x \log{\left(x \right)}^{2} - 2 b^{2} d^{2} n^{2} x \log{\left(x \right)} + 2 b^{2} d^{2} n^{2} x + 2 b^{2} d^{2} n x \log{\left(c \right)} \log{\left(x \right)} - 2 b^{2} d^{2} n x \log{\left(c \right)} + b^{2} d^{2} x \log{\left(c \right)}^{2} + b^{2} d e n^{2} x^{2} \log{\left(x \right)}^{2} - b^{2} d e n^{2} x^{2} \log{\left(x \right)} + \frac{b^{2} d e n^{2} x^{2}}{2} + 2 b^{2} d e n x^{2} \log{\left(c \right)} \log{\left(x \right)} - b^{2} d e n x^{2} \log{\left(c \right)} + b^{2} d e x^{2} \log{\left(c \right)}^{2} + \frac{b^{2} e^{2} n^{2} x^{3} \log{\left(x \right)}^{2}}{3} - \frac{2 b^{2} e^{2} n^{2} x^{3} \log{\left(x \right)}}{9} + \frac{2 b^{2} e^{2} n^{2} x^{3}}{27} + \frac{2 b^{2} e^{2} n x^{3} \log{\left(c \right)} \log{\left(x \right)}}{3} - \frac{2 b^{2} e^{2} n x^{3} \log{\left(c \right)}}{9} + \frac{b^{2} e^{2} x^{3} \log{\left(c \right)}^{2}}{3}"," ",0,"a**2*d**2*x + a**2*d*e*x**2 + a**2*e**2*x**3/3 + 2*a*b*d**2*n*x*log(x) - 2*a*b*d**2*n*x + 2*a*b*d**2*x*log(c) + 2*a*b*d*e*n*x**2*log(x) - a*b*d*e*n*x**2 + 2*a*b*d*e*x**2*log(c) + 2*a*b*e**2*n*x**3*log(x)/3 - 2*a*b*e**2*n*x**3/9 + 2*a*b*e**2*x**3*log(c)/3 + b**2*d**2*n**2*x*log(x)**2 - 2*b**2*d**2*n**2*x*log(x) + 2*b**2*d**2*n**2*x + 2*b**2*d**2*n*x*log(c)*log(x) - 2*b**2*d**2*n*x*log(c) + b**2*d**2*x*log(c)**2 + b**2*d*e*n**2*x**2*log(x)**2 - b**2*d*e*n**2*x**2*log(x) + b**2*d*e*n**2*x**2/2 + 2*b**2*d*e*n*x**2*log(c)*log(x) - b**2*d*e*n*x**2*log(c) + b**2*d*e*x**2*log(c)**2 + b**2*e**2*n**2*x**3*log(x)**2/3 - 2*b**2*e**2*n**2*x**3*log(x)/9 + 2*b**2*e**2*n**2*x**3/27 + 2*b**2*e**2*n*x**3*log(c)*log(x)/3 - 2*b**2*e**2*n*x**3*log(c)/9 + b**2*e**2*x**3*log(c)**2/3","B",0
87,1,398,0,2.106538," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**2/x,x)","a^{2} d^{2} \log{\left(x \right)} + 2 a^{2} d e x + \frac{a^{2} e^{2} x^{2}}{2} + a b d^{2} n \log{\left(x \right)}^{2} + 2 a b d^{2} \log{\left(c \right)} \log{\left(x \right)} + 4 a b d e n x \log{\left(x \right)} - 4 a b d e n x + 4 a b d e x \log{\left(c \right)} + a b e^{2} n x^{2} \log{\left(x \right)} - \frac{a b e^{2} n x^{2}}{2} + a b e^{2} x^{2} \log{\left(c \right)} + \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}^{3}}{3} + b^{2} d^{2} n \log{\left(c \right)} \log{\left(x \right)}^{2} + b^{2} d^{2} \log{\left(c \right)}^{2} \log{\left(x \right)} + 2 b^{2} d e n^{2} x \log{\left(x \right)}^{2} - 4 b^{2} d e n^{2} x \log{\left(x \right)} + 4 b^{2} d e n^{2} x + 4 b^{2} d e n x \log{\left(c \right)} \log{\left(x \right)} - 4 b^{2} d e n x \log{\left(c \right)} + 2 b^{2} d e x \log{\left(c \right)}^{2} + \frac{b^{2} e^{2} n^{2} x^{2} \log{\left(x \right)}^{2}}{2} - \frac{b^{2} e^{2} n^{2} x^{2} \log{\left(x \right)}}{2} + \frac{b^{2} e^{2} n^{2} x^{2}}{4} + b^{2} e^{2} n x^{2} \log{\left(c \right)} \log{\left(x \right)} - \frac{b^{2} e^{2} n x^{2} \log{\left(c \right)}}{2} + \frac{b^{2} e^{2} x^{2} \log{\left(c \right)}^{2}}{2}"," ",0,"a**2*d**2*log(x) + 2*a**2*d*e*x + a**2*e**2*x**2/2 + a*b*d**2*n*log(x)**2 + 2*a*b*d**2*log(c)*log(x) + 4*a*b*d*e*n*x*log(x) - 4*a*b*d*e*n*x + 4*a*b*d*e*x*log(c) + a*b*e**2*n*x**2*log(x) - a*b*e**2*n*x**2/2 + a*b*e**2*x**2*log(c) + b**2*d**2*n**2*log(x)**3/3 + b**2*d**2*n*log(c)*log(x)**2 + b**2*d**2*log(c)**2*log(x) + 2*b**2*d*e*n**2*x*log(x)**2 - 4*b**2*d*e*n**2*x*log(x) + 4*b**2*d*e*n**2*x + 4*b**2*d*e*n*x*log(c)*log(x) - 4*b**2*d*e*n*x*log(c) + 2*b**2*d*e*x*log(c)**2 + b**2*e**2*n**2*x**2*log(x)**2/2 - b**2*e**2*n**2*x**2*log(x)/2 + b**2*e**2*n**2*x**2/4 + b**2*e**2*n*x**2*log(c)*log(x) - b**2*e**2*n*x**2*log(c)/2 + b**2*e**2*x**2*log(c)**2/2","B",0
88,1,384,0,2.062915," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**2/x**2,x)","- \frac{a^{2} d^{2}}{x} + 2 a^{2} d e \log{\left(x \right)} + a^{2} e^{2} x - \frac{2 a b d^{2} n \log{\left(x \right)}}{x} - \frac{2 a b d^{2} n}{x} - \frac{2 a b d^{2} \log{\left(c \right)}}{x} + 2 a b d e n \log{\left(x \right)}^{2} + 4 a b d e \log{\left(c \right)} \log{\left(x \right)} + 2 a b e^{2} n x \log{\left(x \right)} - 2 a b e^{2} n x + 2 a b e^{2} x \log{\left(c \right)} - \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}^{2}}{x} - \frac{2 b^{2} d^{2} n^{2} \log{\left(x \right)}}{x} - \frac{2 b^{2} d^{2} n^{2}}{x} - \frac{2 b^{2} d^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{2 b^{2} d^{2} n \log{\left(c \right)}}{x} - \frac{b^{2} d^{2} \log{\left(c \right)}^{2}}{x} + \frac{2 b^{2} d e n^{2} \log{\left(x \right)}^{3}}{3} + 2 b^{2} d e n \log{\left(c \right)} \log{\left(x \right)}^{2} + 2 b^{2} d e \log{\left(c \right)}^{2} \log{\left(x \right)} + b^{2} e^{2} n^{2} x \log{\left(x \right)}^{2} - 2 b^{2} e^{2} n^{2} x \log{\left(x \right)} + 2 b^{2} e^{2} n^{2} x + 2 b^{2} e^{2} n x \log{\left(c \right)} \log{\left(x \right)} - 2 b^{2} e^{2} n x \log{\left(c \right)} + b^{2} e^{2} x \log{\left(c \right)}^{2}"," ",0,"-a**2*d**2/x + 2*a**2*d*e*log(x) + a**2*e**2*x - 2*a*b*d**2*n*log(x)/x - 2*a*b*d**2*n/x - 2*a*b*d**2*log(c)/x + 2*a*b*d*e*n*log(x)**2 + 4*a*b*d*e*log(c)*log(x) + 2*a*b*e**2*n*x*log(x) - 2*a*b*e**2*n*x + 2*a*b*e**2*x*log(c) - b**2*d**2*n**2*log(x)**2/x - 2*b**2*d**2*n**2*log(x)/x - 2*b**2*d**2*n**2/x - 2*b**2*d**2*n*log(c)*log(x)/x - 2*b**2*d**2*n*log(c)/x - b**2*d**2*log(c)**2/x + 2*b**2*d*e*n**2*log(x)**3/3 + 2*b**2*d*e*n*log(c)*log(x)**2 + 2*b**2*d*e*log(c)**2*log(x) + b**2*e**2*n**2*x*log(x)**2 - 2*b**2*e**2*n**2*x*log(x) + 2*b**2*e**2*n**2*x + 2*b**2*e**2*n*x*log(c)*log(x) - 2*b**2*e**2*n*x*log(c) + b**2*e**2*x*log(c)**2","B",0
89,1,357,0,9.290148," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**2/x**3,x)","- \frac{a^{2} d^{2}}{2 x^{2}} - \frac{2 a^{2} d e}{x} + a^{2} e^{2} \log{\left(x \right)} - \frac{a b d^{2} n}{2 x^{2}} - \frac{a b d^{2} \log{\left(c x^{n} \right)}}{x^{2}} - \frac{4 a b d e n}{x} - \frac{4 a b d e \log{\left(c x^{n} \right)}}{x} - 2 a b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) - \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{b^{2} d^{2} n^{2}}{4 x^{2}} - \frac{b^{2} d^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} d^{2} n \log{\left(c \right)}}{2 x^{2}} - \frac{b^{2} d^{2} \log{\left(c \right)}^{2}}{2 x^{2}} - \frac{2 b^{2} d e n^{2} \log{\left(x \right)}^{2}}{x} - \frac{4 b^{2} d e n^{2} \log{\left(x \right)}}{x} - \frac{4 b^{2} d e n^{2}}{x} - \frac{4 b^{2} d e n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{4 b^{2} d e n \log{\left(c \right)}}{x} - \frac{2 b^{2} d e \log{\left(c \right)}^{2}}{x} - b^{2} e^{2} \left(\begin{cases} - \log{\left(c \right)}^{2} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{3}}{3 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a**2*d**2/(2*x**2) - 2*a**2*d*e/x + a**2*e**2*log(x) - a*b*d**2*n/(2*x**2) - a*b*d**2*log(c*x**n)/x**2 - 4*a*b*d*e*n/x - 4*a*b*d*e*log(c*x**n)/x - 2*a*b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)) - b**2*d**2*n**2*log(x)**2/(2*x**2) - b**2*d**2*n**2*log(x)/(2*x**2) - b**2*d**2*n**2/(4*x**2) - b**2*d**2*n*log(c)*log(x)/x**2 - b**2*d**2*n*log(c)/(2*x**2) - b**2*d**2*log(c)**2/(2*x**2) - 2*b**2*d*e*n**2*log(x)**2/x - 4*b**2*d*e*n**2*log(x)/x - 4*b**2*d*e*n**2/x - 4*b**2*d*e*n*log(c)*log(x)/x - 4*b**2*d*e*n*log(c)/x - 2*b**2*d*e*log(c)**2/x - b**2*e**2*Piecewise((-log(c)**2*log(x), Eq(n, 0)), (-log(c*x**n)**3/(3*n), True))","A",0
90,1,479,0,2.406107," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**2/x**4,x)","- \frac{a^{2} d^{2}}{3 x^{3}} - \frac{a^{2} d e}{x^{2}} - \frac{a^{2} e^{2}}{x} - \frac{2 a b d^{2} n \log{\left(x \right)}}{3 x^{3}} - \frac{2 a b d^{2} n}{9 x^{3}} - \frac{2 a b d^{2} \log{\left(c \right)}}{3 x^{3}} - \frac{2 a b d e n \log{\left(x \right)}}{x^{2}} - \frac{a b d e n}{x^{2}} - \frac{2 a b d e \log{\left(c \right)}}{x^{2}} - \frac{2 a b e^{2} n \log{\left(x \right)}}{x} - \frac{2 a b e^{2} n}{x} - \frac{2 a b e^{2} \log{\left(c \right)}}{x} - \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}^{2}}{3 x^{3}} - \frac{2 b^{2} d^{2} n^{2} \log{\left(x \right)}}{9 x^{3}} - \frac{2 b^{2} d^{2} n^{2}}{27 x^{3}} - \frac{2 b^{2} d^{2} n \log{\left(c \right)} \log{\left(x \right)}}{3 x^{3}} - \frac{2 b^{2} d^{2} n \log{\left(c \right)}}{9 x^{3}} - \frac{b^{2} d^{2} \log{\left(c \right)}^{2}}{3 x^{3}} - \frac{b^{2} d e n^{2} \log{\left(x \right)}^{2}}{x^{2}} - \frac{b^{2} d e n^{2} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} d e n^{2}}{2 x^{2}} - \frac{2 b^{2} d e n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} d e n \log{\left(c \right)}}{x^{2}} - \frac{b^{2} d e \log{\left(c \right)}^{2}}{x^{2}} - \frac{b^{2} e^{2} n^{2} \log{\left(x \right)}^{2}}{x} - \frac{2 b^{2} e^{2} n^{2} \log{\left(x \right)}}{x} - \frac{2 b^{2} e^{2} n^{2}}{x} - \frac{2 b^{2} e^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x} - \frac{2 b^{2} e^{2} n \log{\left(c \right)}}{x} - \frac{b^{2} e^{2} \log{\left(c \right)}^{2}}{x}"," ",0,"-a**2*d**2/(3*x**3) - a**2*d*e/x**2 - a**2*e**2/x - 2*a*b*d**2*n*log(x)/(3*x**3) - 2*a*b*d**2*n/(9*x**3) - 2*a*b*d**2*log(c)/(3*x**3) - 2*a*b*d*e*n*log(x)/x**2 - a*b*d*e*n/x**2 - 2*a*b*d*e*log(c)/x**2 - 2*a*b*e**2*n*log(x)/x - 2*a*b*e**2*n/x - 2*a*b*e**2*log(c)/x - b**2*d**2*n**2*log(x)**2/(3*x**3) - 2*b**2*d**2*n**2*log(x)/(9*x**3) - 2*b**2*d**2*n**2/(27*x**3) - 2*b**2*d**2*n*log(c)*log(x)/(3*x**3) - 2*b**2*d**2*n*log(c)/(9*x**3) - b**2*d**2*log(c)**2/(3*x**3) - b**2*d*e*n**2*log(x)**2/x**2 - b**2*d*e*n**2*log(x)/x**2 - b**2*d*e*n**2/(2*x**2) - 2*b**2*d*e*n*log(c)*log(x)/x**2 - b**2*d*e*n*log(c)/x**2 - b**2*d*e*log(c)**2/x**2 - b**2*e**2*n**2*log(x)**2/x - 2*b**2*e**2*n**2*log(x)/x - 2*b**2*e**2*n**2/x - 2*b**2*e**2*n*log(c)*log(x)/x - 2*b**2*e**2*n*log(c)/x - b**2*e**2*log(c)**2/x","B",0
91,1,512,0,3.495430," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**2/x**5,x)","- \frac{a^{2} d^{2}}{4 x^{4}} - \frac{2 a^{2} d e}{3 x^{3}} - \frac{a^{2} e^{2}}{2 x^{2}} - \frac{a b d^{2} n \log{\left(x \right)}}{2 x^{4}} - \frac{a b d^{2} n}{8 x^{4}} - \frac{a b d^{2} \log{\left(c \right)}}{2 x^{4}} - \frac{4 a b d e n \log{\left(x \right)}}{3 x^{3}} - \frac{4 a b d e n}{9 x^{3}} - \frac{4 a b d e \log{\left(c \right)}}{3 x^{3}} - \frac{a b e^{2} n \log{\left(x \right)}}{x^{2}} - \frac{a b e^{2} n}{2 x^{2}} - \frac{a b e^{2} \log{\left(c \right)}}{x^{2}} - \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}^{2}}{4 x^{4}} - \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}}{8 x^{4}} - \frac{b^{2} d^{2} n^{2}}{32 x^{4}} - \frac{b^{2} d^{2} n \log{\left(c \right)} \log{\left(x \right)}}{2 x^{4}} - \frac{b^{2} d^{2} n \log{\left(c \right)}}{8 x^{4}} - \frac{b^{2} d^{2} \log{\left(c \right)}^{2}}{4 x^{4}} - \frac{2 b^{2} d e n^{2} \log{\left(x \right)}^{2}}{3 x^{3}} - \frac{4 b^{2} d e n^{2} \log{\left(x \right)}}{9 x^{3}} - \frac{4 b^{2} d e n^{2}}{27 x^{3}} - \frac{4 b^{2} d e n \log{\left(c \right)} \log{\left(x \right)}}{3 x^{3}} - \frac{4 b^{2} d e n \log{\left(c \right)}}{9 x^{3}} - \frac{2 b^{2} d e \log{\left(c \right)}^{2}}{3 x^{3}} - \frac{b^{2} e^{2} n^{2} \log{\left(x \right)}^{2}}{2 x^{2}} - \frac{b^{2} e^{2} n^{2} \log{\left(x \right)}}{2 x^{2}} - \frac{b^{2} e^{2} n^{2}}{4 x^{2}} - \frac{b^{2} e^{2} n \log{\left(c \right)} \log{\left(x \right)}}{x^{2}} - \frac{b^{2} e^{2} n \log{\left(c \right)}}{2 x^{2}} - \frac{b^{2} e^{2} \log{\left(c \right)}^{2}}{2 x^{2}}"," ",0,"-a**2*d**2/(4*x**4) - 2*a**2*d*e/(3*x**3) - a**2*e**2/(2*x**2) - a*b*d**2*n*log(x)/(2*x**4) - a*b*d**2*n/(8*x**4) - a*b*d**2*log(c)/(2*x**4) - 4*a*b*d*e*n*log(x)/(3*x**3) - 4*a*b*d*e*n/(9*x**3) - 4*a*b*d*e*log(c)/(3*x**3) - a*b*e**2*n*log(x)/x**2 - a*b*e**2*n/(2*x**2) - a*b*e**2*log(c)/x**2 - b**2*d**2*n**2*log(x)**2/(4*x**4) - b**2*d**2*n**2*log(x)/(8*x**4) - b**2*d**2*n**2/(32*x**4) - b**2*d**2*n*log(c)*log(x)/(2*x**4) - b**2*d**2*n*log(c)/(8*x**4) - b**2*d**2*log(c)**2/(4*x**4) - 2*b**2*d*e*n**2*log(x)**2/(3*x**3) - 4*b**2*d*e*n**2*log(x)/(9*x**3) - 4*b**2*d*e*n**2/(27*x**3) - 4*b**2*d*e*n*log(c)*log(x)/(3*x**3) - 4*b**2*d*e*n*log(c)/(9*x**3) - 2*b**2*d*e*log(c)**2/(3*x**3) - b**2*e**2*n**2*log(x)**2/(2*x**2) - b**2*e**2*n**2*log(x)/(2*x**2) - b**2*e**2*n**2/(4*x**2) - b**2*e**2*n*log(c)*log(x)/x**2 - b**2*e**2*n*log(c)/(2*x**2) - b**2*e**2*log(c)**2/(2*x**2)","B",0
92,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))**2/(e*x+d),x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))**2/(d + e*x), x)","F",0
93,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))**2/(e*x+d),x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))**2/(d + e*x), x)","F",0
94,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))**2/(e*x+d),x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))**2/(d + e*x), x)","F",0
95,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(d + e*x), x)","F",0
96,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x*(d + e*x)), x)","F",0
97,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**2/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**2*(d + e*x)), x)","F",0
98,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**3/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**3*(d + e*x)), x)","F",0
99,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**4/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{4} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**4*(d + e*x)), x)","F",0
100,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))**2/(e*x+d)**2,x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))**2/(d + e*x)**2, x)","F",0
101,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))**2/(e*x+d)**2,x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))**2/(d + e*x)**2, x)","F",0
102,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))**2/(e*x+d)**2,x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))**2/(d + e*x)**2, x)","F",0
103,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(d + e*x)**2, x)","F",0
104,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(e*x+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x*(d + e*x)**2), x)","F",0
105,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**2/(e*x+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{2} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**2*(d + e*x)**2), x)","F",0
106,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**3/(e*x+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{3} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**3*(d + e*x)**2), x)","F",0
107,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))**2/(e*x+d)**3,x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))**2/(d + e*x)**3, x)","F",0
108,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))**2/(e*x+d)**3,x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))**2/(d + e*x)**3, x)","F",0
109,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))**2/(e*x+d)**3,x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))**2/(d + e*x)**3, x)","F",0
110,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(d + e*x)**3, x)","F",0
111,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(e*x+d)**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x*(d + e*x)**3), x)","F",0
112,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**2/(e*x+d)**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{2} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**2*(d + e*x)**3), x)","F",0
113,0,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))**2/(e*x+d)**4,x)","\int \frac{x^{4} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**4*(a + b*log(c*x**n))**2/(d + e*x)**4, x)","F",0
114,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))**2/(e*x+d)**4,x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))**2/(d + e*x)**4, x)","F",0
115,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))**2/(e*x+d)**4,x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))**2/(d + e*x)**4, x)","F",0
116,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))**2/(e*x+d)**4,x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))**2/(d + e*x)**4, x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/(e*x+d)**4,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(d + e*x)**4, x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(e*x+d)**4,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x*(d + e*x)**4), x)","F",0
119,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x**2/(e*x+d)**4,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{x^{2} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(x**2*(d + e*x)**4), x)","F",0
120,1,357,0,55.500422," ","integrate(x*ln(x)**2/(e*x+d)**4,x)","\frac{\left(- d - 3 e x\right) \log{\left(x \right)}^{2}}{6 d^{3} e^{2} + 18 d^{2} e^{3} x + 18 d e^{4} x^{2} + 6 e^{5} x^{3}} + \frac{\left(\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(x \right)}}{e} - \frac{\begin{cases} \frac{x}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 d^{2} e + 2 d e^{2} x} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e} & \text{otherwise} \end{cases}}{e} + \frac{\begin{cases} - \frac{1}{e^{3} x} & \text{for}\: d = 0 \\- \frac{1}{2 d e^{2} + 2 e^{3} x} - \frac{\log{\left(d + e x \right)}}{2 d e^{2}} & \text{otherwise} \end{cases}}{3 d} - \frac{\left(\begin{cases} \frac{1}{e^{3} x} & \text{for}\: d = 0 \\- \frac{1}{2 d \left(\frac{d}{x} + e\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(x \right)}}{3 d} - \frac{2 \left(\begin{cases} - \frac{1}{e^{2} x} & \text{for}\: d = 0 \\- \frac{\log{\left(d^{2} + d e x \right)}}{d e} & \text{otherwise} \end{cases}\right)}{3 d e} + \frac{2 \left(\begin{cases} \frac{1}{e^{2} x} & \text{for}\: d = 0 \\- \frac{1}{\frac{d^{2}}{x} + d e} & \text{otherwise} \end{cases}\right) \log{\left(x \right)}}{3 d e} + \frac{\begin{cases} - \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + \operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}}{3 d e^{2}} - \frac{\left(\begin{cases} \frac{1}{e x} & \text{for}\: d = 0 \\\frac{\log{\left(\frac{d}{x} + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(x \right)}}{3 d e^{2}}"," ",0,"(-d - 3*e*x)*log(x)**2/(6*d**3*e**2 + 18*d**2*e**3*x + 18*d*e**4*x**2 + 6*e**5*x**3) + Piecewise((x/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x)**2), True))*log(x)/e - Piecewise((x/d**3, Eq(e, 0)), (-1/(2*d**2*e + 2*d*e**2*x) - log(x)/(2*d**2*e) + log(d/e + x)/(2*d**2*e), True))/e + Piecewise((-1/(e**3*x), Eq(d, 0)), (-1/(2*d*e**2 + 2*e**3*x) - log(d + e*x)/(2*d*e**2), True))/(3*d) - Piecewise((1/(e**3*x), Eq(d, 0)), (-1/(2*d*(d/x + e)**2), True))*log(x)/(3*d) - 2*Piecewise((-1/(e**2*x), Eq(d, 0)), (-log(d**2 + d*e*x)/(d*e), True))/(3*d*e) + 2*Piecewise((1/(e**2*x), Eq(d, 0)), (-1/(d**2/x + d*e), True))*log(x)/(3*d*e) + Piecewise((-1/(e*x), Eq(d, 0)), (Piecewise((log(e)*log(x) + polylog(2, d*exp_polar(I*pi)/(e*x)), Abs(x) < 1), (-log(e)*log(1/x) + polylog(2, d*exp_polar(I*pi)/(e*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) + polylog(2, d*exp_polar(I*pi)/(e*x)), True))/d, True))/(3*d*e**2) - Piecewise((1/(e*x), Eq(d, 0)), (log(d/x + e)/d, True))*log(x)/(3*d*e**2)","A",0
121,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**3/x/(e*x+d),x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))**3/(x*(d + e*x)), x)","F",0
122,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**3/x/(e*x+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}{x \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**3/(x*(d + e*x)**2), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**3/x/(e*x+d)**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}{x \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**3/(x*(d + e*x)**3), x)","F",0
124,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*ln(c*x**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c x^{n} \right)}} \left(d + e x\right)\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n))*(d + e*x), x)","F",0
125,0,0,0,0.000000," ","integrate((e*x+d)**2*(a+b*ln(c*x**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c x^{n} \right)}} \left(d + e x\right)^{2}\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n))*(d + e*x)**2, x)","F",0
126,0,0,0,0.000000," ","integrate((e*x+d)**3*(a+b*ln(c*x**n))**(1/2),x)","\int \sqrt{a + b \log{\left(c x^{n} \right)}} \left(d + e x\right)^{3}\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n))*(d + e*x)**3, x)","F",0
127,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + b \log{\left(c x^{n} \right)}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n))/(d + e*x), x)","F",0
128,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{a + b \log{\left(c x^{n} \right)}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n))/(d + e*x)**2, x)","F",0
129,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{a + b \log{\left(c x^{n} \right)}}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + b*log(c*x**n))/(d + e*x)**3, x)","F",0
130,1,518,0,16.486440," ","integrate(x**3*(a+b*ln(c*x**n))*(e*x+d)**(1/2),x)","\frac{2 \left(- \frac{a d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 a d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 a d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{a \left(d + e x\right)^{\frac{9}{2}}}{9} - b d^{3} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + 3 b d^{2} \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) - 3 b d \left(\frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right) + b \left(\frac{\left(d + e x\right)^{\frac{9}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{9} - \frac{2 n \left(\frac{d^{5} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{4} e \sqrt{d + e x} + \frac{d^{3} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d^{2} e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{d e \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{e \left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{9 e}\right)\right)}{e^{4}}"," ",0,"2*(-a*d**3*(d + e*x)**(3/2)/3 + 3*a*d**2*(d + e*x)**(5/2)/5 - 3*a*d*(d + e*x)**(7/2)/7 + a*(d + e*x)**(9/2)/9 - b*d**3*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + 3*b*d**2*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) - 3*b*d*((d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e)) + b*((d + e*x)**(9/2)*log(c*(-d/e + (d + e*x)/e)**n)/9 - 2*n*(d**5*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**4*e*sqrt(d + e*x) + d**3*e*(d + e*x)**(3/2)/3 + d**2*e*(d + e*x)**(5/2)/5 + d*e*(d + e*x)**(7/2)/7 + e*(d + e*x)**(9/2)/9)/(9*e)))/e**4","B",0
131,1,364,0,11.157046," ","integrate(x**2*(a+b*ln(c*x**n))*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{a d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 a d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{a \left(d + e x\right)^{\frac{7}{2}}}{7} + b d^{2} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) - 2 b d \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) + b \left(\frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right)\right)}{e^{3}}"," ",0,"2*(a*d**2*(d + e*x)**(3/2)/3 - 2*a*d*(d + e*x)**(5/2)/5 + a*(d + e*x)**(7/2)/7 + b*d**2*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) - 2*b*d*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) + b*((d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e)))/e**3","A",0
132,1,224,0,6.856226," ","integrate(x*(a+b*ln(c*x**n))*(e*x+d)**(1/2),x)","\frac{2 \left(- \frac{a d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{a \left(d + e x\right)^{\frac{5}{2}}}{5} - b d \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + b \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right)\right)}{e^{2}}"," ",0,"2*(-a*d*(d + e*x)**(3/2)/3 + a*(d + e*x)**(5/2)/5 - b*d*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + b*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)))/e**2","A",0
133,1,102,0,3.792478," ","integrate((a+b*ln(c*x**n))*(e*x+d)**(1/2),x)","\frac{2 \left(\frac{a \left(d + e x\right)^{\frac{3}{2}}}{3} + b \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right)\right)}{e}"," ",0,"2*(a*(d + e*x)**(3/2)/3 + b*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)))/e","A",0
134,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x+d)**(1/2)/x,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x}}{x}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x)/x, x)","F",0
135,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x+d)**(1/2)/x**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x)/x**2, x)","F",0
136,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x+d)**(1/2)/x**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x)/x**3, x)","F",0
137,1,1188,0,148.735895," ","integrate(x**3*(e*x+d)**(3/2)*(a+b*ln(c*x**n)),x)","\frac{2 a d \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{4}} + \frac{2 a \left(\frac{d^{4} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{4 d^{3} \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{6 d^{2} \left(d + e x\right)^{\frac{7}{2}}}{7} - \frac{4 d \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{\left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{e^{4}} + \frac{2 b d \left(- d^{3} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + 3 d^{2} \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) - 3 d \left(\frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right) + \frac{\left(d + e x\right)^{\frac{9}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{9} - \frac{2 n \left(\frac{d^{5} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{4} e \sqrt{d + e x} + \frac{d^{3} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d^{2} e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{d e \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{e \left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{9 e}\right)}{e^{4}} + \frac{2 b \left(d^{4} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) - 4 d^{3} \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) + 6 d^{2} \left(\frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right) - 4 d \left(\frac{\left(d + e x\right)^{\frac{9}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{9} - \frac{2 n \left(\frac{d^{5} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{4} e \sqrt{d + e x} + \frac{d^{3} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d^{2} e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{d e \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{e \left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{9 e}\right) + \frac{\left(d + e x\right)^{\frac{11}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{11} - \frac{2 n \left(\frac{d^{6} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{5} e \sqrt{d + e x} + \frac{d^{4} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d^{3} e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{d^{2} e \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{d e \left(d + e x\right)^{\frac{9}{2}}}{9} + \frac{e \left(d + e x\right)^{\frac{11}{2}}}{11}\right)}{11 e}\right)}{e^{4}}"," ",0,"2*a*d*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**4 + 2*a*(d**4*(d + e*x)**(3/2)/3 - 4*d**3*(d + e*x)**(5/2)/5 + 6*d**2*(d + e*x)**(7/2)/7 - 4*d*(d + e*x)**(9/2)/9 + (d + e*x)**(11/2)/11)/e**4 + 2*b*d*(-d**3*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + 3*d**2*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) - 3*d*((d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e)) + (d + e*x)**(9/2)*log(c*(-d/e + (d + e*x)/e)**n)/9 - 2*n*(d**5*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**4*e*sqrt(d + e*x) + d**3*e*(d + e*x)**(3/2)/3 + d**2*e*(d + e*x)**(5/2)/5 + d*e*(d + e*x)**(7/2)/7 + e*(d + e*x)**(9/2)/9)/(9*e))/e**4 + 2*b*(d**4*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) - 4*d**3*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) + 6*d**2*((d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e)) - 4*d*((d + e*x)**(9/2)*log(c*(-d/e + (d + e*x)/e)**n)/9 - 2*n*(d**5*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**4*e*sqrt(d + e*x) + d**3*e*(d + e*x)**(3/2)/3 + d**2*e*(d + e*x)**(5/2)/5 + d*e*(d + e*x)**(7/2)/7 + e*(d + e*x)**(9/2)/9)/(9*e)) + (d + e*x)**(11/2)*log(c*(-d/e + (d + e*x)/e)**n)/11 - 2*n*(d**6*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**5*e*sqrt(d + e*x) + d**4*e*(d + e*x)**(3/2)/3 + d**3*e*(d + e*x)**(5/2)/5 + d**2*e*(d + e*x)**(7/2)/7 + d*e*(d + e*x)**(9/2)/9 + e*(d + e*x)**(11/2)/11)/(11*e))/e**4","B",0
138,1,870,0,105.830485," ","integrate(x**2*(e*x+d)**(3/2)*(a+b*ln(c*x**n)),x)","\frac{2 a d \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{3}} + \frac{2 a \left(- \frac{d^{3} \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{3 d^{2} \left(d + e x\right)^{\frac{5}{2}}}{5} - \frac{3 d \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{\left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{e^{3}} + \frac{2 b d \left(d^{2} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) - 2 d \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) + \frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right)}{e^{3}} + \frac{2 b \left(- d^{3} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + 3 d^{2} \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) - 3 d \left(\frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right) + \frac{\left(d + e x\right)^{\frac{9}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{9} - \frac{2 n \left(\frac{d^{5} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{4} e \sqrt{d + e x} + \frac{d^{3} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d^{2} e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{d e \left(d + e x\right)^{\frac{7}{2}}}{7} + \frac{e \left(d + e x\right)^{\frac{9}{2}}}{9}\right)}{9 e}\right)}{e^{3}}"," ",0,"2*a*d*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**3 + 2*a*(-d**3*(d + e*x)**(3/2)/3 + 3*d**2*(d + e*x)**(5/2)/5 - 3*d*(d + e*x)**(7/2)/7 + (d + e*x)**(9/2)/9)/e**3 + 2*b*d*(d**2*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) - 2*d*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) + (d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e))/e**3 + 2*b*(-d**3*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + 3*d**2*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) - 3*d*((d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e)) + (d + e*x)**(9/2)*log(c*(-d/e + (d + e*x)/e)**n)/9 - 2*n*(d**5*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**4*e*sqrt(d + e*x) + d**3*e*(d + e*x)**(3/2)/3 + d**2*e*(d + e*x)**(5/2)/5 + d*e*(d + e*x)**(7/2)/7 + e*(d + e*x)**(9/2)/9)/(9*e))/e**3","B",0
139,1,583,0,69.886375," ","integrate(x*(e*x+d)**(3/2)*(a+b*ln(c*x**n)),x)","\frac{2 a d \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e^{2}} + \frac{2 a \left(\frac{d^{2} \left(d + e x\right)^{\frac{3}{2}}}{3} - \frac{2 d \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{\left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{e^{2}} + \frac{2 b d \left(- d \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + \frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right)}{e^{2}} + \frac{2 b \left(d^{2} \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) - 2 d \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right) + \frac{\left(d + e x\right)^{\frac{7}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{7} - \frac{2 n \left(\frac{d^{4} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{3} e \sqrt{d + e x} + \frac{d^{2} e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{d e \left(d + e x\right)^{\frac{5}{2}}}{5} + \frac{e \left(d + e x\right)^{\frac{7}{2}}}{7}\right)}{7 e}\right)}{e^{2}}"," ",0,"2*a*d*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e**2 + 2*a*(d**2*(d + e*x)**(3/2)/3 - 2*d*(d + e*x)**(5/2)/5 + (d + e*x)**(7/2)/7)/e**2 + 2*b*d*(-d*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + (d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e))/e**2 + 2*b*(d**2*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) - 2*d*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)) + (d + e*x)**(7/2)*log(c*(-d/e + (d + e*x)/e)**n)/7 - 2*n*(d**4*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**3*e*sqrt(d + e*x) + d**2*e*(d + e*x)**(3/2)/3 + d*e*(d + e*x)**(5/2)/5 + e*(d + e*x)**(7/2)/7)/(7*e))/e**2","B",0
140,1,333,0,38.357759," ","integrate((e*x+d)**(3/2)*(a+b*ln(c*x**n)),x)","a d \left(\begin{cases} \sqrt{d} x & \text{for}\: e = 0 \\\frac{2 \left(d + e x\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) + \frac{2 a \left(- \frac{d \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{\left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{e} + \frac{2 b d \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right)}{e} + \frac{2 b \left(- d \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + \frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right)}{e}"," ",0,"a*d*Piecewise((sqrt(d)*x, Eq(e, 0)), (2*(d + e*x)**(3/2)/(3*e), True)) + 2*a*(-d*(d + e*x)**(3/2)/3 + (d + e*x)**(5/2)/5)/e + 2*b*d*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e))/e + 2*b*(-d*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + (d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e))/e","A",0
141,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a+b*ln(c*x**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a+b*ln(c*x**n))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(a+b*ln(c*x**n))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,1,252,0,27.883504," ","integrate((a+b*ln(c*x**n))/(e*x+d)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d}{\sqrt{d + e x}} - 2 a \left(- \frac{d}{\sqrt{d + e x}} - \sqrt{d + e x}\right) - 2 b d \left(\frac{\log{\left(c x^{n} \right)}}{\sqrt{d + e x}} - \frac{2 n \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d}} \sqrt{d + e x}} \right)}}{d \sqrt{- \frac{1}{d}}}\right) - 2 b \left(- d \left(\frac{\log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{\sqrt{d + e x}} - \frac{2 n \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d}} \sqrt{d + e x}} \right)}}{d \sqrt{- \frac{1}{d}}}\right) - \sqrt{d + e x} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)} - \frac{2 n \left(- e \sqrt{d + e x} - \frac{e \operatorname{atan}{\left(\frac{1}{\sqrt{- \frac{1}{d}} \sqrt{d + e x}} \right)}}{\sqrt{- \frac{1}{d}}}\right)}{e}\right)}{e} & \text{for}\: e \neq 0 \\\frac{a x + b \left(- n x + x \log{\left(c x^{n} \right)}\right)}{\sqrt{d}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d/sqrt(d + e*x) - 2*a*(-d/sqrt(d + e*x) - sqrt(d + e*x)) - 2*b*d*(log(c*x**n)/sqrt(d + e*x) - 2*n*atan(1/(sqrt(-1/d)*sqrt(d + e*x)))/(d*sqrt(-1/d))) - 2*b*(-d*(log(c*(-d/e + (d + e*x)/e)**n)/sqrt(d + e*x) - 2*n*atan(1/(sqrt(-1/d)*sqrt(d + e*x)))/(d*sqrt(-1/d))) - sqrt(d + e*x)*log(c*(-d/e + (d + e*x)/e)**n) - 2*n*(-e*sqrt(d + e*x) - e*atan(1/(sqrt(-1/d)*sqrt(d + e*x)))/sqrt(-1/d))/e))/e, Ne(e, 0)), ((a*x + b*(-n*x + x*log(c*x**n)))/sqrt(d), True))","A",0
148,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*sqrt(d + e*x)), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{3} \sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**3*sqrt(d + e*x)), x)","F",0
151,1,384,0,56.704852," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x+d)**(3/2),x)","\frac{\frac{2 a d^{3}}{\sqrt{d + e x}} + 6 a d^{2} \sqrt{d + e x} - 2 a d \left(d + e x\right)^{\frac{3}{2}} + \frac{2 a \left(d + e x\right)^{\frac{5}{2}}}{5} - 2 b d^{3} \left(\frac{2 n \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} - \frac{\log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{\sqrt{d + e x}}\right) + 6 b d^{2} \left(\sqrt{d + e x} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)} - \frac{2 n \left(\frac{d e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + e \sqrt{d + e x}\right)}{e}\right) - 6 b d \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right) + 2 b \left(\frac{\left(d + e x\right)^{\frac{5}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{5} - \frac{2 n \left(\frac{d^{3} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d^{2} e \sqrt{d + e x} + \frac{d e \left(d + e x\right)^{\frac{3}{2}}}{3} + \frac{e \left(d + e x\right)^{\frac{5}{2}}}{5}\right)}{5 e}\right)}{e^{4}}"," ",0,"(2*a*d**3/sqrt(d + e*x) + 6*a*d**2*sqrt(d + e*x) - 2*a*d*(d + e*x)**(3/2) + 2*a*(d + e*x)**(5/2)/5 - 2*b*d**3*(2*n*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) - log(c*(-d/e + (d + e*x)/e)**n)/sqrt(d + e*x)) + 6*b*d**2*(sqrt(d + e*x)*log(c*(-d/e + (d + e*x)/e)**n) - 2*n*(d*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + e*sqrt(d + e*x))/e) - 6*b*d*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)) + 2*b*((d + e*x)**(5/2)*log(c*(-d/e + (d + e*x)/e)**n)/5 - 2*n*(d**3*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d**2*e*sqrt(d + e*x) + d*e*(d + e*x)**(3/2)/3 + e*(d + e*x)**(5/2)/5)/(5*e)))/e**4","A",0
152,1,262,0,39.945219," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x+d)**(3/2),x)","\frac{- \frac{2 a d^{2}}{\sqrt{d + e x}} - 4 a d \sqrt{d + e x} + \frac{2 a \left(d + e x\right)^{\frac{3}{2}}}{3} + 2 b d^{2} \left(\frac{2 n \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} - \frac{\log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{\sqrt{d + e x}}\right) - 4 b d \left(\sqrt{d + e x} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)} - \frac{2 n \left(\frac{d e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + e \sqrt{d + e x}\right)}{e}\right) + 2 b \left(\frac{\left(d + e x\right)^{\frac{3}{2}} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{3} - \frac{2 n \left(\frac{d^{2} e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + d e \sqrt{d + e x} + \frac{e \left(d + e x\right)^{\frac{3}{2}}}{3}\right)}{3 e}\right)}{e^{3}}"," ",0,"(-2*a*d**2/sqrt(d + e*x) - 4*a*d*sqrt(d + e*x) + 2*a*(d + e*x)**(3/2)/3 + 2*b*d**2*(2*n*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) - log(c*(-d/e + (d + e*x)/e)**n)/sqrt(d + e*x)) - 4*b*d*(sqrt(d + e*x)*log(c*(-d/e + (d + e*x)/e)**n) - 2*n*(d*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + e*sqrt(d + e*x))/e) + 2*b*((d + e*x)**(3/2)*log(c*(-d/e + (d + e*x)/e)**n)/3 - 2*n*(d**2*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + d*e*sqrt(d + e*x) + e*(d + e*x)**(3/2)/3)/(3*e)))/e**3","A",0
153,1,153,0,58.815704," ","integrate(x*(a+b*ln(c*x**n))/(e*x+d)**(3/2),x)","\frac{\frac{2 a d}{\sqrt{d + e x}} + 2 a \sqrt{d + e x} - 2 b d \left(\frac{2 n \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} - \frac{\log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{\sqrt{d + e x}}\right) + 2 b \left(\sqrt{d + e x} \log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)} - \frac{2 n \left(\frac{d e \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} + e \sqrt{d + e x}\right)}{e}\right)}{e^{2}}"," ",0,"(2*a*d/sqrt(d + e*x) + 2*a*sqrt(d + e*x) - 2*b*d*(2*n*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) - log(c*(-d/e + (d + e*x)/e)**n)/sqrt(d + e*x)) + 2*b*(sqrt(d + e*x)*log(c*(-d/e + (d + e*x)/e)**n) - 2*n*(d*e*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) + e*sqrt(d + e*x))/e))/e**2","A",0
154,1,66,0,13.888353," ","integrate((a+b*ln(c*x**n))/(e*x+d)**(3/2),x)","\frac{- \frac{2 a}{\sqrt{d + e x}} + 2 b \left(\frac{2 n \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- d}} \right)}}{\sqrt{- d}} - \frac{\log{\left(c \left(- \frac{d}{e} + \frac{d + e x}{e}\right)^{n} \right)}}{\sqrt{d + e x}}\right)}{e}"," ",0,"(-2*a/sqrt(d + e*x) + 2*b*(2*n*atan(sqrt(d + e*x)/sqrt(-d))/sqrt(-d) - log(c*(-d/e + (d + e*x)/e)**n)/sqrt(d + e*x)))/e","A",0
155,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x+d)**(3/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*(d + e*x)**(3/2)), x)","F",0
157,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(a+b*ln(c*x**n)),x)","\int \frac{x^{2}}{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/((a + b*log(c*x**n))*(d + e*x)), x)","F",0
158,0,0,0,0.000000," ","integrate(x/(e*x+d)/(a+b*ln(c*x**n)),x)","\int \frac{x}{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(x/((a + b*log(c*x**n))*(d + e*x)), x)","F",0
159,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*ln(c*x**n)),x)","\int \frac{1}{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*log(c*x**n))*(d + e*x)), x)","F",0
160,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(a+b*ln(c*x**n)),x)","\int \frac{1}{x \left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*(a + b*log(c*x**n))*(d + e*x)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(a+b*ln(c*x**n)),x)","\int \frac{1}{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*(a + b*log(c*x**n))*(d + e*x)), x)","F",0
162,1,8381,0,40.639976," ","integrate((f*x)**m*(e*x+d)**3*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{- \frac{a d^{3}}{3 x^{3}} - \frac{3 a d^{2} e}{2 x^{2}} - \frac{3 a d e^{2}}{x} + a e^{3} \log{\left(x \right)} + b d^{3} \left(- \frac{n}{9 x^{3}} - \frac{\log{\left(c x^{n} \right)}}{3 x^{3}}\right) + 3 b d^{2} e \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) + 3 b d e^{2} \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e^{3} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)}{f^{4}} & \text{for}\: m = -4 \\\frac{- \frac{a d^{3}}{2 x^{2}} - \frac{3 a d^{2} e}{x} + 3 a d e^{2} \log{\left(x \right)} + a e^{3} x - \frac{b d^{3} n \log{\left(x \right)}}{2 x^{2}} - \frac{b d^{3} n}{4 x^{2}} - \frac{b d^{3} \log{\left(c \right)}}{2 x^{2}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{x} - \frac{3 b d^{2} e n}{x} - \frac{3 b d^{2} e \log{\left(c \right)}}{x} + \frac{3 b d e^{2} n \log{\left(x \right)}^{2}}{2} + 3 b d e^{2} \log{\left(c \right)} \log{\left(x \right)} + b e^{3} n x \log{\left(x \right)} - b e^{3} n x + b e^{3} x \log{\left(c \right)}}{f^{3}} & \text{for}\: m = -3 \\\frac{- \frac{a d^{3}}{x} + 3 a d^{2} e \log{\left(x \right)} + 3 a d e^{2} x + \frac{a e^{3} x^{2}}{2} - \frac{b d^{3} n \log{\left(x \right)}}{x} - \frac{b d^{3} n}{x} - \frac{b d^{3} \log{\left(c \right)}}{x} + \frac{3 b d^{2} e n \log{\left(x \right)}^{2}}{2} + 3 b d^{2} e \log{\left(c \right)} \log{\left(x \right)} + 3 b d e^{2} n x \log{\left(x \right)} - 3 b d e^{2} n x + 3 b d e^{2} x \log{\left(c \right)} + \frac{b e^{3} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{3} n x^{2}}{4} + \frac{b e^{3} x^{2} \log{\left(c \right)}}{2}}{f^{2}} & \text{for}\: m = -2 \\\frac{a d^{3} \log{\left(x \right)} + 3 a d^{2} e x + \frac{3 a d e^{2} x^{2}}{2} + \frac{a e^{3} x^{3}}{3} + \frac{b d^{3} n \log{\left(x \right)}^{2}}{2} + b d^{3} \log{\left(c \right)} \log{\left(x \right)} + 3 b d^{2} e n x \log{\left(x \right)} - 3 b d^{2} e n x + 3 b d^{2} e x \log{\left(c \right)} + \frac{3 b d e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{3 b d e^{2} n x^{2}}{4} + \frac{3 b d e^{2} x^{2} \log{\left(c \right)}}{2} + \frac{b e^{3} n x^{3} \log{\left(x \right)}}{3} - \frac{b e^{3} n x^{3}}{9} + \frac{b e^{3} x^{3} \log{\left(c \right)}}{3}}{f} & \text{for}\: m = -1 \\\frac{a d^{3} f^{m} m^{7} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{19 a d^{3} f^{m} m^{6} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{151 a d^{3} f^{m} m^{5} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{649 a d^{3} f^{m} m^{4} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1624 a d^{3} f^{m} m^{3} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2356 a d^{3} f^{m} m^{2} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1824 a d^{3} f^{m} m x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{576 a d^{3} f^{m} x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3 a d^{2} e f^{m} m^{7} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{54 a d^{2} e f^{m} m^{6} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{402 a d^{2} e f^{m} m^{5} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1596 a d^{2} e f^{m} m^{4} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3627 a d^{2} e f^{m} m^{3} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{4686 a d^{2} e f^{m} m^{2} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3168 a d^{2} e f^{m} m x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{864 a d^{2} e f^{m} x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3 a d e^{2} f^{m} m^{7} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{51 a d e^{2} f^{m} m^{6} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{357 a d e^{2} f^{m} m^{5} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1329 a d e^{2} f^{m} m^{4} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2832 a d e^{2} f^{m} m^{3} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3444 a d e^{2} f^{m} m^{2} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2208 a d e^{2} f^{m} m x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{576 a d e^{2} f^{m} x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{a e^{3} f^{m} m^{7} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{16 a e^{3} f^{m} m^{6} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{106 a e^{3} f^{m} m^{5} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{376 a e^{3} f^{m} m^{4} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{769 a e^{3} f^{m} m^{3} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{904 a e^{3} f^{m} m^{2} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{564 a e^{3} f^{m} m x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{144 a e^{3} f^{m} x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{b d^{3} f^{m} m^{7} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{b d^{3} f^{m} m^{7} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{19 b d^{3} f^{m} m^{6} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{b d^{3} f^{m} m^{6} n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{19 b d^{3} f^{m} m^{6} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{151 b d^{3} f^{m} m^{5} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{18 b d^{3} f^{m} m^{5} n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{151 b d^{3} f^{m} m^{5} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{649 b d^{3} f^{m} m^{4} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{133 b d^{3} f^{m} m^{4} n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{649 b d^{3} f^{m} m^{4} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1624 b d^{3} f^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{516 b d^{3} f^{m} m^{3} n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1624 b d^{3} f^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2356 b d^{3} f^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{1108 b d^{3} f^{m} m^{2} n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2356 b d^{3} f^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1824 b d^{3} f^{m} m n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{1248 b d^{3} f^{m} m n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1824 b d^{3} f^{m} m x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{576 b d^{3} f^{m} n x x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{576 b d^{3} f^{m} n x x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{576 b d^{3} f^{m} x x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3 b d^{2} e f^{m} m^{7} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3 b d^{2} e f^{m} m^{7} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{54 b d^{2} e f^{m} m^{6} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{3 b d^{2} e f^{m} m^{6} n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{54 b d^{2} e f^{m} m^{6} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{402 b d^{2} e f^{m} m^{5} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{48 b d^{2} e f^{m} m^{5} n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{402 b d^{2} e f^{m} m^{5} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1596 b d^{2} e f^{m} m^{4} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{306 b d^{2} e f^{m} m^{4} n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1596 b d^{2} e f^{m} m^{4} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3627 b d^{2} e f^{m} m^{3} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{984 b d^{2} e f^{m} m^{3} n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3627 b d^{2} e f^{m} m^{3} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{4686 b d^{2} e f^{m} m^{2} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{1659 b d^{2} e f^{m} m^{2} n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{4686 b d^{2} e f^{m} m^{2} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3168 b d^{2} e f^{m} m n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{1368 b d^{2} e f^{m} m n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3168 b d^{2} e f^{m} m x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{864 b d^{2} e f^{m} n x^{2} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{432 b d^{2} e f^{m} n x^{2} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{864 b d^{2} e f^{m} x^{2} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3 b d e^{2} f^{m} m^{7} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3 b d e^{2} f^{m} m^{7} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{51 b d e^{2} f^{m} m^{6} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{3 b d e^{2} f^{m} m^{6} n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{51 b d e^{2} f^{m} m^{6} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{357 b d e^{2} f^{m} m^{5} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{42 b d e^{2} f^{m} m^{5} n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{357 b d e^{2} f^{m} m^{5} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1329 b d e^{2} f^{m} m^{4} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{231 b d e^{2} f^{m} m^{4} n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{1329 b d e^{2} f^{m} m^{4} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2832 b d e^{2} f^{m} m^{3} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{636 b d e^{2} f^{m} m^{3} n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2832 b d e^{2} f^{m} m^{3} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3444 b d e^{2} f^{m} m^{2} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{924 b d e^{2} f^{m} m^{2} n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{3444 b d e^{2} f^{m} m^{2} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2208 b d e^{2} f^{m} m n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{672 b d e^{2} f^{m} m n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{2208 b d e^{2} f^{m} m x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{576 b d e^{2} f^{m} n x^{3} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{192 b d e^{2} f^{m} n x^{3} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{576 b d e^{2} f^{m} x^{3} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{b e^{3} f^{m} m^{7} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{b e^{3} f^{m} m^{7} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{16 b e^{3} f^{m} m^{6} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{b e^{3} f^{m} m^{6} n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{16 b e^{3} f^{m} m^{6} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{106 b e^{3} f^{m} m^{5} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{12 b e^{3} f^{m} m^{5} n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{106 b e^{3} f^{m} m^{5} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{376 b e^{3} f^{m} m^{4} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{58 b e^{3} f^{m} m^{4} n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{376 b e^{3} f^{m} m^{4} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{769 b e^{3} f^{m} m^{3} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{144 b e^{3} f^{m} m^{3} n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{769 b e^{3} f^{m} m^{3} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{904 b e^{3} f^{m} m^{2} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{193 b e^{3} f^{m} m^{2} n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{904 b e^{3} f^{m} m^{2} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{564 b e^{3} f^{m} m n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{132 b e^{3} f^{m} m n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{564 b e^{3} f^{m} m x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{144 b e^{3} f^{m} n x^{4} x^{m} \log{\left(x \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} - \frac{36 b e^{3} f^{m} n x^{4} x^{m}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} + \frac{144 b e^{3} f^{m} x^{4} x^{m} \log{\left(c \right)}}{m^{8} + 20 m^{7} + 170 m^{6} + 800 m^{5} + 2273 m^{4} + 3980 m^{3} + 4180 m^{2} + 2400 m + 576} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*d**3/(3*x**3) - 3*a*d**2*e/(2*x**2) - 3*a*d*e**2/x + a*e**3*log(x) + b*d**3*(-n/(9*x**3) - log(c*x**n)/(3*x**3)) + 3*b*d**2*e*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) + 3*b*d*e**2*(-n/x - log(c*x**n)/x) - b*e**3*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)))/f**4, Eq(m, -4)), ((-a*d**3/(2*x**2) - 3*a*d**2*e/x + 3*a*d*e**2*log(x) + a*e**3*x - b*d**3*n*log(x)/(2*x**2) - b*d**3*n/(4*x**2) - b*d**3*log(c)/(2*x**2) - 3*b*d**2*e*n*log(x)/x - 3*b*d**2*e*n/x - 3*b*d**2*e*log(c)/x + 3*b*d*e**2*n*log(x)**2/2 + 3*b*d*e**2*log(c)*log(x) + b*e**3*n*x*log(x) - b*e**3*n*x + b*e**3*x*log(c))/f**3, Eq(m, -3)), ((-a*d**3/x + 3*a*d**2*e*log(x) + 3*a*d*e**2*x + a*e**3*x**2/2 - b*d**3*n*log(x)/x - b*d**3*n/x - b*d**3*log(c)/x + 3*b*d**2*e*n*log(x)**2/2 + 3*b*d**2*e*log(c)*log(x) + 3*b*d*e**2*n*x*log(x) - 3*b*d*e**2*n*x + 3*b*d*e**2*x*log(c) + b*e**3*n*x**2*log(x)/2 - b*e**3*n*x**2/4 + b*e**3*x**2*log(c)/2)/f**2, Eq(m, -2)), ((a*d**3*log(x) + 3*a*d**2*e*x + 3*a*d*e**2*x**2/2 + a*e**3*x**3/3 + b*d**3*n*log(x)**2/2 + b*d**3*log(c)*log(x) + 3*b*d**2*e*n*x*log(x) - 3*b*d**2*e*n*x + 3*b*d**2*e*x*log(c) + 3*b*d*e**2*n*x**2*log(x)/2 - 3*b*d*e**2*n*x**2/4 + 3*b*d*e**2*x**2*log(c)/2 + b*e**3*n*x**3*log(x)/3 - b*e**3*n*x**3/9 + b*e**3*x**3*log(c)/3)/f, Eq(m, -1)), (a*d**3*f**m*m**7*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 19*a*d**3*f**m*m**6*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 151*a*d**3*f**m*m**5*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 649*a*d**3*f**m*m**4*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1624*a*d**3*f**m*m**3*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2356*a*d**3*f**m*m**2*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1824*a*d**3*f**m*m*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 576*a*d**3*f**m*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3*a*d**2*e*f**m*m**7*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 54*a*d**2*e*f**m*m**6*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 402*a*d**2*e*f**m*m**5*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1596*a*d**2*e*f**m*m**4*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3627*a*d**2*e*f**m*m**3*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 4686*a*d**2*e*f**m*m**2*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3168*a*d**2*e*f**m*m*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 864*a*d**2*e*f**m*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3*a*d*e**2*f**m*m**7*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 51*a*d*e**2*f**m*m**6*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 357*a*d*e**2*f**m*m**5*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1329*a*d*e**2*f**m*m**4*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2832*a*d*e**2*f**m*m**3*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3444*a*d*e**2*f**m*m**2*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2208*a*d*e**2*f**m*m*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 576*a*d*e**2*f**m*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + a*e**3*f**m*m**7*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 16*a*e**3*f**m*m**6*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 106*a*e**3*f**m*m**5*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 376*a*e**3*f**m*m**4*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 769*a*e**3*f**m*m**3*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 904*a*e**3*f**m*m**2*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 564*a*e**3*f**m*m*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 144*a*e**3*f**m*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + b*d**3*f**m*m**7*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + b*d**3*f**m*m**7*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 19*b*d**3*f**m*m**6*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - b*d**3*f**m*m**6*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 19*b*d**3*f**m*m**6*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 151*b*d**3*f**m*m**5*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 18*b*d**3*f**m*m**5*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 151*b*d**3*f**m*m**5*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 649*b*d**3*f**m*m**4*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 133*b*d**3*f**m*m**4*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 649*b*d**3*f**m*m**4*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1624*b*d**3*f**m*m**3*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 516*b*d**3*f**m*m**3*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1624*b*d**3*f**m*m**3*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2356*b*d**3*f**m*m**2*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 1108*b*d**3*f**m*m**2*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2356*b*d**3*f**m*m**2*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1824*b*d**3*f**m*m*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 1248*b*d**3*f**m*m*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1824*b*d**3*f**m*m*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 576*b*d**3*f**m*n*x*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 576*b*d**3*f**m*n*x*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 576*b*d**3*f**m*x*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3*b*d**2*e*f**m*m**7*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3*b*d**2*e*f**m*m**7*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 54*b*d**2*e*f**m*m**6*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 3*b*d**2*e*f**m*m**6*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 54*b*d**2*e*f**m*m**6*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 402*b*d**2*e*f**m*m**5*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 48*b*d**2*e*f**m*m**5*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 402*b*d**2*e*f**m*m**5*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1596*b*d**2*e*f**m*m**4*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 306*b*d**2*e*f**m*m**4*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1596*b*d**2*e*f**m*m**4*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3627*b*d**2*e*f**m*m**3*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 984*b*d**2*e*f**m*m**3*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3627*b*d**2*e*f**m*m**3*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 4686*b*d**2*e*f**m*m**2*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 1659*b*d**2*e*f**m*m**2*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 4686*b*d**2*e*f**m*m**2*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3168*b*d**2*e*f**m*m*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 1368*b*d**2*e*f**m*m*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3168*b*d**2*e*f**m*m*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 864*b*d**2*e*f**m*n*x**2*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 432*b*d**2*e*f**m*n*x**2*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 864*b*d**2*e*f**m*x**2*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3*b*d*e**2*f**m*m**7*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3*b*d*e**2*f**m*m**7*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 51*b*d*e**2*f**m*m**6*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 3*b*d*e**2*f**m*m**6*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 51*b*d*e**2*f**m*m**6*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 357*b*d*e**2*f**m*m**5*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 42*b*d*e**2*f**m*m**5*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 357*b*d*e**2*f**m*m**5*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1329*b*d*e**2*f**m*m**4*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 231*b*d*e**2*f**m*m**4*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 1329*b*d*e**2*f**m*m**4*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2832*b*d*e**2*f**m*m**3*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 636*b*d*e**2*f**m*m**3*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2832*b*d*e**2*f**m*m**3*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3444*b*d*e**2*f**m*m**2*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 924*b*d*e**2*f**m*m**2*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 3444*b*d*e**2*f**m*m**2*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2208*b*d*e**2*f**m*m*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 672*b*d*e**2*f**m*m*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 2208*b*d*e**2*f**m*m*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 576*b*d*e**2*f**m*n*x**3*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 192*b*d*e**2*f**m*n*x**3*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 576*b*d*e**2*f**m*x**3*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + b*e**3*f**m*m**7*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + b*e**3*f**m*m**7*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 16*b*e**3*f**m*m**6*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - b*e**3*f**m*m**6*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 16*b*e**3*f**m*m**6*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 106*b*e**3*f**m*m**5*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 12*b*e**3*f**m*m**5*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 106*b*e**3*f**m*m**5*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 376*b*e**3*f**m*m**4*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 58*b*e**3*f**m*m**4*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 376*b*e**3*f**m*m**4*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 769*b*e**3*f**m*m**3*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 144*b*e**3*f**m*m**3*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 769*b*e**3*f**m*m**3*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 904*b*e**3*f**m*m**2*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 193*b*e**3*f**m*m**2*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 904*b*e**3*f**m*m**2*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 564*b*e**3*f**m*m*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 132*b*e**3*f**m*m*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 564*b*e**3*f**m*m*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 144*b*e**3*f**m*n*x**4*x**m*log(x)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) - 36*b*e**3*f**m*n*x**4*x**m/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576) + 144*b*e**3*f**m*x**4*x**m*log(c)/(m**8 + 20*m**7 + 170*m**6 + 800*m**5 + 2273*m**4 + 3980*m**3 + 4180*m**2 + 2400*m + 576), True))","A",0
163,1,3815,0,20.289798," ","integrate((f*x)**m*(e*x+d)**2*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{- \frac{a d^{2}}{2 x^{2}} - \frac{2 a d e}{x} + a e^{2} \log{\left(x \right)} + b d^{2} \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) + 2 b d e \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)}{f^{3}} & \text{for}\: m = -3 \\\frac{- \frac{a d^{2}}{x} + 2 a d e \log{\left(x \right)} + a e^{2} x - \frac{b d^{2} n \log{\left(x \right)}}{x} - \frac{b d^{2} n}{x} - \frac{b d^{2} \log{\left(c \right)}}{x} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} + b e^{2} n x \log{\left(x \right)} - b e^{2} n x + b e^{2} x \log{\left(c \right)}}{f^{2}} & \text{for}\: m = -2 \\\frac{a d^{2} \log{\left(x \right)} + 2 a d e x + \frac{a e^{2} x^{2}}{2} + \frac{b d^{2} n \log{\left(x \right)}^{2}}{2} + b d^{2} \log{\left(c \right)} \log{\left(x \right)} + 2 b d e n x \log{\left(x \right)} - 2 b d e n x + 2 b d e x \log{\left(c \right)} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{2} n x^{2}}{4} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2}}{f} & \text{for}\: m = -1 \\\frac{a d^{2} f^{m} m^{5} x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{11 a d^{2} f^{m} m^{4} x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{47 a d^{2} f^{m} m^{3} x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{97 a d^{2} f^{m} m^{2} x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{96 a d^{2} f^{m} m x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{36 a d^{2} f^{m} x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{2 a d e f^{m} m^{5} x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{20 a d e f^{m} m^{4} x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{76 a d e f^{m} m^{3} x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{136 a d e f^{m} m^{2} x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{114 a d e f^{m} m x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{36 a d e f^{m} x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{a e^{2} f^{m} m^{5} x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{9 a e^{2} f^{m} m^{4} x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{31 a e^{2} f^{m} m^{3} x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{51 a e^{2} f^{m} m^{2} x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{40 a e^{2} f^{m} m x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{12 a e^{2} f^{m} x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{b d^{2} f^{m} m^{5} n x x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{b d^{2} f^{m} m^{5} x x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{11 b d^{2} f^{m} m^{4} n x x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{b d^{2} f^{m} m^{4} n x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{11 b d^{2} f^{m} m^{4} x x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{47 b d^{2} f^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{10 b d^{2} f^{m} m^{3} n x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{47 b d^{2} f^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{97 b d^{2} f^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{37 b d^{2} f^{m} m^{2} n x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{97 b d^{2} f^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{96 b d^{2} f^{m} m n x x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{60 b d^{2} f^{m} m n x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{96 b d^{2} f^{m} m x x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{36 b d^{2} f^{m} n x x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{36 b d^{2} f^{m} n x x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{36 b d^{2} f^{m} x x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{2 b d e f^{m} m^{5} n x^{2} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{2 b d e f^{m} m^{5} x^{2} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{20 b d e f^{m} m^{4} n x^{2} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{2 b d e f^{m} m^{4} n x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{20 b d e f^{m} m^{4} x^{2} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{76 b d e f^{m} m^{3} n x^{2} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{16 b d e f^{m} m^{3} n x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{76 b d e f^{m} m^{3} x^{2} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{136 b d e f^{m} m^{2} n x^{2} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{44 b d e f^{m} m^{2} n x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{136 b d e f^{m} m^{2} x^{2} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{114 b d e f^{m} m n x^{2} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{48 b d e f^{m} m n x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{114 b d e f^{m} m x^{2} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{36 b d e f^{m} n x^{2} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{18 b d e f^{m} n x^{2} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{36 b d e f^{m} x^{2} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{b e^{2} f^{m} m^{5} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{b e^{2} f^{m} m^{5} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{9 b e^{2} f^{m} m^{4} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{b e^{2} f^{m} m^{4} n x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{9 b e^{2} f^{m} m^{4} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{31 b e^{2} f^{m} m^{3} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{6 b e^{2} f^{m} m^{3} n x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{31 b e^{2} f^{m} m^{3} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{51 b e^{2} f^{m} m^{2} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{13 b e^{2} f^{m} m^{2} n x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{51 b e^{2} f^{m} m^{2} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{40 b e^{2} f^{m} m n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{12 b e^{2} f^{m} m n x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{40 b e^{2} f^{m} m x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{12 b e^{2} f^{m} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} - \frac{4 b e^{2} f^{m} n x^{3} x^{m}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} + \frac{12 b e^{2} f^{m} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 12 m^{5} + 58 m^{4} + 144 m^{3} + 193 m^{2} + 132 m + 36} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*d**2/(2*x**2) - 2*a*d*e/x + a*e**2*log(x) + b*d**2*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) + 2*b*d*e*(-n/x - log(c*x**n)/x) - b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)))/f**3, Eq(m, -3)), ((-a*d**2/x + 2*a*d*e*log(x) + a*e**2*x - b*d**2*n*log(x)/x - b*d**2*n/x - b*d**2*log(c)/x + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) + b*e**2*n*x*log(x) - b*e**2*n*x + b*e**2*x*log(c))/f**2, Eq(m, -2)), ((a*d**2*log(x) + 2*a*d*e*x + a*e**2*x**2/2 + b*d**2*n*log(x)**2/2 + b*d**2*log(c)*log(x) + 2*b*d*e*n*x*log(x) - 2*b*d*e*n*x + 2*b*d*e*x*log(c) + b*e**2*n*x**2*log(x)/2 - b*e**2*n*x**2/4 + b*e**2*x**2*log(c)/2)/f, Eq(m, -1)), (a*d**2*f**m*m**5*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 11*a*d**2*f**m*m**4*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 47*a*d**2*f**m*m**3*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 97*a*d**2*f**m*m**2*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 96*a*d**2*f**m*m*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 36*a*d**2*f**m*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 2*a*d*e*f**m*m**5*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 20*a*d*e*f**m*m**4*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 76*a*d*e*f**m*m**3*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 136*a*d*e*f**m*m**2*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 114*a*d*e*f**m*m*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 36*a*d*e*f**m*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + a*e**2*f**m*m**5*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 9*a*e**2*f**m*m**4*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 31*a*e**2*f**m*m**3*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 51*a*e**2*f**m*m**2*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 40*a*e**2*f**m*m*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 12*a*e**2*f**m*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + b*d**2*f**m*m**5*n*x*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + b*d**2*f**m*m**5*x*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 11*b*d**2*f**m*m**4*n*x*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - b*d**2*f**m*m**4*n*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 11*b*d**2*f**m*m**4*x*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 47*b*d**2*f**m*m**3*n*x*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 10*b*d**2*f**m*m**3*n*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 47*b*d**2*f**m*m**3*x*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 97*b*d**2*f**m*m**2*n*x*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 37*b*d**2*f**m*m**2*n*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 97*b*d**2*f**m*m**2*x*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 96*b*d**2*f**m*m*n*x*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 60*b*d**2*f**m*m*n*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 96*b*d**2*f**m*m*x*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 36*b*d**2*f**m*n*x*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 36*b*d**2*f**m*n*x*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 36*b*d**2*f**m*x*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 2*b*d*e*f**m*m**5*n*x**2*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 2*b*d*e*f**m*m**5*x**2*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 20*b*d*e*f**m*m**4*n*x**2*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 2*b*d*e*f**m*m**4*n*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 20*b*d*e*f**m*m**4*x**2*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 76*b*d*e*f**m*m**3*n*x**2*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 16*b*d*e*f**m*m**3*n*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 76*b*d*e*f**m*m**3*x**2*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 136*b*d*e*f**m*m**2*n*x**2*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 44*b*d*e*f**m*m**2*n*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 136*b*d*e*f**m*m**2*x**2*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 114*b*d*e*f**m*m*n*x**2*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 48*b*d*e*f**m*m*n*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 114*b*d*e*f**m*m*x**2*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 36*b*d*e*f**m*n*x**2*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 18*b*d*e*f**m*n*x**2*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 36*b*d*e*f**m*x**2*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + b*e**2*f**m*m**5*n*x**3*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + b*e**2*f**m*m**5*x**3*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 9*b*e**2*f**m*m**4*n*x**3*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - b*e**2*f**m*m**4*n*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 9*b*e**2*f**m*m**4*x**3*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 31*b*e**2*f**m*m**3*n*x**3*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 6*b*e**2*f**m*m**3*n*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 31*b*e**2*f**m*m**3*x**3*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 51*b*e**2*f**m*m**2*n*x**3*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 13*b*e**2*f**m*m**2*n*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 51*b*e**2*f**m*m**2*x**3*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 40*b*e**2*f**m*m*n*x**3*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 12*b*e**2*f**m*m*n*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 40*b*e**2*f**m*m*x**3*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 12*b*e**2*f**m*n*x**3*x**m*log(x)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) - 4*b*e**2*f**m*n*x**3*x**m/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36) + 12*b*e**2*f**m*x**3*x**m*log(c)/(m**6 + 12*m**5 + 58*m**4 + 144*m**3 + 193*m**2 + 132*m + 36), True))","A",0
164,1,1238,0,10.293806," ","integrate((f*x)**m*(e*x+d)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{- \frac{a d}{x} + a e \log{\left(x \right)} + b d \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)}{f^{2}} & \text{for}\: m = -2 \\\frac{a d \log{\left(x \right)} + a e x + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + b e n x \log{\left(x \right)} - b e n x + b e x \log{\left(c \right)}}{f} & \text{for}\: m = -1 \\\frac{a d f^{m} m^{3} x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{5 a d f^{m} m^{2} x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{8 a d f^{m} m x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{4 a d f^{m} x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{a e f^{m} m^{3} x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{4 a e f^{m} m^{2} x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{5 a e f^{m} m x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{2 a e f^{m} x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{b d f^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{b d f^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{5 b d f^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} - \frac{b d f^{m} m^{2} n x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{5 b d f^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{8 b d f^{m} m n x x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} - \frac{4 b d f^{m} m n x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{8 b d f^{m} m x x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{4 b d f^{m} n x x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} - \frac{4 b d f^{m} n x x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{4 b d f^{m} x x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{b e f^{m} m^{3} n x^{2} x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{b e f^{m} m^{3} x^{2} x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{4 b e f^{m} m^{2} n x^{2} x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} - \frac{b e f^{m} m^{2} n x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{4 b e f^{m} m^{2} x^{2} x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{5 b e f^{m} m n x^{2} x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} - \frac{2 b e f^{m} m n x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{5 b e f^{m} m x^{2} x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{2 b e f^{m} n x^{2} x^{m} \log{\left(x \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} - \frac{b e f^{m} n x^{2} x^{m}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} + \frac{2 b e f^{m} x^{2} x^{m} \log{\left(c \right)}}{m^{4} + 6 m^{3} + 13 m^{2} + 12 m + 4} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*d/x + a*e*log(x) + b*d*(-n/x - log(c*x**n)/x) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)))/f**2, Eq(m, -2)), ((a*d*log(x) + a*e*x + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x*log(x) - b*e*n*x + b*e*x*log(c))/f, Eq(m, -1)), (a*d*f**m*m**3*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 5*a*d*f**m*m**2*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 8*a*d*f**m*m*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 4*a*d*f**m*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + a*e*f**m*m**3*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 4*a*e*f**m*m**2*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 5*a*e*f**m*m*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 2*a*e*f**m*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + b*d*f**m*m**3*n*x*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + b*d*f**m*m**3*x*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 5*b*d*f**m*m**2*n*x*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) - b*d*f**m*m**2*n*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 5*b*d*f**m*m**2*x*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 8*b*d*f**m*m*n*x*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) - 4*b*d*f**m*m*n*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 8*b*d*f**m*m*x*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 4*b*d*f**m*n*x*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) - 4*b*d*f**m*n*x*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 4*b*d*f**m*x*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + b*e*f**m*m**3*n*x**2*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + b*e*f**m*m**3*x**2*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 4*b*e*f**m*m**2*n*x**2*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) - b*e*f**m*m**2*n*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 4*b*e*f**m*m**2*x**2*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 5*b*e*f**m*m*n*x**2*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) - 2*b*e*f**m*m*n*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 5*b*e*f**m*m*x**2*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 2*b*e*f**m*n*x**2*x**m*log(x)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) - b*e*f**m*n*x**2*x**m/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4) + 2*b*e*f**m*x**2*x**m*log(c)/(m**4 + 6*m**3 + 13*m**2 + 12*m + 4), True))","A",0
165,1,192,0,10.176311," ","integrate((f*x)**m*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a f^{m} m x x^{m}}{m^{2} + 2 m + 1} + \frac{a f^{m} x x^{m}}{m^{2} + 2 m + 1} + \frac{b f^{m} m n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} + \frac{b f^{m} m x x^{m} \log{\left(c \right)}}{m^{2} + 2 m + 1} + \frac{b f^{m} n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} - \frac{b f^{m} n x x^{m}}{m^{2} + 2 m + 1} + \frac{b f^{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}}{f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**m*m*x*x**m/(m**2 + 2*m + 1) + a*f**m*x*x**m/(m**2 + 2*m + 1) + b*f**m*m*n*x*x**m*log(x)/(m**2 + 2*m + 1) + b*f**m*m*x*x**m*log(c)/(m**2 + 2*m + 1) + b*f**m*n*x*x**m*log(x)/(m**2 + 2*m + 1) - b*f**m*n*x*x**m/(m**2 + 2*m + 1) + b*f**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))/f, True))","A",0
166,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))/(e*x+d),x)","\int \frac{\left(f x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x}\, dx"," ",0,"Integral((f*x)**m*(a + b*log(c*x**n))/(d + e*x), x)","F",0
167,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))/(e*x+d)**2,x)","\int \frac{\left(f x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((f*x)**m*(a + b*log(c*x**n))/(d + e*x)**2, x)","F",0
168,0,0,0,0.000000," ","integrate(x*(b*x+a)**m*ln(c*x**n),x)","\int x \left(a + b x\right)^{m} \log{\left(c x^{n} \right)}\, dx"," ",0,"Integral(x*(a + b*x)**m*log(c*x**n), x)","F",0
169,1,233,0,27.792773," ","integrate((b*x+a)**m*ln(c*x**n),x)","- n \left(\begin{cases} a^{m} x & \text{for}\: \left(b = 0 \wedge m \neq -1\right) \vee b = 0 \\- \frac{b^{2} b^{m} m \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{m} \Phi\left(1 + \frac{b x}{a}, 1, m + 2\right) \Gamma\left(m + 2\right)}{a b m \Gamma\left(m + 3\right) + a b \Gamma\left(m + 3\right)} - \frac{2 b^{2} b^{m} \left(\frac{a}{b} + x\right)^{2} \left(\frac{a}{b} + x\right)^{m} \Phi\left(1 + \frac{b x}{a}, 1, m + 2\right) \Gamma\left(m + 2\right)}{a b m \Gamma\left(m + 3\right) + a b \Gamma\left(m + 3\right)} & \text{for}\: m > -\infty \wedge m < \infty \wedge m \neq -1 \\\frac{\begin{cases} \log{\left(a \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{b x e^{i \pi}}{a}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(a \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{b x e^{i \pi}}{a}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(a \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(a \right)} - \operatorname{Li}_{2}\left(\frac{b x e^{i \pi}}{a}\right) & \text{otherwise} \end{cases}}{b} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} a^{m} x & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x\right)^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left(a + b x \right)} & \text{otherwise} \end{cases}}{b} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-n*Piecewise((a**m*x, Eq(b, 0) | (Eq(b, 0) & Ne(m, -1))), (-b**2*b**m*m*(a/b + x)**2*(a/b + x)**m*lerchphi(1 + b*x/a, 1, m + 2)*gamma(m + 2)/(a*b*m*gamma(m + 3) + a*b*gamma(m + 3)) - 2*b**2*b**m*(a/b + x)**2*(a/b + x)**m*lerchphi(1 + b*x/a, 1, m + 2)*gamma(m + 2)/(a*b*m*gamma(m + 3) + a*b*gamma(m + 3)), (m > -oo) & (m < oo) & Ne(m, -1)), (Piecewise((log(a)*log(x) - polylog(2, b*x*exp_polar(I*pi)/a), Abs(x) < 1), (-log(a)*log(1/x) - polylog(2, b*x*exp_polar(I*pi)/a), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(a) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(a) - polylog(2, b*x*exp_polar(I*pi)/a), True))/b, True)) + Piecewise((a**m*x, Eq(b, 0)), (Piecewise(((a + b*x)**(m + 1)/(m + 1), Ne(m, -1)), (log(a + b*x), True))/b, True))*log(c*x**n)","A",0
170,0,0,0,0.000000," ","integrate((b*x+a)**m*ln(c*x**n)/x,x)","\int \frac{\left(a + b x\right)^{m} \log{\left(c x^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*x)**m*log(c*x**n)/x, x)","F",0
171,1,87,0,9.202325," ","integrate(x**5*(e*x**2+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{6}}{6} + \frac{a e x^{8}}{8} + \frac{b d n x^{6} \log{\left(x \right)}}{6} - \frac{b d n x^{6}}{36} + \frac{b d x^{6} \log{\left(c \right)}}{6} + \frac{b e n x^{8} \log{\left(x \right)}}{8} - \frac{b e n x^{8}}{64} + \frac{b e x^{8} \log{\left(c \right)}}{8}"," ",0,"a*d*x**6/6 + a*e*x**8/8 + b*d*n*x**6*log(x)/6 - b*d*n*x**6/36 + b*d*x**6*log(c)/6 + b*e*n*x**8*log(x)/8 - b*e*n*x**8/64 + b*e*x**8*log(c)/8","B",0
172,1,87,0,3.667449," ","integrate(x**3*(e*x**2+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{4}}{4} + \frac{a e x^{6}}{6} + \frac{b d n x^{4} \log{\left(x \right)}}{4} - \frac{b d n x^{4}}{16} + \frac{b d x^{4} \log{\left(c \right)}}{4} + \frac{b e n x^{6} \log{\left(x \right)}}{6} - \frac{b e n x^{6}}{36} + \frac{b e x^{6} \log{\left(c \right)}}{6}"," ",0,"a*d*x**4/4 + a*e*x**6/6 + b*d*n*x**4*log(x)/4 - b*d*n*x**4/16 + b*d*x**4*log(c)/4 + b*e*n*x**6*log(x)/6 - b*e*n*x**6/36 + b*e*x**6*log(c)/6","B",0
173,1,87,0,1.441854," ","integrate(x*(e*x**2+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{2}}{2} + \frac{a e x^{4}}{4} + \frac{b d n x^{2} \log{\left(x \right)}}{2} - \frac{b d n x^{2}}{4} + \frac{b d x^{2} \log{\left(c \right)}}{2} + \frac{b e n x^{4} \log{\left(x \right)}}{4} - \frac{b e n x^{4}}{16} + \frac{b e x^{4} \log{\left(c \right)}}{4}"," ",0,"a*d*x**2/2 + a*e*x**4/4 + b*d*n*x**2*log(x)/2 - b*d*n*x**2/4 + b*d*x**2*log(c)/2 + b*e*n*x**4*log(x)/4 - b*e*n*x**4/16 + b*e*x**4*log(c)/4","B",0
174,1,71,0,0.909586," ","integrate((e*x**2+d)*(a+b*ln(c*x**n))/x,x)","a d \log{\left(x \right)} + \frac{a e x^{2}}{2} + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + \frac{b e n x^{2} \log{\left(x \right)}}{2} - \frac{b e n x^{2}}{4} + \frac{b e x^{2} \log{\left(c \right)}}{2}"," ",0,"a*d*log(x) + a*e*x**2/2 + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x**2*log(x)/2 - b*e*n*x**2/4 + b*e*x**2*log(c)/2","A",0
175,1,63,0,4.574057," ","integrate((e*x**2+d)*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d}{2 x^{2}} + a e \log{\left(x \right)} + b d \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a*d/(2*x**2) + a*e*log(x) + b*d*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True))","A",0
176,1,88,0,2.568402," ","integrate((e*x**2+d)*(a+b*ln(c*x**n))/x**5,x)","- \frac{a d}{4 x^{4}} - \frac{a e}{2 x^{2}} - \frac{b d n \log{\left(x \right)}}{4 x^{4}} - \frac{b d n}{16 x^{4}} - \frac{b d \log{\left(c \right)}}{4 x^{4}} - \frac{b e n \log{\left(x \right)}}{2 x^{2}} - \frac{b e n}{4 x^{2}} - \frac{b e \log{\left(c \right)}}{2 x^{2}}"," ",0,"-a*d/(4*x**4) - a*e/(2*x**2) - b*d*n*log(x)/(4*x**4) - b*d*n/(16*x**4) - b*d*log(c)/(4*x**4) - b*e*n*log(x)/(2*x**2) - b*e*n/(4*x**2) - b*e*log(c)/(2*x**2)","A",0
177,1,87,0,5.844012," ","integrate(x**4*(e*x**2+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{5}}{5} + \frac{a e x^{7}}{7} + \frac{b d n x^{5} \log{\left(x \right)}}{5} - \frac{b d n x^{5}}{25} + \frac{b d x^{5} \log{\left(c \right)}}{5} + \frac{b e n x^{7} \log{\left(x \right)}}{7} - \frac{b e n x^{7}}{49} + \frac{b e x^{7} \log{\left(c \right)}}{7}"," ",0,"a*d*x**5/5 + a*e*x**7/7 + b*d*n*x**5*log(x)/5 - b*d*n*x**5/25 + b*d*x**5*log(c)/5 + b*e*n*x**7*log(x)/7 - b*e*n*x**7/49 + b*e*x**7*log(c)/7","B",0
178,1,87,0,2.308715," ","integrate(x**2*(e*x**2+d)*(a+b*ln(c*x**n)),x)","\frac{a d x^{3}}{3} + \frac{a e x^{5}}{5} + \frac{b d n x^{3} \log{\left(x \right)}}{3} - \frac{b d n x^{3}}{9} + \frac{b d x^{3} \log{\left(c \right)}}{3} + \frac{b e n x^{5} \log{\left(x \right)}}{5} - \frac{b e n x^{5}}{25} + \frac{b e x^{5} \log{\left(c \right)}}{5}"," ",0,"a*d*x**3/3 + a*e*x**5/5 + b*d*n*x**3*log(x)/3 - b*d*n*x**3/9 + b*d*x**3*log(c)/3 + b*e*n*x**5*log(x)/5 - b*e*n*x**5/25 + b*e*x**5*log(c)/5","B",0
179,1,73,0,0.857019," ","integrate((e*x**2+d)*(a+b*ln(c*x**n)),x)","a d x + \frac{a e x^{3}}{3} + b d n x \log{\left(x \right)} - b d n x + b d x \log{\left(c \right)} + \frac{b e n x^{3} \log{\left(x \right)}}{3} - \frac{b e n x^{3}}{9} + \frac{b e x^{3} \log{\left(c \right)}}{3}"," ",0,"a*d*x + a*e*x**3/3 + b*d*n*x*log(x) - b*d*n*x + b*d*x*log(c) + b*e*n*x**3*log(x)/3 - b*e*n*x**3/9 + b*e*x**3*log(c)/3","A",0
180,1,60,0,0.893723," ","integrate((e*x**2+d)*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d}{x} + a e x - \frac{b d n \log{\left(x \right)}}{x} - \frac{b d n}{x} - \frac{b d \log{\left(c \right)}}{x} + b e n x \log{\left(x \right)} - b e n x + b e x \log{\left(c \right)}"," ",0,"-a*d/x + a*e*x - b*d*n*log(x)/x - b*d*n/x - b*d*log(c)/x + b*e*n*x*log(x) - b*e*n*x + b*e*x*log(c)","A",0
181,1,75,0,1.642122," ","integrate((e*x**2+d)*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d}{3 x^{3}} - \frac{a e}{x} - \frac{b d n \log{\left(x \right)}}{3 x^{3}} - \frac{b d n}{9 x^{3}} - \frac{b d \log{\left(c \right)}}{3 x^{3}} - \frac{b e n \log{\left(x \right)}}{x} - \frac{b e n}{x} - \frac{b e \log{\left(c \right)}}{x}"," ",0,"-a*d/(3*x**3) - a*e/x - b*d*n*log(x)/(3*x**3) - b*d*n/(9*x**3) - b*d*log(c)/(3*x**3) - b*e*n*log(x)/x - b*e*n/x - b*e*log(c)/x","A",0
182,1,88,0,3.912564," ","integrate((e*x**2+d)*(a+b*ln(c*x**n))/x**6,x)","- \frac{a d}{5 x^{5}} - \frac{a e}{3 x^{3}} - \frac{b d n \log{\left(x \right)}}{5 x^{5}} - \frac{b d n}{25 x^{5}} - \frac{b d \log{\left(c \right)}}{5 x^{5}} - \frac{b e n \log{\left(x \right)}}{3 x^{3}} - \frac{b e n}{9 x^{3}} - \frac{b e \log{\left(c \right)}}{3 x^{3}}"," ",0,"-a*d/(5*x**5) - a*e/(3*x**3) - b*d*n*log(x)/(5*x**5) - b*d*n/(25*x**5) - b*d*log(c)/(5*x**5) - b*e*n*log(x)/(3*x**3) - b*e*n/(9*x**3) - b*e*log(c)/(3*x**3)","A",0
183,1,151,0,21.661050," ","integrate(x**5*(e*x**2+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{6}}{6} + \frac{a d e x^{8}}{4} + \frac{a e^{2} x^{10}}{10} + \frac{b d^{2} n x^{6} \log{\left(x \right)}}{6} - \frac{b d^{2} n x^{6}}{36} + \frac{b d^{2} x^{6} \log{\left(c \right)}}{6} + \frac{b d e n x^{8} \log{\left(x \right)}}{4} - \frac{b d e n x^{8}}{32} + \frac{b d e x^{8} \log{\left(c \right)}}{4} + \frac{b e^{2} n x^{10} \log{\left(x \right)}}{10} - \frac{b e^{2} n x^{10}}{100} + \frac{b e^{2} x^{10} \log{\left(c \right)}}{10}"," ",0,"a*d**2*x**6/6 + a*d*e*x**8/4 + a*e**2*x**10/10 + b*d**2*n*x**6*log(x)/6 - b*d**2*n*x**6/36 + b*d**2*x**6*log(c)/6 + b*d*e*n*x**8*log(x)/4 - b*d*e*n*x**8/32 + b*d*e*x**8*log(c)/4 + b*e**2*n*x**10*log(x)/10 - b*e**2*n*x**10/100 + b*e**2*x**10*log(c)/10","B",0
184,1,151,0,9.636200," ","integrate(x**3*(e*x**2+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{4}}{4} + \frac{a d e x^{6}}{3} + \frac{a e^{2} x^{8}}{8} + \frac{b d^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b d^{2} n x^{4}}{16} + \frac{b d^{2} x^{4} \log{\left(c \right)}}{4} + \frac{b d e n x^{6} \log{\left(x \right)}}{3} - \frac{b d e n x^{6}}{18} + \frac{b d e x^{6} \log{\left(c \right)}}{3} + \frac{b e^{2} n x^{8} \log{\left(x \right)}}{8} - \frac{b e^{2} n x^{8}}{64} + \frac{b e^{2} x^{8} \log{\left(c \right)}}{8}"," ",0,"a*d**2*x**4/4 + a*d*e*x**6/3 + a*e**2*x**8/8 + b*d**2*n*x**4*log(x)/4 - b*d**2*n*x**4/16 + b*d**2*x**4*log(c)/4 + b*d*e*n*x**6*log(x)/3 - b*d*e*n*x**6/18 + b*d*e*x**6*log(c)/3 + b*e**2*n*x**8*log(x)/8 - b*e**2*n*x**8/64 + b*e**2*x**8*log(c)/8","B",0
185,1,151,0,3.912886," ","integrate(x*(e*x**2+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{2}}{2} + \frac{a d e x^{4}}{2} + \frac{a e^{2} x^{6}}{6} + \frac{b d^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b d^{2} n x^{2}}{4} + \frac{b d^{2} x^{2} \log{\left(c \right)}}{2} + \frac{b d e n x^{4} \log{\left(x \right)}}{2} - \frac{b d e n x^{4}}{8} + \frac{b d e x^{4} \log{\left(c \right)}}{2} + \frac{b e^{2} n x^{6} \log{\left(x \right)}}{6} - \frac{b e^{2} n x^{6}}{36} + \frac{b e^{2} x^{6} \log{\left(c \right)}}{6}"," ",0,"a*d**2*x**2/2 + a*d*e*x**4/2 + a*e**2*x**6/6 + b*d**2*n*x**2*log(x)/2 - b*d**2*n*x**2/4 + b*d**2*x**2*log(c)/2 + b*d*e*n*x**4*log(x)/2 - b*d*e*n*x**4/8 + b*d*e*x**4*log(c)/2 + b*e**2*n*x**6*log(x)/6 - b*e**2*n*x**6/36 + b*e**2*x**6*log(c)/6","B",0
186,1,129,0,2.610029," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x,x)","a d^{2} \log{\left(x \right)} + a d e x^{2} + \frac{a e^{2} x^{4}}{4} + \frac{b d^{2} n \log{\left(x \right)}^{2}}{2} + b d^{2} \log{\left(c \right)} \log{\left(x \right)} + b d e n x^{2} \log{\left(x \right)} - \frac{b d e n x^{2}}{2} + b d e x^{2} \log{\left(c \right)} + \frac{b e^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b e^{2} n x^{4}}{16} + \frac{b e^{2} x^{4} \log{\left(c \right)}}{4}"," ",0,"a*d**2*log(x) + a*d*e*x**2 + a*e**2*x**4/4 + b*d**2*n*log(x)**2/2 + b*d**2*log(c)*log(x) + b*d*e*n*x**2*log(x) - b*d*e*n*x**2/2 + b*d*e*x**2*log(c) + b*e**2*n*x**4*log(x)/4 - b*e**2*n*x**4/16 + b*e**2*x**4*log(c)/4","A",0
187,1,136,0,2.754840," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d^{2}}{2 x^{2}} + 2 a d e \log{\left(x \right)} + \frac{a e^{2} x^{2}}{2} - \frac{b d^{2} n \log{\left(x \right)}}{2 x^{2}} - \frac{b d^{2} n}{4 x^{2}} - \frac{b d^{2} \log{\left(c \right)}}{2 x^{2}} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{2} n x^{2}}{4} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2}"," ",0,"-a*d**2/(2*x**2) + 2*a*d*e*log(x) + a*e**2*x**2/2 - b*d**2*n*log(x)/(2*x**2) - b*d**2*n/(4*x**2) - b*d**2*log(c)/(2*x**2) + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) + b*e**2*n*x**2*log(x)/2 - b*e**2*n*x**2/4 + b*e**2*x**2*log(c)/2","A",0
188,1,105,0,6.165764," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x**5,x)","- \frac{a d^{2}}{4 x^{4}} - \frac{a d e}{x^{2}} + a e^{2} \log{\left(x \right)} + b d^{2} \left(- \frac{n}{16 x^{4}} - \frac{\log{\left(c x^{n} \right)}}{4 x^{4}}\right) + 2 b d e \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) - b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)"," ",0,"-a*d**2/(4*x**4) - a*d*e/x**2 + a*e**2*log(x) + b*d**2*(-n/(16*x**4) - log(c*x**n)/(4*x**4)) + 2*b*d*e*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) - b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True))","A",0
189,1,158,0,14.498844," ","integrate(x**4*(e*x**2+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{5}}{5} + \frac{2 a d e x^{7}}{7} + \frac{a e^{2} x^{9}}{9} + \frac{b d^{2} n x^{5} \log{\left(x \right)}}{5} - \frac{b d^{2} n x^{5}}{25} + \frac{b d^{2} x^{5} \log{\left(c \right)}}{5} + \frac{2 b d e n x^{7} \log{\left(x \right)}}{7} - \frac{2 b d e n x^{7}}{49} + \frac{2 b d e x^{7} \log{\left(c \right)}}{7} + \frac{b e^{2} n x^{9} \log{\left(x \right)}}{9} - \frac{b e^{2} n x^{9}}{81} + \frac{b e^{2} x^{9} \log{\left(c \right)}}{9}"," ",0,"a*d**2*x**5/5 + 2*a*d*e*x**7/7 + a*e**2*x**9/9 + b*d**2*n*x**5*log(x)/5 - b*d**2*n*x**5/25 + b*d**2*x**5*log(c)/5 + 2*b*d*e*n*x**7*log(x)/7 - 2*b*d*e*n*x**7/49 + 2*b*d*e*x**7*log(c)/7 + b*e**2*n*x**9*log(x)/9 - b*e**2*n*x**9/81 + b*e**2*x**9*log(c)/9","B",0
190,1,158,0,6.175290," ","integrate(x**2*(e*x**2+d)**2*(a+b*ln(c*x**n)),x)","\frac{a d^{2} x^{3}}{3} + \frac{2 a d e x^{5}}{5} + \frac{a e^{2} x^{7}}{7} + \frac{b d^{2} n x^{3} \log{\left(x \right)}}{3} - \frac{b d^{2} n x^{3}}{9} + \frac{b d^{2} x^{3} \log{\left(c \right)}}{3} + \frac{2 b d e n x^{5} \log{\left(x \right)}}{5} - \frac{2 b d e n x^{5}}{25} + \frac{2 b d e x^{5} \log{\left(c \right)}}{5} + \frac{b e^{2} n x^{7} \log{\left(x \right)}}{7} - \frac{b e^{2} n x^{7}}{49} + \frac{b e^{2} x^{7} \log{\left(c \right)}}{7}"," ",0,"a*d**2*x**3/3 + 2*a*d*e*x**5/5 + a*e**2*x**7/7 + b*d**2*n*x**3*log(x)/3 - b*d**2*n*x**3/9 + b*d**2*x**3*log(c)/3 + 2*b*d*e*n*x**5*log(x)/5 - 2*b*d*e*n*x**5/25 + 2*b*d*e*x**5*log(c)/5 + b*e**2*n*x**7*log(x)/7 - b*e**2*n*x**7/49 + b*e**2*x**7*log(c)/7","B",0
191,1,144,0,2.534833," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n)),x)","a d^{2} x + \frac{2 a d e x^{3}}{3} + \frac{a e^{2} x^{5}}{5} + b d^{2} n x \log{\left(x \right)} - b d^{2} n x + b d^{2} x \log{\left(c \right)} + \frac{2 b d e n x^{3} \log{\left(x \right)}}{3} - \frac{2 b d e n x^{3}}{9} + \frac{2 b d e x^{3} \log{\left(c \right)}}{3} + \frac{b e^{2} n x^{5} \log{\left(x \right)}}{5} - \frac{b e^{2} n x^{5}}{25} + \frac{b e^{2} x^{5} \log{\left(c \right)}}{5}"," ",0,"a*d**2*x + 2*a*d*e*x**3/3 + a*e**2*x**5/5 + b*d**2*n*x*log(x) - b*d**2*n*x + b*d**2*x*log(c) + 2*b*d*e*n*x**3*log(x)/3 - 2*b*d*e*n*x**3/9 + 2*b*d*e*x**3*log(c)/3 + b*e**2*n*x**5*log(x)/5 - b*e**2*n*x**5/25 + b*e**2*x**5*log(c)/5","A",0
192,1,131,0,2.624044," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d^{2}}{x} + 2 a d e x + \frac{a e^{2} x^{3}}{3} - \frac{b d^{2} n \log{\left(x \right)}}{x} - \frac{b d^{2} n}{x} - \frac{b d^{2} \log{\left(c \right)}}{x} + 2 b d e n x \log{\left(x \right)} - 2 b d e n x + 2 b d e x \log{\left(c \right)} + \frac{b e^{2} n x^{3} \log{\left(x \right)}}{3} - \frac{b e^{2} n x^{3}}{9} + \frac{b e^{2} x^{3} \log{\left(c \right)}}{3}"," ",0,"-a*d**2/x + 2*a*d*e*x + a*e**2*x**3/3 - b*d**2*n*log(x)/x - b*d**2*n/x - b*d**2*log(c)/x + 2*b*d*e*n*x*log(x) - 2*b*d*e*n*x + 2*b*d*e*x*log(c) + b*e**2*n*x**3*log(x)/3 - b*e**2*n*x**3/9 + b*e**2*x**3*log(c)/3","A",0
193,1,131,0,2.764121," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d^{2}}{3 x^{3}} - \frac{2 a d e}{x} + a e^{2} x - \frac{b d^{2} n \log{\left(x \right)}}{3 x^{3}} - \frac{b d^{2} n}{9 x^{3}} - \frac{b d^{2} \log{\left(c \right)}}{3 x^{3}} - \frac{2 b d e n \log{\left(x \right)}}{x} - \frac{2 b d e n}{x} - \frac{2 b d e \log{\left(c \right)}}{x} + b e^{2} n x \log{\left(x \right)} - b e^{2} n x + b e^{2} x \log{\left(c \right)}"," ",0,"-a*d**2/(3*x**3) - 2*a*d*e/x + a*e**2*x - b*d**2*n*log(x)/(3*x**3) - b*d**2*n/(9*x**3) - b*d**2*log(c)/(3*x**3) - 2*b*d*e*n*log(x)/x - 2*b*d*e*n/x - 2*b*d*e*log(c)/x + b*e**2*n*x*log(x) - b*e**2*n*x + b*e**2*x*log(c)","A",0
194,1,146,0,4.211474," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x**6,x)","- \frac{a d^{2}}{5 x^{5}} - \frac{2 a d e}{3 x^{3}} - \frac{a e^{2}}{x} - \frac{b d^{2} n \log{\left(x \right)}}{5 x^{5}} - \frac{b d^{2} n}{25 x^{5}} - \frac{b d^{2} \log{\left(c \right)}}{5 x^{5}} - \frac{2 b d e n \log{\left(x \right)}}{3 x^{3}} - \frac{2 b d e n}{9 x^{3}} - \frac{2 b d e \log{\left(c \right)}}{3 x^{3}} - \frac{b e^{2} n \log{\left(x \right)}}{x} - \frac{b e^{2} n}{x} - \frac{b e^{2} \log{\left(c \right)}}{x}"," ",0,"-a*d**2/(5*x**5) - 2*a*d*e/(3*x**3) - a*e**2/x - b*d**2*n*log(x)/(5*x**5) - b*d**2*n/(25*x**5) - b*d**2*log(c)/(5*x**5) - 2*b*d*e*n*log(x)/(3*x**3) - 2*b*d*e*n/(9*x**3) - 2*b*d*e*log(c)/(3*x**3) - b*e**2*n*log(x)/x - b*e**2*n/x - b*e**2*log(c)/x","A",0
195,1,160,0,10.080460," ","integrate((e*x**2+d)**2*(a+b*ln(c*x**n))/x**8,x)","- \frac{a d^{2}}{7 x^{7}} - \frac{2 a d e}{5 x^{5}} - \frac{a e^{2}}{3 x^{3}} - \frac{b d^{2} n \log{\left(x \right)}}{7 x^{7}} - \frac{b d^{2} n}{49 x^{7}} - \frac{b d^{2} \log{\left(c \right)}}{7 x^{7}} - \frac{2 b d e n \log{\left(x \right)}}{5 x^{5}} - \frac{2 b d e n}{25 x^{5}} - \frac{2 b d e \log{\left(c \right)}}{5 x^{5}} - \frac{b e^{2} n \log{\left(x \right)}}{3 x^{3}} - \frac{b e^{2} n}{9 x^{3}} - \frac{b e^{2} \log{\left(c \right)}}{3 x^{3}}"," ",0,"-a*d**2/(7*x**7) - 2*a*d*e/(5*x**5) - a*e**2/(3*x**3) - b*d**2*n*log(x)/(7*x**7) - b*d**2*n/(49*x**7) - b*d**2*log(c)/(7*x**7) - 2*b*d*e*n*log(x)/(5*x**5) - 2*b*d*e*n/(25*x**5) - 2*b*d*e*log(c)/(5*x**5) - b*e**2*n*log(x)/(3*x**3) - b*e**2*n/(9*x**3) - b*e**2*log(c)/(3*x**3)","A",0
196,1,230,0,47.088195," ","integrate(x**5*(e*x**2+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{6}}{6} + \frac{3 a d^{2} e x^{8}}{8} + \frac{3 a d e^{2} x^{10}}{10} + \frac{a e^{3} x^{12}}{12} + \frac{b d^{3} n x^{6} \log{\left(x \right)}}{6} - \frac{b d^{3} n x^{6}}{36} + \frac{b d^{3} x^{6} \log{\left(c \right)}}{6} + \frac{3 b d^{2} e n x^{8} \log{\left(x \right)}}{8} - \frac{3 b d^{2} e n x^{8}}{64} + \frac{3 b d^{2} e x^{8} \log{\left(c \right)}}{8} + \frac{3 b d e^{2} n x^{10} \log{\left(x \right)}}{10} - \frac{3 b d e^{2} n x^{10}}{100} + \frac{3 b d e^{2} x^{10} \log{\left(c \right)}}{10} + \frac{b e^{3} n x^{12} \log{\left(x \right)}}{12} - \frac{b e^{3} n x^{12}}{144} + \frac{b e^{3} x^{12} \log{\left(c \right)}}{12}"," ",0,"a*d**3*x**6/6 + 3*a*d**2*e*x**8/8 + 3*a*d*e**2*x**10/10 + a*e**3*x**12/12 + b*d**3*n*x**6*log(x)/6 - b*d**3*n*x**6/36 + b*d**3*x**6*log(c)/6 + 3*b*d**2*e*n*x**8*log(x)/8 - 3*b*d**2*e*n*x**8/64 + 3*b*d**2*e*x**8*log(c)/8 + 3*b*d*e**2*n*x**10*log(x)/10 - 3*b*d*e**2*n*x**10/100 + 3*b*d*e**2*x**10*log(c)/10 + b*e**3*n*x**12*log(x)/12 - b*e**3*n*x**12/144 + b*e**3*x**12*log(c)/12","B",0
197,1,223,0,22.603007," ","integrate(x**3*(e*x**2+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{4}}{4} + \frac{a d^{2} e x^{6}}{2} + \frac{3 a d e^{2} x^{8}}{8} + \frac{a e^{3} x^{10}}{10} + \frac{b d^{3} n x^{4} \log{\left(x \right)}}{4} - \frac{b d^{3} n x^{4}}{16} + \frac{b d^{3} x^{4} \log{\left(c \right)}}{4} + \frac{b d^{2} e n x^{6} \log{\left(x \right)}}{2} - \frac{b d^{2} e n x^{6}}{12} + \frac{b d^{2} e x^{6} \log{\left(c \right)}}{2} + \frac{3 b d e^{2} n x^{8} \log{\left(x \right)}}{8} - \frac{3 b d e^{2} n x^{8}}{64} + \frac{3 b d e^{2} x^{8} \log{\left(c \right)}}{8} + \frac{b e^{3} n x^{10} \log{\left(x \right)}}{10} - \frac{b e^{3} n x^{10}}{100} + \frac{b e^{3} x^{10} \log{\left(c \right)}}{10}"," ",0,"a*d**3*x**4/4 + a*d**2*e*x**6/2 + 3*a*d*e**2*x**8/8 + a*e**3*x**10/10 + b*d**3*n*x**4*log(x)/4 - b*d**3*n*x**4/16 + b*d**3*x**4*log(c)/4 + b*d**2*e*n*x**6*log(x)/2 - b*d**2*e*n*x**6/12 + b*d**2*e*x**6*log(c)/2 + 3*b*d*e**2*n*x**8*log(x)/8 - 3*b*d*e**2*n*x**8/64 + 3*b*d*e**2*x**8*log(c)/8 + b*e**3*n*x**10*log(x)/10 - b*e**3*n*x**10/100 + b*e**3*x**10*log(c)/10","A",0
198,1,223,0,9.985784," ","integrate(x*(e*x**2+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{2}}{2} + \frac{3 a d^{2} e x^{4}}{4} + \frac{a d e^{2} x^{6}}{2} + \frac{a e^{3} x^{8}}{8} + \frac{b d^{3} n x^{2} \log{\left(x \right)}}{2} - \frac{b d^{3} n x^{2}}{4} + \frac{b d^{3} x^{2} \log{\left(c \right)}}{2} + \frac{3 b d^{2} e n x^{4} \log{\left(x \right)}}{4} - \frac{3 b d^{2} e n x^{4}}{16} + \frac{3 b d^{2} e x^{4} \log{\left(c \right)}}{4} + \frac{b d e^{2} n x^{6} \log{\left(x \right)}}{2} - \frac{b d e^{2} n x^{6}}{12} + \frac{b d e^{2} x^{6} \log{\left(c \right)}}{2} + \frac{b e^{3} n x^{8} \log{\left(x \right)}}{8} - \frac{b e^{3} n x^{8}}{64} + \frac{b e^{3} x^{8} \log{\left(c \right)}}{8}"," ",0,"a*d**3*x**2/2 + 3*a*d**2*e*x**4/4 + a*d*e**2*x**6/2 + a*e**3*x**8/8 + b*d**3*n*x**2*log(x)/2 - b*d**3*n*x**2/4 + b*d**3*x**2*log(c)/2 + 3*b*d**2*e*n*x**4*log(x)/4 - 3*b*d**2*e*n*x**4/16 + 3*b*d**2*e*x**4*log(c)/4 + b*d*e**2*n*x**6*log(x)/2 - b*d*e**2*n*x**6/12 + b*d*e**2*x**6*log(c)/2 + b*e**3*n*x**8*log(x)/8 - b*e**3*n*x**8/64 + b*e**3*x**8*log(c)/8","B",0
199,1,212,0,6.658863," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x,x)","a d^{3} \log{\left(x \right)} + \frac{3 a d^{2} e x^{2}}{2} + \frac{3 a d e^{2} x^{4}}{4} + \frac{a e^{3} x^{6}}{6} + \frac{b d^{3} n \log{\left(x \right)}^{2}}{2} + b d^{3} \log{\left(c \right)} \log{\left(x \right)} + \frac{3 b d^{2} e n x^{2} \log{\left(x \right)}}{2} - \frac{3 b d^{2} e n x^{2}}{4} + \frac{3 b d^{2} e x^{2} \log{\left(c \right)}}{2} + \frac{3 b d e^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{3 b d e^{2} n x^{4}}{16} + \frac{3 b d e^{2} x^{4} \log{\left(c \right)}}{4} + \frac{b e^{3} n x^{6} \log{\left(x \right)}}{6} - \frac{b e^{3} n x^{6}}{36} + \frac{b e^{3} x^{6} \log{\left(c \right)}}{6}"," ",0,"a*d**3*log(x) + 3*a*d**2*e*x**2/2 + 3*a*d*e**2*x**4/4 + a*e**3*x**6/6 + b*d**3*n*log(x)**2/2 + b*d**3*log(c)*log(x) + 3*b*d**2*e*n*x**2*log(x)/2 - 3*b*d**2*e*n*x**2/4 + 3*b*d**2*e*x**2*log(c)/2 + 3*b*d*e**2*n*x**4*log(x)/4 - 3*b*d*e**2*n*x**4/16 + 3*b*d*e**2*x**4*log(c)/4 + b*e**3*n*x**6*log(x)/6 - b*e**3*n*x**6/36 + b*e**3*x**6*log(c)/6","A",0
200,1,209,0,6.848531," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d^{3}}{2 x^{2}} + 3 a d^{2} e \log{\left(x \right)} + \frac{3 a d e^{2} x^{2}}{2} + \frac{a e^{3} x^{4}}{4} - \frac{b d^{3} n \log{\left(x \right)}}{2 x^{2}} - \frac{b d^{3} n}{4 x^{2}} - \frac{b d^{3} \log{\left(c \right)}}{2 x^{2}} + \frac{3 b d^{2} e n \log{\left(x \right)}^{2}}{2} + 3 b d^{2} e \log{\left(c \right)} \log{\left(x \right)} + \frac{3 b d e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{3 b d e^{2} n x^{2}}{4} + \frac{3 b d e^{2} x^{2} \log{\left(c \right)}}{2} + \frac{b e^{3} n x^{4} \log{\left(x \right)}}{4} - \frac{b e^{3} n x^{4}}{16} + \frac{b e^{3} x^{4} \log{\left(c \right)}}{4}"," ",0,"-a*d**3/(2*x**2) + 3*a*d**2*e*log(x) + 3*a*d*e**2*x**2/2 + a*e**3*x**4/4 - b*d**3*n*log(x)/(2*x**2) - b*d**3*n/(4*x**2) - b*d**3*log(c)/(2*x**2) + 3*b*d**2*e*n*log(x)**2/2 + 3*b*d**2*e*log(c)*log(x) + 3*b*d*e**2*n*x**2*log(x)/2 - 3*b*d*e**2*n*x**2/4 + 3*b*d*e**2*x**2*log(c)/2 + b*e**3*n*x**4*log(x)/4 - b*e**3*n*x**4/16 + b*e**3*x**4*log(c)/4","A",0
201,1,209,0,6.919293," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**5,x)","- \frac{a d^{3}}{4 x^{4}} - \frac{3 a d^{2} e}{2 x^{2}} + 3 a d e^{2} \log{\left(x \right)} + \frac{a e^{3} x^{2}}{2} - \frac{b d^{3} n \log{\left(x \right)}}{4 x^{4}} - \frac{b d^{3} n}{16 x^{4}} - \frac{b d^{3} \log{\left(c \right)}}{4 x^{4}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{2 x^{2}} - \frac{3 b d^{2} e n}{4 x^{2}} - \frac{3 b d^{2} e \log{\left(c \right)}}{2 x^{2}} + \frac{3 b d e^{2} n \log{\left(x \right)}^{2}}{2} + 3 b d e^{2} \log{\left(c \right)} \log{\left(x \right)} + \frac{b e^{3} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{3} n x^{2}}{4} + \frac{b e^{3} x^{2} \log{\left(c \right)}}{2}"," ",0,"-a*d**3/(4*x**4) - 3*a*d**2*e/(2*x**2) + 3*a*d*e**2*log(x) + a*e**3*x**2/2 - b*d**3*n*log(x)/(4*x**4) - b*d**3*n/(16*x**4) - b*d**3*log(c)/(4*x**4) - 3*b*d**2*e*n*log(x)/(2*x**2) - 3*b*d**2*e*n/(4*x**2) - 3*b*d**2*e*log(c)/(2*x**2) + 3*b*d*e**2*n*log(x)**2/2 + 3*b*d*e**2*log(c)*log(x) + b*e**3*n*x**2*log(x)/2 - b*e**3*n*x**2/4 + b*e**3*x**2*log(c)/2","A",0
202,1,223,0,32.866745," ","integrate(x**4*(e*x**2+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{5}}{5} + \frac{3 a d^{2} e x^{7}}{7} + \frac{a d e^{2} x^{9}}{3} + \frac{a e^{3} x^{11}}{11} + \frac{b d^{3} n x^{5} \log{\left(x \right)}}{5} - \frac{b d^{3} n x^{5}}{25} + \frac{b d^{3} x^{5} \log{\left(c \right)}}{5} + \frac{3 b d^{2} e n x^{7} \log{\left(x \right)}}{7} - \frac{3 b d^{2} e n x^{7}}{49} + \frac{3 b d^{2} e x^{7} \log{\left(c \right)}}{7} + \frac{b d e^{2} n x^{9} \log{\left(x \right)}}{3} - \frac{b d e^{2} n x^{9}}{27} + \frac{b d e^{2} x^{9} \log{\left(c \right)}}{3} + \frac{b e^{3} n x^{11} \log{\left(x \right)}}{11} - \frac{b e^{3} n x^{11}}{121} + \frac{b e^{3} x^{11} \log{\left(c \right)}}{11}"," ",0,"a*d**3*x**5/5 + 3*a*d**2*e*x**7/7 + a*d*e**2*x**9/3 + a*e**3*x**11/11 + b*d**3*n*x**5*log(x)/5 - b*d**3*n*x**5/25 + b*d**3*x**5*log(c)/5 + 3*b*d**2*e*n*x**7*log(x)/7 - 3*b*d**2*e*n*x**7/49 + 3*b*d**2*e*x**7*log(c)/7 + b*d*e**2*n*x**9*log(x)/3 - b*d*e**2*n*x**9/27 + b*d*e**2*x**9*log(c)/3 + b*e**3*n*x**11*log(x)/11 - b*e**3*n*x**11/121 + b*e**3*x**11*log(c)/11","B",0
203,1,230,0,15.397554," ","integrate(x**2*(e*x**2+d)**3*(a+b*ln(c*x**n)),x)","\frac{a d^{3} x^{3}}{3} + \frac{3 a d^{2} e x^{5}}{5} + \frac{3 a d e^{2} x^{7}}{7} + \frac{a e^{3} x^{9}}{9} + \frac{b d^{3} n x^{3} \log{\left(x \right)}}{3} - \frac{b d^{3} n x^{3}}{9} + \frac{b d^{3} x^{3} \log{\left(c \right)}}{3} + \frac{3 b d^{2} e n x^{5} \log{\left(x \right)}}{5} - \frac{3 b d^{2} e n x^{5}}{25} + \frac{3 b d^{2} e x^{5} \log{\left(c \right)}}{5} + \frac{3 b d e^{2} n x^{7} \log{\left(x \right)}}{7} - \frac{3 b d e^{2} n x^{7}}{49} + \frac{3 b d e^{2} x^{7} \log{\left(c \right)}}{7} + \frac{b e^{3} n x^{9} \log{\left(x \right)}}{9} - \frac{b e^{3} n x^{9}}{81} + \frac{b e^{3} x^{9} \log{\left(c \right)}}{9}"," ",0,"a*d**3*x**3/3 + 3*a*d**2*e*x**5/5 + 3*a*d*e**2*x**7/7 + a*e**3*x**9/9 + b*d**3*n*x**3*log(x)/3 - b*d**3*n*x**3/9 + b*d**3*x**3*log(c)/3 + 3*b*d**2*e*n*x**5*log(x)/5 - 3*b*d**2*e*n*x**5/25 + 3*b*d**2*e*x**5*log(c)/5 + 3*b*d*e**2*n*x**7*log(x)/7 - 3*b*d*e**2*n*x**7/49 + 3*b*d*e**2*x**7*log(c)/7 + b*e**3*n*x**9*log(x)/9 - b*e**3*n*x**9/81 + b*e**3*x**9*log(c)/9","B",0
204,1,204,0,6.602502," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n)),x)","a d^{3} x + a d^{2} e x^{3} + \frac{3 a d e^{2} x^{5}}{5} + \frac{a e^{3} x^{7}}{7} + b d^{3} n x \log{\left(x \right)} - b d^{3} n x + b d^{3} x \log{\left(c \right)} + b d^{2} e n x^{3} \log{\left(x \right)} - \frac{b d^{2} e n x^{3}}{3} + b d^{2} e x^{3} \log{\left(c \right)} + \frac{3 b d e^{2} n x^{5} \log{\left(x \right)}}{5} - \frac{3 b d e^{2} n x^{5}}{25} + \frac{3 b d e^{2} x^{5} \log{\left(c \right)}}{5} + \frac{b e^{3} n x^{7} \log{\left(x \right)}}{7} - \frac{b e^{3} n x^{7}}{49} + \frac{b e^{3} x^{7} \log{\left(c \right)}}{7}"," ",0,"a*d**3*x + a*d**2*e*x**3 + 3*a*d*e**2*x**5/5 + a*e**3*x**7/7 + b*d**3*n*x*log(x) - b*d**3*n*x + b*d**3*x*log(c) + b*d**2*e*n*x**3*log(x) - b*d**2*e*n*x**3/3 + b*d**2*e*x**3*log(c) + 3*b*d*e**2*n*x**5*log(x)/5 - 3*b*d*e**2*n*x**5/25 + 3*b*d*e**2*x**5*log(c)/5 + b*e**3*n*x**7*log(x)/7 - b*e**3*n*x**7/49 + b*e**3*x**7*log(c)/7","A",0
205,1,190,0,6.772099," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d^{3}}{x} + 3 a d^{2} e x + a d e^{2} x^{3} + \frac{a e^{3} x^{5}}{5} - \frac{b d^{3} n \log{\left(x \right)}}{x} - \frac{b d^{3} n}{x} - \frac{b d^{3} \log{\left(c \right)}}{x} + 3 b d^{2} e n x \log{\left(x \right)} - 3 b d^{2} e n x + 3 b d^{2} e x \log{\left(c \right)} + b d e^{2} n x^{3} \log{\left(x \right)} - \frac{b d e^{2} n x^{3}}{3} + b d e^{2} x^{3} \log{\left(c \right)} + \frac{b e^{3} n x^{5} \log{\left(x \right)}}{5} - \frac{b e^{3} n x^{5}}{25} + \frac{b e^{3} x^{5} \log{\left(c \right)}}{5}"," ",0,"-a*d**3/x + 3*a*d**2*e*x + a*d*e**2*x**3 + a*e**3*x**5/5 - b*d**3*n*log(x)/x - b*d**3*n/x - b*d**3*log(c)/x + 3*b*d**2*e*n*x*log(x) - 3*b*d**2*e*n*x + 3*b*d**2*e*x*log(c) + b*d*e**2*n*x**3*log(x) - b*d*e**2*n*x**3/3 + b*d*e**2*x**3*log(c) + b*e**3*n*x**5*log(x)/5 - b*e**3*n*x**5/25 + b*e**3*x**5*log(c)/5","A",0
206,1,202,0,6.919197," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d^{3}}{3 x^{3}} - \frac{3 a d^{2} e}{x} + 3 a d e^{2} x + \frac{a e^{3} x^{3}}{3} - \frac{b d^{3} n \log{\left(x \right)}}{3 x^{3}} - \frac{b d^{3} n}{9 x^{3}} - \frac{b d^{3} \log{\left(c \right)}}{3 x^{3}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{x} - \frac{3 b d^{2} e n}{x} - \frac{3 b d^{2} e \log{\left(c \right)}}{x} + 3 b d e^{2} n x \log{\left(x \right)} - 3 b d e^{2} n x + 3 b d e^{2} x \log{\left(c \right)} + \frac{b e^{3} n x^{3} \log{\left(x \right)}}{3} - \frac{b e^{3} n x^{3}}{9} + \frac{b e^{3} x^{3} \log{\left(c \right)}}{3}"," ",0,"-a*d**3/(3*x**3) - 3*a*d**2*e/x + 3*a*d*e**2*x + a*e**3*x**3/3 - b*d**3*n*log(x)/(3*x**3) - b*d**3*n/(9*x**3) - b*d**3*log(c)/(3*x**3) - 3*b*d**2*e*n*log(x)/x - 3*b*d**2*e*n/x - 3*b*d**2*e*log(c)/x + 3*b*d*e**2*n*x*log(x) - 3*b*d*e**2*n*x + 3*b*d*e**2*x*log(c) + b*e**3*n*x**3*log(x)/3 - b*e**3*n*x**3/9 + b*e**3*x**3*log(c)/3","A",0
207,1,190,0,6.971907," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**6,x)","- \frac{a d^{3}}{5 x^{5}} - \frac{a d^{2} e}{x^{3}} - \frac{3 a d e^{2}}{x} + a e^{3} x - \frac{b d^{3} n \log{\left(x \right)}}{5 x^{5}} - \frac{b d^{3} n}{25 x^{5}} - \frac{b d^{3} \log{\left(c \right)}}{5 x^{5}} - \frac{b d^{2} e n \log{\left(x \right)}}{x^{3}} - \frac{b d^{2} e n}{3 x^{3}} - \frac{b d^{2} e \log{\left(c \right)}}{x^{3}} - \frac{3 b d e^{2} n \log{\left(x \right)}}{x} - \frac{3 b d e^{2} n}{x} - \frac{3 b d e^{2} \log{\left(c \right)}}{x} + b e^{3} n x \log{\left(x \right)} - b e^{3} n x + b e^{3} x \log{\left(c \right)}"," ",0,"-a*d**3/(5*x**5) - a*d**2*e/x**3 - 3*a*d*e**2/x + a*e**3*x - b*d**3*n*log(x)/(5*x**5) - b*d**3*n/(25*x**5) - b*d**3*log(c)/(5*x**5) - b*d**2*e*n*log(x)/x**3 - b*d**2*e*n/(3*x**3) - b*d**2*e*log(c)/x**3 - 3*b*d*e**2*n*log(x)/x - 3*b*d*e**2*n/x - 3*b*d*e**2*log(c)/x + b*e**3*n*x*log(x) - b*e**3*n*x + b*e**3*x*log(c)","A",0
208,1,206,0,10.392358," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**8,x)","- \frac{a d^{3}}{7 x^{7}} - \frac{3 a d^{2} e}{5 x^{5}} - \frac{a d e^{2}}{x^{3}} - \frac{a e^{3}}{x} - \frac{b d^{3} n \log{\left(x \right)}}{7 x^{7}} - \frac{b d^{3} n}{49 x^{7}} - \frac{b d^{3} \log{\left(c \right)}}{7 x^{7}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{5 x^{5}} - \frac{3 b d^{2} e n}{25 x^{5}} - \frac{3 b d^{2} e \log{\left(c \right)}}{5 x^{5}} - \frac{b d e^{2} n \log{\left(x \right)}}{x^{3}} - \frac{b d e^{2} n}{3 x^{3}} - \frac{b d e^{2} \log{\left(c \right)}}{x^{3}} - \frac{b e^{3} n \log{\left(x \right)}}{x} - \frac{b e^{3} n}{x} - \frac{b e^{3} \log{\left(c \right)}}{x}"," ",0,"-a*d**3/(7*x**7) - 3*a*d**2*e/(5*x**5) - a*d*e**2/x**3 - a*e**3/x - b*d**3*n*log(x)/(7*x**7) - b*d**3*n/(49*x**7) - b*d**3*log(c)/(7*x**7) - 3*b*d**2*e*n*log(x)/(5*x**5) - 3*b*d**2*e*n/(25*x**5) - 3*b*d**2*e*log(c)/(5*x**5) - b*d*e**2*n*log(x)/x**3 - b*d*e**2*n/(3*x**3) - b*d*e**2*log(c)/x**3 - b*e**3*n*log(x)/x - b*e**3*n/x - b*e**3*log(c)/x","A",0
209,1,231,0,23.035669," ","integrate((e*x**2+d)**3*(a+b*ln(c*x**n))/x**10,x)","- \frac{a d^{3}}{9 x^{9}} - \frac{3 a d^{2} e}{7 x^{7}} - \frac{3 a d e^{2}}{5 x^{5}} - \frac{a e^{3}}{3 x^{3}} - \frac{b d^{3} n \log{\left(x \right)}}{9 x^{9}} - \frac{b d^{3} n}{81 x^{9}} - \frac{b d^{3} \log{\left(c \right)}}{9 x^{9}} - \frac{3 b d^{2} e n \log{\left(x \right)}}{7 x^{7}} - \frac{3 b d^{2} e n}{49 x^{7}} - \frac{3 b d^{2} e \log{\left(c \right)}}{7 x^{7}} - \frac{3 b d e^{2} n \log{\left(x \right)}}{5 x^{5}} - \frac{3 b d e^{2} n}{25 x^{5}} - \frac{3 b d e^{2} \log{\left(c \right)}}{5 x^{5}} - \frac{b e^{3} n \log{\left(x \right)}}{3 x^{3}} - \frac{b e^{3} n}{9 x^{3}} - \frac{b e^{3} \log{\left(c \right)}}{3 x^{3}}"," ",0,"-a*d**3/(9*x**9) - 3*a*d**2*e/(7*x**7) - 3*a*d*e**2/(5*x**5) - a*e**3/(3*x**3) - b*d**3*n*log(x)/(9*x**9) - b*d**3*n/(81*x**9) - b*d**3*log(c)/(9*x**9) - 3*b*d**2*e*n*log(x)/(7*x**7) - 3*b*d**2*e*n/(49*x**7) - 3*b*d**2*e*log(c)/(7*x**7) - 3*b*d*e**2*n*log(x)/(5*x**5) - 3*b*d*e**2*n/(25*x**5) - 3*b*d*e**2*log(c)/(5*x**5) - b*e**3*n*log(x)/(3*x**3) - b*e**3*n/(9*x**3) - b*e**3*log(c)/(3*x**3)","A",0
210,1,235,0,90.775908," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x**2+d),x)","\frac{a d^{2} \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right)}{2 e^{2}} - \frac{a d x^{2}}{2 e^{2}} + \frac{a x^{4}}{4 e} - \frac{b d^{2} n \left(\begin{cases} \frac{x^{2}}{2 d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{2 e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{2 e^{2}} + \frac{b d n x^{2}}{4 e^{2}} - \frac{b d x^{2} \log{\left(c x^{n} \right)}}{2 e^{2}} - \frac{b n x^{4}}{16 e} + \frac{b x^{4} \log{\left(c x^{n} \right)}}{4 e}"," ",0,"a*d**2*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))/(2*e**2) - a*d*x**2/(2*e**2) + a*x**4/(4*e) - b*d**2*n*Piecewise((x**2/(2*d), Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/e, True))/(2*e**2) + b*d**2*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))*log(c*x**n)/(2*e**2) + b*d*n*x**2/(4*e**2) - b*d*x**2*log(c*x**n)/(2*e**2) - b*n*x**4/(16*e) + b*x**4*log(c*x**n)/(4*e)","A",0
211,1,180,0,34.148849," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x**2+d),x)","- \frac{a d \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right)}{2 e} + \frac{a x^{2}}{2 e} + \frac{b d n \left(\begin{cases} \frac{x^{2}}{2 d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{2 e} - \frac{b d \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{2 e} - \frac{b n x^{2}}{4 e} + \frac{b x^{2} \log{\left(c x^{n} \right)}}{2 e}"," ",0,"-a*d*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))/(2*e) + a*x**2/(2*e) + b*d*n*Piecewise((x**2/(2*d), Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/e, True))/(2*e) - b*d*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))*log(c*x**n)/(2*e) - b*n*x**2/(4*e) + b*x**2*log(c*x**n)/(2*e)","A",0
212,1,119,0,7.825397," ","integrate(x*(a+b*ln(c*x**n))/(e*x**2+d),x)","\frac{a \log{\left(d + e x^{2} \right)}}{2 e} - \frac{b n \left(\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}\right)}{2 e} + \frac{b \log{\left(c x^{n} \right)} \log{\left(d + e x^{2} \right)}}{2 e}"," ",0,"a*log(d + e*x**2)/(2*e) - b*n*Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/(2*e) + b*log(c*x**n)*log(d + e*x**2)/(2*e)","A",0
213,1,124,0,16.735826," ","integrate((a+b*ln(c*x**n))/x/(e*x**2+d),x)","\frac{a \log{\left(x \right)}}{d} - \frac{a \log{\left(d + e x^{2} \right)}}{2 d} + \frac{b n \left(\begin{cases} \log{\left(e \right)} \log{\left(x \right)} + \frac{\operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x^{2}}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} + \frac{\operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x^{2}}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + \frac{\operatorname{Li}_{2}\left(\frac{d e^{i \pi}}{e x^{2}}\right)}{2} & \text{otherwise} \end{cases}\right)}{2 d} - \frac{b \log{\left(c x^{n} \right)} \log{\left(\frac{d}{x^{2}} + e \right)}}{2 d}"," ",0,"a*log(x)/d - a*log(d + e*x**2)/(2*d) + b*n*Piecewise((log(e)*log(x) + polylog(2, d*exp_polar(I*pi)/(e*x**2))/2, Abs(x) < 1), (-log(e)*log(1/x) + polylog(2, d*exp_polar(I*pi)/(e*x**2))/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) + polylog(2, d*exp_polar(I*pi)/(e*x**2))/2, True))/(2*d) - b*log(c*x**n)*log(d/x**2 + e)/(2*d)","A",0
214,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x**2+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**5/(e*x**2+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,0,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))/(e*x**2+d),x)","\int \frac{x^{4} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x**4*(a + b*log(c*x**n))/(d + e*x**2), x)","F",0
217,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x**2+d),x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/(d + e*x**2), x)","F",0
218,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**2+d),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{d + e x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d + e*x**2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x**2+d),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*(d + e*x**2)), x)","F",0
220,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(e*x**2+d),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{4} \left(d + e x^{2}\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**4*(d + e*x**2)), x)","F",0
221,1,294,0,112.337982," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\frac{a d^{2} \left(\begin{cases} \frac{x^{2}}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x^{2}} & \text{otherwise} \end{cases}\right)}{2 e^{2}} - \frac{a d \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{a x^{2}}{2 e^{2}} - \frac{b d^{2} n \left(\begin{cases} \frac{x^{2}}{2 d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x^{2} \right)}}{2 d e} & \text{otherwise} \end{cases}\right)}{2 e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x^{2}}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{2 e^{2}} + \frac{b d n \left(\begin{cases} \frac{x^{2}}{2 d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{b d \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} - \frac{b n x^{2}}{4 e^{2}} + \frac{b x^{2} \log{\left(c x^{n} \right)}}{2 e^{2}}"," ",0,"a*d**2*Piecewise((x**2/d**2, Eq(e, 0)), (-1/(d*e + e**2*x**2), True))/(2*e**2) - a*d*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))/e**2 + a*x**2/(2*e**2) - b*d**2*n*Piecewise((x**2/(2*d**2), Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x**2)/(2*d*e), True))/(2*e**2) + b*d**2*Piecewise((x**2/d**2, Eq(e, 0)), (-1/(d*e + e**2*x**2), True))*log(c*x**n)/(2*e**2) + b*d*n*Piecewise((x**2/(2*d), Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/e, True))/e**2 - b*d*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))*log(c*x**n)/e**2 - b*n*x**2/(4*e**2) + b*x**2*log(c*x**n)/(2*e**2)","A",0
222,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,1,366,0,59.945928," ","integrate(x*(a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\begin{cases} \tilde{\infty} \left(- \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}}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{- \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}}}{e^{2}} & \text{for}\: d = 0 \\\frac{\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}}{d^{2}} & \text{for}\: e = 0 \\- \frac{2 a d}{4 d^{2} e + 4 d e^{2} x^{2}} - \frac{b d n \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{4 d^{2} e + 4 d e^{2} x^{2}} - \frac{b d n \log{\left(i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{4 d^{2} e + 4 d e^{2} x^{2}} + \frac{2 b e n x^{2} \log{\left(x \right)}}{4 d^{2} e + 4 d e^{2} x^{2}} - \frac{b e n x^{2} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{4 d^{2} e + 4 d e^{2} x^{2}} - \frac{b e n x^{2} \log{\left(i \sqrt{d} \sqrt{\frac{1}{e}} + x \right)}}{4 d^{2} e + 4 d e^{2} x^{2}} + \frac{2 b e x^{2} \log{\left(c \right)}}{4 d^{2} e + 4 d e^{2} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2)), Eq(d, 0) & Eq(e, 0)), ((-a/(2*x**2) - b*n*log(x)/(2*x**2) - b*n/(4*x**2) - b*log(c)/(2*x**2))/e**2, Eq(d, 0)), ((a*x**2/2 + b*n*x**2*log(x)/2 - b*n*x**2/4 + b*x**2*log(c)/2)/d**2, Eq(e, 0)), (-2*a*d/(4*d**2*e + 4*d*e**2*x**2) - b*d*n*log(-I*sqrt(d)*sqrt(1/e) + x)/(4*d**2*e + 4*d*e**2*x**2) - b*d*n*log(I*sqrt(d)*sqrt(1/e) + x)/(4*d**2*e + 4*d*e**2*x**2) + 2*b*e*n*x**2*log(x)/(4*d**2*e + 4*d*e**2*x**2) - b*e*n*x**2*log(-I*sqrt(d)*sqrt(1/e) + x)/(4*d**2*e + 4*d*e**2*x**2) - b*e*n*x**2*log(I*sqrt(d)*sqrt(1/e) + x)/(4*d**2*e + 4*d*e**2*x**2) + 2*b*e*x**2*log(c)/(4*d**2*e + 4*d*e**2*x**2), True))","A",0
224,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,0,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\int \frac{x^{4} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**4*(a + b*log(c*x**n))/(d + e*x**2)**2, x)","F",0
227,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/(d + e*x**2)**2, x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d + e*x**2)**2, x)","F",0
229,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x**2+d)**2,x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*(d + e*x**2)**2), x)","F",0
230,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,1,381,0,163.085208," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x**2+d)**3,x)","\frac{a d^{2} \left(\begin{cases} \frac{x^{2}}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x^{2}\right)^{2}} & \text{otherwise} \end{cases}\right)}{2 e^{2}} - \frac{a d \left(\begin{cases} \frac{x^{2}}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x^{2}} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{a \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right)}{2 e^{2}} - \frac{b d^{2} n \left(\begin{cases} \frac{x^{2}}{2 d^{3}} & \text{for}\: e = 0 \\- \frac{1}{4 d^{2} e + 4 d e^{2} x^{2}} - \frac{\log{\left(x \right)}}{2 d^{2} e} + \frac{\log{\left(\frac{d}{e} + x^{2} \right)}}{4 d^{2} e} & \text{otherwise} \end{cases}\right)}{2 e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x^{2}}{d^{3}} & \text{for}\: e = 0 \\- \frac{1}{2 e \left(d + e x^{2}\right)^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{2 e^{2}} + \frac{b d n \left(\begin{cases} \frac{x^{2}}{2 d^{2}} & \text{for}\: e = 0 \\- \frac{\log{\left(x \right)}}{d e} + \frac{\log{\left(\frac{d}{e} + x^{2} \right)}}{2 d e} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{b d \left(\begin{cases} \frac{x^{2}}{d^{2}} & \text{for}\: e = 0 \\- \frac{1}{d e + e^{2} x^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} - \frac{b n \left(\begin{cases} \frac{x^{2}}{2 d} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} - \frac{\operatorname{Li}_{2}\left(\frac{e x^{2} e^{i \pi}}{d}\right)}{2} & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right)}{2 e^{2}} + \frac{b \left(\begin{cases} \frac{x^{2}}{d} & \text{for}\: e = 0 \\\frac{\log{\left(d + e x^{2} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{2 e^{2}}"," ",0,"a*d**2*Piecewise((x**2/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x**2)**2), True))/(2*e**2) - a*d*Piecewise((x**2/d**2, Eq(e, 0)), (-1/(d*e + e**2*x**2), True))/e**2 + a*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))/(2*e**2) - b*d**2*n*Piecewise((x**2/(2*d**3), Eq(e, 0)), (-1/(4*d**2*e + 4*d*e**2*x**2) - log(x)/(2*d**2*e) + log(d/e + x**2)/(4*d**2*e), True))/(2*e**2) + b*d**2*Piecewise((x**2/d**3, Eq(e, 0)), (-1/(2*e*(d + e*x**2)**2), True))*log(c*x**n)/(2*e**2) + b*d*n*Piecewise((x**2/(2*d**2), Eq(e, 0)), (-log(x)/(d*e) + log(d/e + x**2)/(2*d*e), True))/e**2 - b*d*Piecewise((x**2/d**2, Eq(e, 0)), (-1/(d*e + e**2*x**2), True))*log(c*x**n)/e**2 - b*n*Piecewise((x**2/(2*d), Eq(e, 0)), (Piecewise((log(d)*log(x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, Abs(x) < 1), (-log(d)*log(1/x) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) - polylog(2, e*x**2*exp_polar(I*pi)/d)/2, True))/e, True))/(2*e**2) + b*Piecewise((x**2/d, Eq(e, 0)), (log(d + e*x**2)/e, True))*log(c*x**n)/(2*e**2)","A",0
232,-1,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(e*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,1,78,0,8.245328," ","integrate(x*ln(c*x**2)/(-c*x**2+1),x)","\frac{\begin{cases} i \pi \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(c x^{2}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(c x^{2}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \frac{\operatorname{Li}_{2}\left(c x^{2}\right)}{2} & \text{otherwise} \end{cases}}{c} - \frac{\log{\left(c x^{2} \right)} \log{\left(c x^{2} - 1 \right)}}{2 c}"," ",0,"Piecewise((I*pi*log(x) - polylog(2, c*x**2)/2, Abs(x) < 1), (-I*pi*log(1/x) - polylog(2, c*x**2)/2, 1/Abs(x) < 1), (-I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) - polylog(2, c*x**2)/2, True))/c - log(c*x**2)*log(c*x**2 - 1)/(2*c)","C",0
242,1,102,0,6.184546," ","integrate(x*ln(x**2/c)/(-x**2+c),x)","\begin{cases} \log{\left(c \right)} \log{\left(x \right)} + i \pi \log{\left(x \right)} - \frac{\operatorname{Li}_{2}\left(\frac{x^{2}}{c}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(c \right)} \log{\left(\frac{1}{x} \right)} - i \pi \log{\left(\frac{1}{x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{x^{2}}{c}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(c \right)} - i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(c \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \frac{\operatorname{Li}_{2}\left(\frac{x^{2}}{c}\right)}{2} & \text{otherwise} \end{cases} - \frac{\log{\left(\frac{x^{2}}{c} \right)} \log{\left(- c + x^{2} \right)}}{2}"," ",0,"Piecewise((log(c)*log(x) + I*pi*log(x) - polylog(2, x**2/c)/2, Abs(x) < 1), (-log(c)*log(1/x) - I*pi*log(1/x) - polylog(2, x**2/c)/2, 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(c) - I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(c) + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) - polylog(2, x**2/c)/2, True)) - log(x**2/c)*log(-c + x**2)/2","A",0
243,0,0,0,0.000000," ","integrate(ln(x)/(-x**2+1),x)","- \int \frac{\log{\left(x \right)}}{x^{2} - 1}\, dx"," ",0,"-Integral(log(x)/(x**2 - 1), x)","F",0
244,0,0,0,0.000000," ","integrate(ln(x)/(x**2+1),x)","\int \frac{\log{\left(x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(log(x)/(x**2 + 1), x)","F",0
245,0,0,0,0.000000," ","integrate((a+b*ln(c*x))/(-e*x**2+1),x)","- \int \frac{a}{e x^{2} - 1}\, dx - \int \frac{b \log{\left(c x \right)}}{e x^{2} - 1}\, dx"," ",0,"-Integral(a/(e*x**2 - 1), x) - Integral(b*log(c*x)/(e*x**2 - 1), x)","F",0
246,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(-e*x**2+1),x)","- \int \frac{a}{e x^{2} - 1}\, dx - \int \frac{b \log{\left(c x^{n} \right)}}{e x^{2} - 1}\, dx"," ",0,"-Integral(a/(e*x**2 - 1), x) - Integral(b*log(c*x**n)/(e*x**2 - 1), x)","F",0
247,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/(e*x**2+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2/(d + e*x**2)**2, x)","F",0
248,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**3/(e*x**2+d)**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{3}}{\left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**3/(d + e*x**2)**2, x)","F",0
249,0,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(a+b*ln(c*x**n)),x)","\int \frac{1}{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*log(c*x**n))*(d + e*x**2)**2), x)","F",0
250,-1,0,0,0.000000," ","integrate(1/(e*x**2+d)**2/(a+b*ln(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,0,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*x**n))*(e*x**2+d)**(1/2),x)","\int x^{5} \left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**5*(a + b*log(c*x**n))*sqrt(d + e*x**2), x)","F",0
252,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))*(e*x**2+d)**(1/2),x)","\int x^{3} \left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))*sqrt(d + e*x**2), x)","F",0
253,1,155,0,23.110498," ","integrate(x*(a+b*ln(c*x**n))*(e*x**2+d)**(1/2),x)","a \left(\begin{cases} \frac{\sqrt{d} x^{2}}{2} & \text{for}\: e = 0 \\\frac{\left(d + e x^{2}\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) - b n \left(\begin{cases} \frac{\sqrt{d} x^{2}}{4} & \text{for}\: e = 0 \\\frac{4 d^{\frac{3}{2}} \sqrt{1 + \frac{e x^{2}}{d}}}{9 e} + \frac{d^{\frac{3}{2}} \log{\left(\frac{e x^{2}}{d} \right)}}{6 e} - \frac{d^{\frac{3}{2}} \log{\left(\sqrt{1 + \frac{e x^{2}}{d}} + 1 \right)}}{3 e} + \frac{\sqrt{d} x^{2} \sqrt{1 + \frac{e x^{2}}{d}}}{9} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{\sqrt{d} x^{2}}{2} & \text{for}\: e = 0 \\\frac{\left(d + e x^{2}\right)^{\frac{3}{2}}}{3 e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"a*Piecewise((sqrt(d)*x**2/2, Eq(e, 0)), ((d + e*x**2)**(3/2)/(3*e), True)) - b*n*Piecewise((sqrt(d)*x**2/4, Eq(e, 0)), (4*d**(3/2)*sqrt(1 + e*x**2/d)/(9*e) + d**(3/2)*log(e*x**2/d)/(6*e) - d**(3/2)*log(sqrt(1 + e*x**2/d) + 1)/(3*e) + sqrt(d)*x**2*sqrt(1 + e*x**2/d)/9, True)) + b*Piecewise((sqrt(d)*x**2/2, Eq(e, 0)), ((d + e*x**2)**(3/2)/(3*e), True))*log(c*x**n)","A",0
254,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2)/x,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}}{x}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2)/x, x)","F",0
255,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2)/x**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2)/x**3, x)","F",0
256,0,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))*(e*x**2+d)**(1/2),x)","\int x^{4} \left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**4*(a + b*log(c*x**n))*sqrt(d + e*x**2), x)","F",0
257,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))*(e*x**2+d)**(1/2),x)","\int x^{2} \left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))*sqrt(d + e*x**2), x)","F",0
258,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2),x)","\int \left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2), x)","F",0
259,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2)/x**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2)/x**2, x)","F",0
260,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2)/x**4,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2)/x**4, x)","F",0
261,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2)/x**6,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}}{x^{6}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2)/x**6, x)","F",0
262,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))*(e*x**2+d)**(1/2)/x**8,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{2}}}{x^{8}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**2)/x**8, x)","F",0
263,-1,0,0,0.000000," ","integrate(x**5*(e*x**2+d)**(3/2)*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,0,0,0,0.000000," ","integrate(x**3*(e*x**2+d)**(3/2)*(a+b*ln(c*x**n)),x)","\int x^{3} \left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))*(d + e*x**2)**(3/2), x)","F",0
265,0,0,0,0.000000," ","integrate(x*(e*x**2+d)**(3/2)*(a+b*ln(c*x**n)),x)","\int x \left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))*(d + e*x**2)**(3/2), x)","F",0
266,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((a + b*log(c*x**n))*(d + e*x**2)**(3/2)/x, x)","F",0
267,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*(d + e*x**2)**(3/2)/x**3, x)","F",0
268,0,0,0,0.000000," ","integrate(x**2*(e*x**2+d)**(3/2)*(a+b*ln(c*x**n)),x)","\int x^{2} \left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))*(d + e*x**2)**(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n)),x)","\int \left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*(d + e*x**2)**(3/2), x)","F",0
270,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x**2,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*(d + e*x**2)**(3/2)/x**2, x)","F",0
271,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x**4,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*(d + e*x**2)**(3/2)/x**4, x)","F",0
272,0,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x**6,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \left(d + e x^{2}\right)^{\frac{3}{2}}}{x^{6}}\, dx"," ",0,"Integral((a + b*log(c*x**n))*(d + e*x**2)**(3/2)/x**6, x)","F",0
273,-1,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((e*x**2+d)**(3/2)*(a+b*ln(c*x**n))/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,1,65,0,25.550736," ","integrate(x*ln(x)*(x**2+4)**(1/2),x)","\frac{\left(x^{2} + 4\right)^{\frac{3}{2}} \log{\left(x \right)}}{3} - \frac{\left(x^{2} + 4\right)^{\frac{3}{2}}}{9} - \frac{4 \sqrt{x^{2} + 4}}{3} - \frac{4 \log{\left(\sqrt{x^{2} + 4} - 2 \right)}}{3} + \frac{4 \log{\left(\sqrt{x^{2} + 4} + 2 \right)}}{3}"," ",0,"(x**2 + 4)**(3/2)*log(x)/3 - (x**2 + 4)**(3/2)/9 - 4*sqrt(x**2 + 4)/3 - 4*log(sqrt(x**2 + 4) - 2)/3 + 4*log(sqrt(x**2 + 4) + 2)/3","A",0
276,0,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x**2+d)**(1/2),x)","\int \frac{x^{5} \left(a + b \log{\left(c x^{n} \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**5*(a + b*log(c*x**n))/sqrt(d + e*x**2), x)","F",0
277,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x**2+d)**(1/2),x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))/sqrt(d + e*x**2), x)","F",0
278,1,126,0,4.812972," ","integrate(x*(a+b*ln(c*x**n))/(e*x**2+d)**(1/2),x)","a \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d}} & \text{for}\: e = 0 \\\frac{\sqrt{d + e x^{2}}}{e} & \text{otherwise} \end{cases}\right) - b n \left(\begin{cases} \frac{x^{2}}{4 \sqrt{d}} & \text{for}\: e = 0 \\- \frac{\sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d}}{\sqrt{e} x} \right)}}{e} + \frac{d}{e^{\frac{3}{2}} x \sqrt{\frac{d}{e x^{2}} + 1}} + \frac{x}{\sqrt{e} \sqrt{\frac{d}{e x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d}} & \text{for}\: e = 0 \\\frac{\sqrt{d + e x^{2}}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"a*Piecewise((x**2/(2*sqrt(d)), Eq(e, 0)), (sqrt(d + e*x**2)/e, True)) - b*n*Piecewise((x**2/(4*sqrt(d)), Eq(e, 0)), (-sqrt(d)*asinh(sqrt(d)/(sqrt(e)*x))/e + d/(e**(3/2)*x*sqrt(d/(e*x**2) + 1)) + x/(sqrt(e)*sqrt(d/(e*x**2) + 1)), True)) + b*Piecewise((x**2/(2*sqrt(d)), Eq(e, 0)), (sqrt(d + e*x**2)/e, True))*log(c*x**n)","A",0
279,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x**2+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x*sqrt(d + e*x**2)), x)","F",0
280,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x**2+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{3} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**3*sqrt(d + e*x**2)), x)","F",0
281,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x**2+d)**(1/2),x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/sqrt(d + e*x**2), x)","F",0
282,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**2+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{\sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/sqrt(d + e*x**2), x)","F",0
283,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x**2+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*sqrt(d + e*x**2)), x)","F",0
284,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(e*x**2+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{4} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**4*sqrt(d + e*x**2)), x)","F",0
285,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**6/(e*x**2+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{6} \sqrt{d + e x^{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**6*sqrt(d + e*x**2)), x)","F",0
286,-1,0,0,0.000000," ","integrate(x**7*(a+b*ln(c*x**n))/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,1,163,0,47.867469," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x**2+d)**(3/2),x)","a \left(\begin{cases} \frac{x^{4}}{4 d^{\frac{3}{2}}} & \text{for}\: e = 0 \\\frac{d}{e^{2} \sqrt{d + e x^{2}}} + \frac{\sqrt{d + e x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) - b n \left(\begin{cases} \frac{x^{4}}{16 d^{\frac{3}{2}}} & \text{for}\: e = 0 \\- \frac{2 \sqrt{d} \operatorname{asinh}{\left(\frac{\sqrt{d}}{\sqrt{e} x} \right)}}{e^{2}} + \frac{d}{e^{\frac{5}{2}} x \sqrt{\frac{d}{e x^{2}} + 1}} + \frac{x}{e^{\frac{3}{2}} \sqrt{\frac{d}{e x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{x^{4}}{4 d^{\frac{3}{2}}} & \text{for}\: e = 0 \\\frac{d}{e^{2} \sqrt{d + e x^{2}}} + \frac{\sqrt{d + e x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"a*Piecewise((x**4/(4*d**(3/2)), Eq(e, 0)), (d/(e**2*sqrt(d + e*x**2)) + sqrt(d + e*x**2)/e**2, True)) - b*n*Piecewise((x**4/(16*d**(3/2)), Eq(e, 0)), (-2*sqrt(d)*asinh(sqrt(d)/(sqrt(e)*x))/e**2 + d/(e**(5/2)*x*sqrt(d/(e*x**2) + 1)) + x/(e**(3/2)*sqrt(d/(e*x**2) + 1)), True)) + b*Piecewise((x**4/(4*d**(3/2)), Eq(e, 0)), (d/(e**2*sqrt(d + e*x**2)) + sqrt(d + e*x**2)/e**2, True))*log(c*x**n)","A",0
289,1,80,0,12.773355," ","integrate(x*(a+b*ln(c*x**n))/(e*x**2+d)**(3/2),x)","- \frac{a}{e \sqrt{d + e x^{2}}} - b n \left(\begin{cases} \frac{x^{2}}{4 d^{\frac{3}{2}}} & \text{for}\: e = 0 \\\frac{\operatorname{asinh}{\left(\frac{\sqrt{d}}{\sqrt{e} x} \right)}}{\sqrt{d} e} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{x^{2}}{2 d^{\frac{3}{2}}} & \text{for}\: e = 0 \\- \frac{1}{e \sqrt{d + e x^{2}}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-a/(e*sqrt(d + e*x**2)) - b*n*Piecewise((x**2/(4*d**(3/2)), Eq(e, 0)), (asinh(sqrt(d)/(sqrt(e)*x))/(sqrt(d)*e), True)) + b*Piecewise((x**2/(2*d**(3/2)), Eq(e, 0)), (-1/(e*sqrt(d + e*x**2)), True))*log(c*x**n)","A",0
290,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x**2+d)**(3/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x*(d + e*x**2)**(3/2)), x)","F",0
291,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x**2+d)**(3/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{3} \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**3*(d + e*x**2)**(3/2)), x)","F",0
292,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x**2+d)**(3/2),x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/(d + e*x**2)**(3/2), x)","F",0
293,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**2+d)**(3/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{\left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d + e*x**2)**(3/2), x)","F",0
294,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x**2+d)**(3/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \left(d + e x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*(d + e*x**2)**(3/2)), x)","F",0
295,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**6/(e*x**2+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate(x**7*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate(x**5*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,1,333,0,57.188314," ","integrate(x**3*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","a \left(\begin{cases} \frac{x^{4}}{4 d^{\frac{5}{2}}} & \text{for}\: e = 0 \\\frac{d}{3 e^{2} \left(d + e x^{2}\right)^{\frac{3}{2}}} - \frac{1}{e^{2} \sqrt{d + e x^{2}}} & \text{otherwise} \end{cases}\right) - b n \left(\begin{cases} \frac{x^{4}}{16 d^{\frac{5}{2}}} & \text{for}\: e = 0 \\\frac{2 d^{4} \sqrt{1 + \frac{e x^{2}}{d}}}{6 d^{\frac{9}{2}} e^{2} + 6 d^{\frac{7}{2}} e^{3} x^{2}} + \frac{d^{4} \log{\left(\frac{e x^{2}}{d} \right)}}{6 d^{\frac{9}{2}} e^{2} + 6 d^{\frac{7}{2}} e^{3} x^{2}} - \frac{2 d^{4} \log{\left(\sqrt{1 + \frac{e x^{2}}{d}} + 1 \right)}}{6 d^{\frac{9}{2}} e^{2} + 6 d^{\frac{7}{2}} e^{3} x^{2}} + \frac{d^{3} x^{2} \log{\left(\frac{e x^{2}}{d} \right)}}{6 d^{\frac{9}{2}} e + 6 d^{\frac{7}{2}} e^{2} x^{2}} - \frac{2 d^{3} x^{2} \log{\left(\sqrt{1 + \frac{e x^{2}}{d}} + 1 \right)}}{6 d^{\frac{9}{2}} e + 6 d^{\frac{7}{2}} e^{2} x^{2}} + \frac{\operatorname{asinh}{\left(\frac{\sqrt{d}}{\sqrt{e} x} \right)}}{\sqrt{d} e^{2}} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{x^{4}}{4 d^{\frac{5}{2}}} & \text{for}\: e = 0 \\\frac{d}{3 e^{2} \left(d + e x^{2}\right)^{\frac{3}{2}}} - \frac{1}{e^{2} \sqrt{d + e x^{2}}} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"a*Piecewise((x**4/(4*d**(5/2)), Eq(e, 0)), (d/(3*e**2*(d + e*x**2)**(3/2)) - 1/(e**2*sqrt(d + e*x**2)), True)) - b*n*Piecewise((x**4/(16*d**(5/2)), Eq(e, 0)), (2*d**4*sqrt(1 + e*x**2/d)/(6*d**(9/2)*e**2 + 6*d**(7/2)*e**3*x**2) + d**4*log(e*x**2/d)/(6*d**(9/2)*e**2 + 6*d**(7/2)*e**3*x**2) - 2*d**4*log(sqrt(1 + e*x**2/d) + 1)/(6*d**(9/2)*e**2 + 6*d**(7/2)*e**3*x**2) + d**3*x**2*log(e*x**2/d)/(6*d**(9/2)*e + 6*d**(7/2)*e**2*x**2) - 2*d**3*x**2*log(sqrt(1 + e*x**2/d) + 1)/(6*d**(9/2)*e + 6*d**(7/2)*e**2*x**2) + asinh(sqrt(d)/(sqrt(e)*x))/(sqrt(d)*e**2), True)) + b*Piecewise((x**4/(4*d**(5/2)), Eq(e, 0)), (d/(3*e**2*(d + e*x**2)**(3/2)) - 1/(e**2*sqrt(d + e*x**2)), True))*log(c*x**n)","A",0
300,1,245,0,33.603771," ","integrate(x*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","- \frac{a}{3 e \left(d + e x^{2}\right)^{\frac{3}{2}}} + \frac{2 b d^{3} n \sqrt{1 + \frac{e x^{2}}{d}}}{6 d^{\frac{9}{2}} e + 6 d^{\frac{7}{2}} e^{2} x^{2}} + \frac{b d^{3} n \log{\left(\frac{e x^{2}}{d} \right)}}{6 d^{\frac{9}{2}} e + 6 d^{\frac{7}{2}} e^{2} x^{2}} - \frac{2 b d^{3} n \log{\left(\sqrt{1 + \frac{e x^{2}}{d}} + 1 \right)}}{6 d^{\frac{9}{2}} e + 6 d^{\frac{7}{2}} e^{2} x^{2}} + \frac{b d^{2} n x^{2} \log{\left(\frac{e x^{2}}{d} \right)}}{6 d^{\frac{9}{2}} + 6 d^{\frac{7}{2}} e x^{2}} - \frac{2 b d^{2} n x^{2} \log{\left(\sqrt{1 + \frac{e x^{2}}{d}} + 1 \right)}}{6 d^{\frac{9}{2}} + 6 d^{\frac{7}{2}} e x^{2}} - \frac{b \log{\left(c x^{n} \right)}}{3 e \left(d + e x^{2}\right)^{\frac{3}{2}}}"," ",0,"-a/(3*e*(d + e*x**2)**(3/2)) + 2*b*d**3*n*sqrt(1 + e*x**2/d)/(6*d**(9/2)*e + 6*d**(7/2)*e**2*x**2) + b*d**3*n*log(e*x**2/d)/(6*d**(9/2)*e + 6*d**(7/2)*e**2*x**2) - 2*b*d**3*n*log(sqrt(1 + e*x**2/d) + 1)/(6*d**(9/2)*e + 6*d**(7/2)*e**2*x**2) + b*d**2*n*x**2*log(e*x**2/d)/(6*d**(9/2) + 6*d**(7/2)*e*x**2) - 2*b*d**2*n*x**2*log(sqrt(1 + e*x**2/d) + 1)/(6*d**(9/2) + 6*d**(7/2)*e*x**2) - b*log(c*x**n)/(3*e*(d + e*x**2)**(3/2))","B",0
301,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate(x**6*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(x**4*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(e*x**2+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)}{\sqrt{d - e x} \sqrt{d + e x}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))/(sqrt(d - e*x)*sqrt(d + e*x)), x)","F",0
310,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)}{\sqrt{d - e x} \sqrt{d + e x}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))/(sqrt(d - e*x)*sqrt(d + e*x)), x)","F",0
311,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x \sqrt{d - e x} \sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x*sqrt(d - e*x)*sqrt(d + e*x)), x)","F",0
312,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{\sqrt{d - e x} \sqrt{d + e x}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/(sqrt(d - e*x)*sqrt(d + e*x)), x)","F",0
314,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{\sqrt{d - e x} \sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(sqrt(d - e*x)*sqrt(d + e*x)), x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \sqrt{d - e x} \sqrt{d + e x}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*sqrt(d - e*x)*sqrt(d + e*x)), x)","F",0
316,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**4/(-e*x+d)**(1/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,1,29,0,2.681599," ","integrate(x*ln(x)/(x**2-1)**(1/2),x)","\sqrt{x^{2} - 1} \log{\left(x \right)} - \begin{cases} \sqrt{x^{2} - 1} - \operatorname{acos}{\left(\frac{1}{x} \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"sqrt(x**2 - 1)*log(x) - Piecewise((sqrt(x**2 - 1) - acos(1/x), (x > -1) & (x < 1)))","A",0
318,-1,0,0,0.000000," ","integrate((f*x)**m*(e*x**2+d)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,1,3850,0,64.062824," ","integrate((f*x)**m*(e*x**2+d)**2*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{- \frac{a d^{2}}{4 x^{4}} - \frac{a d e}{x^{2}} + a e^{2} \log{\left(x \right)} + b d^{2} \left(- \frac{n}{16 x^{4}} - \frac{\log{\left(c x^{n} \right)}}{4 x^{4}}\right) + 2 b d e \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) - b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)}{f^{5}} & \text{for}\: m = -5 \\\frac{- \frac{a d^{2}}{2 x^{2}} + 2 a d e \log{\left(x \right)} + \frac{a e^{2} x^{2}}{2} - \frac{b d^{2} n \log{\left(x \right)}}{2 x^{2}} - \frac{b d^{2} n}{4 x^{2}} - \frac{b d^{2} \log{\left(c \right)}}{2 x^{2}} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{2} n x^{2}}{4} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2}}{f^{3}} & \text{for}\: m = -3 \\\frac{a d^{2} \log{\left(x \right)} + a d e x^{2} + \frac{a e^{2} x^{4}}{4} + \frac{b d^{2} n \log{\left(x \right)}^{2}}{2} + b d^{2} \log{\left(c \right)} \log{\left(x \right)} + b d e n x^{2} \log{\left(x \right)} - \frac{b d e n x^{2}}{2} + b d e x^{2} \log{\left(c \right)} + \frac{b e^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b e^{2} n x^{4}}{16} + \frac{b e^{2} x^{4} \log{\left(c \right)}}{4}}{f} & \text{for}\: m = -1 \\\frac{a d^{2} f^{m} m^{5} x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{17 a d^{2} f^{m} m^{4} x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{110 a d^{2} f^{m} m^{3} x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{334 a d^{2} f^{m} m^{2} x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{465 a d^{2} f^{m} m x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{225 a d^{2} f^{m} x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{2 a d e f^{m} m^{5} x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{30 a d e f^{m} m^{4} x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{164 a d e f^{m} m^{3} x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{396 a d e f^{m} m^{2} x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{410 a d e f^{m} m x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{150 a d e f^{m} x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{a e^{2} f^{m} m^{5} x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{13 a e^{2} f^{m} m^{4} x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{62 a e^{2} f^{m} m^{3} x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{134 a e^{2} f^{m} m^{2} x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{129 a e^{2} f^{m} m x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{45 a e^{2} f^{m} x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{b d^{2} f^{m} m^{5} n x x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{b d^{2} f^{m} m^{5} x x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{17 b d^{2} f^{m} m^{4} n x x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{b d^{2} f^{m} m^{4} n x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{17 b d^{2} f^{m} m^{4} x x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{110 b d^{2} f^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{16 b d^{2} f^{m} m^{3} n x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{110 b d^{2} f^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{334 b d^{2} f^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{94 b d^{2} f^{m} m^{2} n x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{334 b d^{2} f^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{465 b d^{2} f^{m} m n x x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{240 b d^{2} f^{m} m n x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{465 b d^{2} f^{m} m x x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{225 b d^{2} f^{m} n x x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{225 b d^{2} f^{m} n x x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{225 b d^{2} f^{m} x x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{2 b d e f^{m} m^{5} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{2 b d e f^{m} m^{5} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{30 b d e f^{m} m^{4} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{2 b d e f^{m} m^{4} n x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{30 b d e f^{m} m^{4} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{164 b d e f^{m} m^{3} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{24 b d e f^{m} m^{3} n x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{164 b d e f^{m} m^{3} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{396 b d e f^{m} m^{2} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{92 b d e f^{m} m^{2} n x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{396 b d e f^{m} m^{2} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{410 b d e f^{m} m n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{120 b d e f^{m} m n x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{410 b d e f^{m} m x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{150 b d e f^{m} n x^{3} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{50 b d e f^{m} n x^{3} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{150 b d e f^{m} x^{3} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{b e^{2} f^{m} m^{5} n x^{5} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{b e^{2} f^{m} m^{5} x^{5} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{13 b e^{2} f^{m} m^{4} n x^{5} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{b e^{2} f^{m} m^{4} n x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{13 b e^{2} f^{m} m^{4} x^{5} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{62 b e^{2} f^{m} m^{3} n x^{5} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{8 b e^{2} f^{m} m^{3} n x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{62 b e^{2} f^{m} m^{3} x^{5} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{134 b e^{2} f^{m} m^{2} n x^{5} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{22 b e^{2} f^{m} m^{2} n x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{134 b e^{2} f^{m} m^{2} x^{5} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{129 b e^{2} f^{m} m n x^{5} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{24 b e^{2} f^{m} m n x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{129 b e^{2} f^{m} m x^{5} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{45 b e^{2} f^{m} n x^{5} x^{m} \log{\left(x \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} - \frac{9 b e^{2} f^{m} n x^{5} x^{m}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} + \frac{45 b e^{2} f^{m} x^{5} x^{m} \log{\left(c \right)}}{m^{6} + 18 m^{5} + 127 m^{4} + 444 m^{3} + 799 m^{2} + 690 m + 225} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*d**2/(4*x**4) - a*d*e/x**2 + a*e**2*log(x) + b*d**2*(-n/(16*x**4) - log(c*x**n)/(4*x**4)) + 2*b*d*e*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) - b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)))/f**5, Eq(m, -5)), ((-a*d**2/(2*x**2) + 2*a*d*e*log(x) + a*e**2*x**2/2 - b*d**2*n*log(x)/(2*x**2) - b*d**2*n/(4*x**2) - b*d**2*log(c)/(2*x**2) + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) + b*e**2*n*x**2*log(x)/2 - b*e**2*n*x**2/4 + b*e**2*x**2*log(c)/2)/f**3, Eq(m, -3)), ((a*d**2*log(x) + a*d*e*x**2 + a*e**2*x**4/4 + b*d**2*n*log(x)**2/2 + b*d**2*log(c)*log(x) + b*d*e*n*x**2*log(x) - b*d*e*n*x**2/2 + b*d*e*x**2*log(c) + b*e**2*n*x**4*log(x)/4 - b*e**2*n*x**4/16 + b*e**2*x**4*log(c)/4)/f, Eq(m, -1)), (a*d**2*f**m*m**5*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 17*a*d**2*f**m*m**4*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 110*a*d**2*f**m*m**3*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 334*a*d**2*f**m*m**2*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 465*a*d**2*f**m*m*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 225*a*d**2*f**m*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 2*a*d*e*f**m*m**5*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 30*a*d*e*f**m*m**4*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 164*a*d*e*f**m*m**3*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 396*a*d*e*f**m*m**2*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 410*a*d*e*f**m*m*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 150*a*d*e*f**m*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + a*e**2*f**m*m**5*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 13*a*e**2*f**m*m**4*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 62*a*e**2*f**m*m**3*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 134*a*e**2*f**m*m**2*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 129*a*e**2*f**m*m*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 45*a*e**2*f**m*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + b*d**2*f**m*m**5*n*x*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + b*d**2*f**m*m**5*x*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 17*b*d**2*f**m*m**4*n*x*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - b*d**2*f**m*m**4*n*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 17*b*d**2*f**m*m**4*x*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 110*b*d**2*f**m*m**3*n*x*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 16*b*d**2*f**m*m**3*n*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 110*b*d**2*f**m*m**3*x*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 334*b*d**2*f**m*m**2*n*x*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 94*b*d**2*f**m*m**2*n*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 334*b*d**2*f**m*m**2*x*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 465*b*d**2*f**m*m*n*x*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 240*b*d**2*f**m*m*n*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 465*b*d**2*f**m*m*x*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 225*b*d**2*f**m*n*x*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 225*b*d**2*f**m*n*x*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 225*b*d**2*f**m*x*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 2*b*d*e*f**m*m**5*n*x**3*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 2*b*d*e*f**m*m**5*x**3*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 30*b*d*e*f**m*m**4*n*x**3*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 2*b*d*e*f**m*m**4*n*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 30*b*d*e*f**m*m**4*x**3*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 164*b*d*e*f**m*m**3*n*x**3*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 24*b*d*e*f**m*m**3*n*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 164*b*d*e*f**m*m**3*x**3*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 396*b*d*e*f**m*m**2*n*x**3*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 92*b*d*e*f**m*m**2*n*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 396*b*d*e*f**m*m**2*x**3*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 410*b*d*e*f**m*m*n*x**3*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 120*b*d*e*f**m*m*n*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 410*b*d*e*f**m*m*x**3*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 150*b*d*e*f**m*n*x**3*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 50*b*d*e*f**m*n*x**3*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 150*b*d*e*f**m*x**3*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + b*e**2*f**m*m**5*n*x**5*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + b*e**2*f**m*m**5*x**5*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 13*b*e**2*f**m*m**4*n*x**5*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - b*e**2*f**m*m**4*n*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 13*b*e**2*f**m*m**4*x**5*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 62*b*e**2*f**m*m**3*n*x**5*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 8*b*e**2*f**m*m**3*n*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 62*b*e**2*f**m*m**3*x**5*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 134*b*e**2*f**m*m**2*n*x**5*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 22*b*e**2*f**m*m**2*n*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 134*b*e**2*f**m*m**2*x**5*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 129*b*e**2*f**m*m*n*x**5*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 24*b*e**2*f**m*m*n*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 129*b*e**2*f**m*m*x**5*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 45*b*e**2*f**m*n*x**5*x**m*log(x)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) - 9*b*e**2*f**m*n*x**5*x**m/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225) + 45*b*e**2*f**m*x**5*x**m*log(c)/(m**6 + 18*m**5 + 127*m**4 + 444*m**3 + 799*m**2 + 690*m + 225), True))","A",0
320,1,1261,0,15.804210," ","integrate((f*x)**m*(e*x**2+d)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{- \frac{a d}{2 x^{2}} + a e \log{\left(x \right)} + b d \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right)}{f^{3}} & \text{for}\: m = -3 \\\frac{a d \log{\left(x \right)} + \frac{a e x^{2}}{2} + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + \frac{b e n x^{2} \log{\left(x \right)}}{2} - \frac{b e n x^{2}}{4} + \frac{b e x^{2} \log{\left(c \right)}}{2}}{f} & \text{for}\: m = -1 \\\frac{a d f^{m} m^{3} x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{7 a d f^{m} m^{2} x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{15 a d f^{m} m x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{9 a d f^{m} x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{a e f^{m} m^{3} x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{5 a e f^{m} m^{2} x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{7 a e f^{m} m x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{3 a e f^{m} x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{b d f^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{b d f^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{7 b d f^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} - \frac{b d f^{m} m^{2} n x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{7 b d f^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{15 b d f^{m} m n x x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} - \frac{6 b d f^{m} m n x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{15 b d f^{m} m x x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{9 b d f^{m} n x x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} - \frac{9 b d f^{m} n x x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{9 b d f^{m} x x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{b e f^{m} m^{3} n x^{3} x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{b e f^{m} m^{3} x^{3} x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{5 b e f^{m} m^{2} n x^{3} x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} - \frac{b e f^{m} m^{2} n x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{5 b e f^{m} m^{2} x^{3} x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{7 b e f^{m} m n x^{3} x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} - \frac{2 b e f^{m} m n x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{7 b e f^{m} m x^{3} x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{3 b e f^{m} n x^{3} x^{m} \log{\left(x \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} - \frac{b e f^{m} n x^{3} x^{m}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} + \frac{3 b e f^{m} x^{3} x^{m} \log{\left(c \right)}}{m^{4} + 8 m^{3} + 22 m^{2} + 24 m + 9} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-a*d/(2*x**2) + a*e*log(x) + b*d*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)))/f**3, Eq(m, -3)), ((a*d*log(x) + a*e*x**2/2 + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x**2*log(x)/2 - b*e*n*x**2/4 + b*e*x**2*log(c)/2)/f, Eq(m, -1)), (a*d*f**m*m**3*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 7*a*d*f**m*m**2*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 15*a*d*f**m*m*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 9*a*d*f**m*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + a*e*f**m*m**3*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 5*a*e*f**m*m**2*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 7*a*e*f**m*m*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 3*a*e*f**m*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + b*d*f**m*m**3*n*x*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + b*d*f**m*m**3*x*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 7*b*d*f**m*m**2*n*x*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) - b*d*f**m*m**2*n*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 7*b*d*f**m*m**2*x*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 15*b*d*f**m*m*n*x*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) - 6*b*d*f**m*m*n*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 15*b*d*f**m*m*x*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 9*b*d*f**m*n*x*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) - 9*b*d*f**m*n*x*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 9*b*d*f**m*x*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + b*e*f**m*m**3*n*x**3*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + b*e*f**m*m**3*x**3*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 5*b*e*f**m*m**2*n*x**3*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) - b*e*f**m*m**2*n*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 5*b*e*f**m*m**2*x**3*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 7*b*e*f**m*m*n*x**3*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) - 2*b*e*f**m*m*n*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 7*b*e*f**m*m*x**3*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 3*b*e*f**m*n*x**3*x**m*log(x)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) - b*e*f**m*n*x**3*x**m/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9) + 3*b*e*f**m*x**3*x**m*log(c)/(m**4 + 8*m**3 + 22*m**2 + 24*m + 9), True))","A",0
321,1,192,0,9.890744," ","integrate((f*x)**m*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a f^{m} m x x^{m}}{m^{2} + 2 m + 1} + \frac{a f^{m} x x^{m}}{m^{2} + 2 m + 1} + \frac{b f^{m} m n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} + \frac{b f^{m} m x x^{m} \log{\left(c \right)}}{m^{2} + 2 m + 1} + \frac{b f^{m} n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} - \frac{b f^{m} n x x^{m}}{m^{2} + 2 m + 1} + \frac{b f^{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}}{f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**m*m*x*x**m/(m**2 + 2*m + 1) + a*f**m*x*x**m/(m**2 + 2*m + 1) + b*f**m*m*n*x*x**m*log(x)/(m**2 + 2*m + 1) + b*f**m*m*x*x**m*log(c)/(m**2 + 2*m + 1) + b*f**m*n*x*x**m*log(x)/(m**2 + 2*m + 1) - b*f**m*n*x*x**m/(m**2 + 2*m + 1) + b*f**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))/f, True))","A",0
322,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))/(e*x**2+d),x)","\int \frac{\left(f x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{2}}\, dx"," ",0,"Integral((f*x)**m*(a + b*log(c*x**n))/(d + e*x**2), x)","F",0
323,-1,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))/(e*x**2+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**3/(e*x**3+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/(e*x**3+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(e*x**3+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(1/(e*x**3+d)**2/(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(1/(e*x**3+d)**2/(a+b*ln(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,1,298,0,164.127542," ","integrate(x**3*(a+b*ln(c*x**n))/(d+e/x),x)","\frac{a x^{4}}{4 d} - \frac{a e x^{3}}{3 d^{2}} + \frac{a e^{2} x^{2}}{2 d^{3}} + \frac{a e^{4} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{a e^{3} x}{d^{4}} - \frac{b n x^{4}}{16 d} + \frac{b x^{4} \log{\left(c x^{n} \right)}}{4 d} + \frac{b e n x^{3}}{9 d^{2}} - \frac{b e x^{3} \log{\left(c x^{n} \right)}}{3 d^{2}} - \frac{b e^{2} n x^{2}}{4 d^{3}} + \frac{b e^{2} x^{2} \log{\left(c x^{n} \right)}}{2 d^{3}} - \frac{b e^{4} n \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{b e^{4} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{4}} + \frac{b e^{3} n x}{d^{4}} - \frac{b e^{3} x \log{\left(c x^{n} \right)}}{d^{4}}"," ",0,"a*x**4/(4*d) - a*e*x**3/(3*d**2) + a*e**2*x**2/(2*d**3) + a*e**4*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d**4 - a*e**3*x/d**4 - b*n*x**4/(16*d) + b*x**4*log(c*x**n)/(4*d) + b*e*n*x**3/(9*d**2) - b*e*x**3*log(c*x**n)/(3*d**2) - b*e**2*n*x**2/(4*d**3) + b*e**2*x**2*log(c*x**n)/(2*d**3) - b*e**4*n*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d**4 + b*e**4*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x**n)/d**4 + b*e**3*n*x/d**4 - b*e**3*x*log(c*x**n)/d**4","A",0
330,1,248,0,138.052420," ","integrate(x**2*(a+b*ln(c*x**n))/(d+e/x),x)","\frac{a x^{3}}{3 d} - \frac{a e x^{2}}{2 d^{2}} - \frac{a e^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{a e^{2} x}{d^{3}} - \frac{b n x^{3}}{9 d} + \frac{b x^{3} \log{\left(c x^{n} \right)}}{3 d} + \frac{b e n x^{2}}{4 d^{2}} - \frac{b e x^{2} \log{\left(c x^{n} \right)}}{2 d^{2}} + \frac{b e^{3} n \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b e^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{3}} - \frac{b e^{2} n x}{d^{3}} + \frac{b e^{2} x \log{\left(c x^{n} \right)}}{d^{3}}"," ",0,"a*x**3/(3*d) - a*e*x**2/(2*d**2) - a*e**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d**3 + a*e**2*x/d**3 - b*n*x**3/(9*d) + b*x**3*log(c*x**n)/(3*d) + b*e*n*x**2/(4*d**2) - b*e*x**2*log(c*x**n)/(2*d**2) + b*e**3*n*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d**3 - b*e**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x**n)/d**3 - b*e**2*n*x/d**3 + b*e**2*x*log(c*x**n)/d**3","A",0
331,1,199,0,114.154898," ","integrate(x*(a+b*ln(c*x**n))/(d+e/x),x)","\frac{a x^{2}}{2 d} + \frac{a e^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{a e x}{d^{2}} - \frac{b n x^{2}}{4 d} + \frac{b x^{2} \log{\left(c x^{n} \right)}}{2 d} - \frac{b e^{2} n \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{b e^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d^{2}} + \frac{b e n x}{d^{2}} - \frac{b e x \log{\left(c x^{n} \right)}}{d^{2}}"," ",0,"a*x**2/(2*d) + a*e**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d**2 - a*e*x/d**2 - b*n*x**2/(4*d) + b*x**2*log(c*x**n)/(2*d) - b*e**2*n*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d**2 + b*e**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x**n)/d**2 + b*e*n*x/d**2 - b*e*x*log(c*x**n)/d**2","A",0
332,1,144,0,72.457154," ","integrate((a+b*ln(c*x**n))/(d+e/x),x)","- \frac{a e \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d} + \frac{a x}{d} + \frac{b e n \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d} - \frac{b e \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{d} - \frac{b n x}{d} + \frac{b x \log{\left(c x^{n} \right)}}{d}"," ",0,"-a*e*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d + a*x/d + b*e*n*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d - b*e*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x**n)/d - b*n*x/d + b*x*log(c*x**n)/d","A",0
333,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(d+e/x)/x,x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{d x + e}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d*x + e), x)","F",0
334,1,156,0,14.688565," ","integrate((a+b*ln(c*x**n))/(d+e/x)/x**2,x)","\frac{2 a d \left(\begin{cases} - \frac{x}{e} - \frac{1}{2 d} & \text{for}\: d = 0 \\\frac{\log{\left(2 d x \right)}}{2 d} & \text{otherwise} \end{cases}\right)}{e} - \frac{2 a d \left(\begin{cases} \frac{x}{e} + \frac{1}{2 d} & \text{for}\: d = 0 \\\frac{\log{\left(2 d x + 2 e \right)}}{2 d} & \text{otherwise} \end{cases}\right)}{e} + b n \left(\begin{cases} - \frac{1}{d x} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right) - b \left(\begin{cases} \frac{1}{d x} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{x} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"2*a*d*Piecewise((-x/e - 1/(2*d), Eq(d, 0)), (log(2*d*x)/(2*d), True))/e - 2*a*d*Piecewise((x/e + 1/(2*d), Eq(d, 0)), (log(2*d*x + 2*e)/(2*d), True))/e + b*n*Piecewise((-1/(d*x), Eq(e, 0)), (Piecewise((log(d)*log(x) + polylog(2, e*exp_polar(I*pi)/(d*x)), Abs(x) < 1), (-log(d)*log(1/x) + polylog(2, e*exp_polar(I*pi)/(d*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) + polylog(2, e*exp_polar(I*pi)/(d*x)), True))/e, True)) - b*Piecewise((1/(d*x), Eq(e, 0)), (log(d + e/x)/e, True))*log(c*x**n)","C",0
335,1,197,0,64.250458," ","integrate((a+b*ln(c*x**n))/(d+e/x)/x**3,x)","\frac{a d^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{a d \log{\left(x \right)}}{e^{2}} - \frac{a}{e x} - \frac{b d^{2} n \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{2}} + \frac{b d n \log{\left(x \right)}^{2}}{2 e^{2}} - \frac{b d \log{\left(x \right)} \log{\left(c x^{n} \right)}}{e^{2}} - \frac{b n}{e x} - \frac{b \log{\left(c x^{n} \right)}}{e x}"," ",0,"a*d**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/e**2 - a*d*log(x)/e**2 - a/(e*x) - b*d**2*n*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/e**2 + b*d**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x**n)/e**2 + b*d*n*log(x)**2/(2*e**2) - b*d*log(x)*log(c*x**n)/e**2 - b*n/(e*x) - b*log(c*x**n)/(e*x)","A",0
336,1,246,0,88.474592," ","integrate((a+b*ln(c*x**n))/(d+e/x)/x**4,x)","- \frac{a d^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{a d^{2} \log{\left(x \right)}}{e^{3}} + \frac{a d}{e^{2} x} - \frac{a}{2 e x^{2}} + \frac{b d^{3} n \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{b d^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}}{e^{3}} - \frac{b d^{2} n \log{\left(x \right)}^{2}}{2 e^{3}} + \frac{b d^{2} \log{\left(x \right)} \log{\left(c x^{n} \right)}}{e^{3}} + \frac{b d n}{e^{2} x} + \frac{b d \log{\left(c x^{n} \right)}}{e^{2} x} - \frac{b n}{4 e x^{2}} - \frac{b \log{\left(c x^{n} \right)}}{2 e x^{2}}"," ",0,"-a*d**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/e**3 + a*d**2*log(x)/e**3 + a*d/(e**2*x) - a/(2*e*x**2) + b*d**3*n*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/e**3 - b*d**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x**n)/e**3 - b*d**2*n*log(x)**2/(2*e**3) + b*d**2*log(x)*log(c*x**n)/e**3 + b*d*n/(e**2*x) + b*d*log(c*x**n)/(e**2*x) - b*n/(4*e*x**2) - b*log(c*x**n)/(2*e*x**2)","A",0
337,1,280,0,161.982936," ","integrate(x**3*(a+b*ln(c*x))/(d+e/x),x)","\frac{a x^{4}}{4 d} - \frac{a e x^{3}}{3 d^{2}} + \frac{a e^{2} x^{2}}{2 d^{3}} + \frac{a e^{4} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{4}} - \frac{a e^{3} x}{d^{4}} + \frac{b x^{4} \log{\left(c x \right)}}{4 d} - \frac{b x^{4}}{16 d} - \frac{b e x^{3} \log{\left(c x \right)}}{3 d^{2}} + \frac{b e x^{3}}{9 d^{2}} + \frac{b e^{2} x^{2} \log{\left(c x \right)}}{2 d^{3}} - \frac{b e^{2} x^{2}}{4 d^{3}} - \frac{b e^{4} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{4}} + \frac{b e^{4} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}}{d^{4}} - \frac{b e^{3} x \log{\left(c x \right)}}{d^{4}} + \frac{b e^{3} x}{d^{4}}"," ",0,"a*x**4/(4*d) - a*e*x**3/(3*d**2) + a*e**2*x**2/(2*d**3) + a*e**4*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d**4 - a*e**3*x/d**4 + b*x**4*log(c*x)/(4*d) - b*x**4/(16*d) - b*e*x**3*log(c*x)/(3*d**2) + b*e*x**3/(9*d**2) + b*e**2*x**2*log(c*x)/(2*d**3) - b*e**2*x**2/(4*d**3) - b*e**4*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d**4 + b*e**4*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x)/d**4 - b*e**3*x*log(c*x)/d**4 + b*e**3*x/d**4","A",0
338,1,235,0,136.434036," ","integrate(x**2*(a+b*ln(c*x))/(d+e/x),x)","\frac{a x^{3}}{3 d} - \frac{a e x^{2}}{2 d^{2}} - \frac{a e^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} + \frac{a e^{2} x}{d^{3}} + \frac{b x^{3} \log{\left(c x \right)}}{3 d} - \frac{b x^{3}}{9 d} - \frac{b e x^{2} \log{\left(c x \right)}}{2 d^{2}} + \frac{b e x^{2}}{4 d^{2}} + \frac{b e^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{3}} - \frac{b e^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}}{d^{3}} + \frac{b e^{2} x \log{\left(c x \right)}}{d^{3}} - \frac{b e^{2} x}{d^{3}}"," ",0,"a*x**3/(3*d) - a*e*x**2/(2*d**2) - a*e**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d**3 + a*e**2*x/d**3 + b*x**3*log(c*x)/(3*d) - b*x**3/(9*d) - b*e*x**2*log(c*x)/(2*d**2) + b*e*x**2/(4*d**2) + b*e**3*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d**3 - b*e**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x)/d**3 + b*e**2*x*log(c*x)/d**3 - b*e**2*x/d**3","A",0
339,1,189,0,112.582790," ","integrate(x*(a+b*ln(c*x))/(d+e/x),x)","\frac{a x^{2}}{2 d} + \frac{a e^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} - \frac{a e x}{d^{2}} + \frac{b x^{2} \log{\left(c x \right)}}{2 d} - \frac{b x^{2}}{4 d} - \frac{b e^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d^{2}} + \frac{b e^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}}{d^{2}} - \frac{b e x \log{\left(c x \right)}}{d^{2}} + \frac{b e x}{d^{2}}"," ",0,"a*x**2/(2*d) + a*e**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d**2 - a*e*x/d**2 + b*x**2*log(c*x)/(2*d) - b*x**2/(4*d) - b*e**2*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d**2 + b*e**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x)/d**2 - b*e*x*log(c*x)/d**2 + b*e*x/d**2","A",0
340,1,138,0,71.222320," ","integrate((a+b*ln(c*x))/(d+e/x),x)","- \frac{a e \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{d} + \frac{a x}{d} + \frac{b e \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{d} - \frac{b e \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}}{d} + \frac{b x \log{\left(c x \right)}}{d} - \frac{b x}{d}"," ",0,"-a*e*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/d + a*x/d + b*e*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/d - b*e*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x)/d + b*x*log(c*x)/d - b*x/d","A",0
341,0,0,0,0.000000," ","integrate((a+b*ln(c*x))/(d+e/x)/x,x)","\int \frac{a + b \log{\left(c x \right)}}{d x + e}\, dx"," ",0,"Integral((a + b*log(c*x))/(d*x + e), x)","F",0
342,1,153,0,14.258153," ","integrate((a+b*ln(c*x))/(d+e/x)/x**2,x)","\frac{2 a d \left(\begin{cases} - \frac{x}{e} - \frac{1}{2 d} & \text{for}\: d = 0 \\\frac{\log{\left(2 d x \right)}}{2 d} & \text{otherwise} \end{cases}\right)}{e} - \frac{2 a d \left(\begin{cases} \frac{x}{e} + \frac{1}{2 d} & \text{for}\: d = 0 \\\frac{\log{\left(2 d x + 2 e \right)}}{2 d} & \text{otherwise} \end{cases}\right)}{e} + b \left(\begin{cases} - \frac{1}{d x} & \text{for}\: e = 0 \\\frac{\begin{cases} \log{\left(d \right)} \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(d \right)} \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(d \right)} + \operatorname{Li}_{2}\left(\frac{e e^{i \pi}}{d x}\right) & \text{otherwise} \end{cases}}{e} & \text{otherwise} \end{cases}\right) - b \left(\begin{cases} \frac{1}{d x} & \text{for}\: e = 0 \\\frac{\log{\left(d + \frac{e}{x} \right)}}{e} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}"," ",0,"2*a*d*Piecewise((-x/e - 1/(2*d), Eq(d, 0)), (log(2*d*x)/(2*d), True))/e - 2*a*d*Piecewise((x/e + 1/(2*d), Eq(d, 0)), (log(2*d*x + 2*e)/(2*d), True))/e + b*Piecewise((-1/(d*x), Eq(e, 0)), (Piecewise((log(d)*log(x) + polylog(2, e*exp_polar(I*pi)/(d*x)), Abs(x) < 1), (-log(d)*log(1/x) + polylog(2, e*exp_polar(I*pi)/(d*x)), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(d) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(d) + polylog(2, e*exp_polar(I*pi)/(d*x)), True))/e, True)) - b*Piecewise((1/(d*x), Eq(e, 0)), (log(d + e/x)/e, True))*log(c*x)","C",0
343,1,187,0,62.911166," ","integrate((a+b*ln(c*x))/(d+e/x)/x**3,x)","\frac{a d^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{e^{2}} - \frac{a d \log{\left(x \right)}}{e^{2}} - \frac{a}{e x} - \frac{b d^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{e^{2}} + \frac{b d^{2} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}}{e^{2}} + \frac{b d \log{\left(x \right)}^{2}}{2 e^{2}} - \frac{b d \log{\left(x \right)} \log{\left(c x \right)}}{e^{2}} - \frac{b \log{\left(c x \right)}}{e x} - \frac{b}{e x}"," ",0,"a*d**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/e**2 - a*d*log(x)/e**2 - a/(e*x) - b*d**2*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/e**2 + b*d**2*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x)/e**2 + b*d*log(x)**2/(2*e**2) - b*d*log(x)*log(c*x)/e**2 - b*log(c*x)/(e*x) - b/(e*x)","A",0
344,1,233,0,86.813880," ","integrate((a+b*ln(c*x))/(d+e/x)/x**4,x)","- \frac{a d^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right)}{e^{3}} + \frac{a d^{2} \log{\left(x \right)}}{e^{3}} + \frac{a d}{e^{2} x} - \frac{a}{2 e x^{2}} + \frac{b d^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\begin{cases} \log{\left(e \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(e \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} \log{\left(e \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(e \right)} - \operatorname{Li}_{2}\left(\frac{d x e^{i \pi}}{e}\right) & \text{otherwise} \end{cases}}{d} & \text{otherwise} \end{cases}\right)}{e^{3}} - \frac{b d^{3} \left(\begin{cases} \frac{x}{e} & \text{for}\: d = 0 \\\frac{\log{\left(d x + e \right)}}{d} & \text{otherwise} \end{cases}\right) \log{\left(c x \right)}}{e^{3}} - \frac{b d^{2} \log{\left(x \right)}^{2}}{2 e^{3}} + \frac{b d^{2} \log{\left(x \right)} \log{\left(c x \right)}}{e^{3}} + \frac{b d \log{\left(c x \right)}}{e^{2} x} + \frac{b d}{e^{2} x} - \frac{b \log{\left(c x \right)}}{2 e x^{2}} - \frac{b}{4 e x^{2}}"," ",0,"-a*d**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))/e**3 + a*d**2*log(x)/e**3 + a*d/(e**2*x) - a/(2*e*x**2) + b*d**3*Piecewise((x/e, Eq(d, 0)), (Piecewise((log(e)*log(x) - polylog(2, d*x*exp_polar(I*pi)/e), Abs(x) < 1), (-log(e)*log(1/x) - polylog(2, d*x*exp_polar(I*pi)/e), 1/Abs(x) < 1), (-meijerg(((), (1, 1)), ((0, 0), ()), x)*log(e) + meijerg(((1, 1), ()), ((), (0, 0)), x)*log(e) - polylog(2, d*x*exp_polar(I*pi)/e), True))/d, True))/e**3 - b*d**3*Piecewise((x/e, Eq(d, 0)), (log(d*x + e)/d, True))*log(c*x)/e**3 - b*d**2*log(x)**2/(2*e**3) + b*d**2*log(x)*log(c*x)/e**3 + b*d*log(c*x)/(e**2*x) + b*d/(e**2*x) - b*log(c*x)/(2*e*x**2) - b/(4*e*x**2)","A",0
345,-2,0,0,0.000000," ","integrate(x**(-1+n)*ln(e*x**n)/(1-e*x**n),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
346,-2,0,0,0.000000," ","integrate(x**(-1+n)*ln(x**n/d)/(d-x**n),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
347,-2,0,0,0.000000," ","integrate(x**(-1+n)*ln(-e*x**n/d)/(d+e*x**n),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
348,1,71,0,9.319679," ","integrate(ln(a/x)/(a*x-x**2),x)","- \left(\begin{cases} - \frac{1}{x} & \text{for}\: a = 0 \\\frac{\log{\left(\frac{a}{x} - 1 \right)}}{a} & \text{otherwise} \end{cases}\right) \log{\left(\frac{a}{x} \right)} - \begin{cases} \frac{1}{x} & \text{for}\: a = 0 \\\frac{\begin{cases} i \pi \log{\left(x \right)} + \operatorname{Li}_{2}\left(\frac{a}{x}\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} + \operatorname{Li}_{2}\left(\frac{a}{x}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} + \operatorname{Li}_{2}\left(\frac{a}{x}\right) & \text{otherwise} \end{cases}}{a} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((-1/x, Eq(a, 0)), (log(a/x - 1)/a, True))*log(a/x) - Piecewise((1/x, Eq(a, 0)), (Piecewise((I*pi*log(x) + polylog(2, a/x), Abs(x) < 1), (-I*pi*log(1/x) + polylog(2, a/x), 1/Abs(x) < 1), (-I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) + polylog(2, a/x), True))/a, True))","C",0
349,1,78,0,11.313619," ","integrate(ln(a/x**2)/(-x**3+a*x),x)","- \frac{\begin{cases} i \pi \log{\left(x \right)} + \frac{\operatorname{Li}_{2}\left(\frac{a}{x^{2}}\right)}{2} & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} + \frac{\operatorname{Li}_{2}\left(\frac{a}{x^{2}}\right)}{2} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix}  & 1, 1 \\0, 0 &  \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 &  \\ & 0, 0 \end{matrix} \middle| {x} \right)} + \frac{\operatorname{Li}_{2}\left(\frac{a}{x^{2}}\right)}{2} & \text{otherwise} \end{cases}}{a} - \frac{\log{\left(\frac{a}{x^{2}} \right)} \log{\left(\frac{a}{x^{2}} - 1 \right)}}{2 a}"," ",0,"-Piecewise((I*pi*log(x) + polylog(2, a/x**2)/2, Abs(x) < 1), (-I*pi*log(1/x) + polylog(2, a/x**2)/2, 1/Abs(x) < 1), (-I*pi*meijerg(((), (1, 1)), ((0, 0), ()), x) + I*pi*meijerg(((1, 1), ()), ((), (0, 0)), x) + polylog(2, a/x**2)/2, True))/a - log(a/x**2)*log(a/x**2 - 1)/(2*a)","C",0
350,0,0,0,0.000000," ","integrate(ln(a*x**(1-n))/(a*x-x**n),x)","\int \frac{\log{\left(a x x^{- n} \right)}}{a x - x^{n}}\, dx"," ",0,"Integral(log(a*x*x**(-n))/(a*x - x**n), x)","F",0
351,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(d+e*x**m)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(d+e*x**m)**2*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(d+e*x**m)*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,1,148,0,22.250730," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n)),x)","\begin{cases} \tilde{\infty} \left(a x + b n x \log{\left(x \right)} - b n x + b x \log{\left(c \right)}\right) & \text{for}\: f = 0 \wedge m = 0 \\\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}}{f} & \text{for}\: m = 0 \\0^{m - 1} \left(a x + b n x \log{\left(x \right)} - b n x + b x \log{\left(c \right)}\right) & \text{for}\: f = 0 \\\frac{a f^{m} x^{m}}{f m} + \frac{b f^{m} n x^{m} \log{\left(x \right)}}{f m} + \frac{b f^{m} x^{m} \log{\left(c \right)}}{f m} - \frac{b f^{m} n x^{m}}{f m^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(a*x + b*n*x*log(x) - b*n*x + b*x*log(c)), Eq(f, 0) & Eq(m, 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))/f, Eq(m, 0)), (0**(m - 1)*(a*x + b*n*x*log(x) - b*n*x + b*x*log(c)), Eq(f, 0)), (a*f**m*x**m/(f*m) + b*f**m*n*x**m*log(x)/(f*m) + b*f**m*x**m*log(c)/(f*m) - b*f**m*n*x**m/(f*m**2), True))","A",0
355,0,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))/(d+e*x**m),x)","\int \frac{\left(f x\right)^{m - 1} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{m}}\, dx"," ",0,"Integral((f*x)**(m - 1)*(a + b*log(c*x**n))/(d + e*x**m), x)","F",0
356,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))/(d+e*x**m)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))/(d+e*x**m)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))/(d+e*x**m)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(d+e*x**m)**3*(a+b*ln(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(d+e*x**m)**2*(a+b*ln(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(d+e*x**m)*(a+b*ln(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,1,490,0,68.771799," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))**2,x)","\begin{cases} \tilde{\infty} \left(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}\right) & \text{for}\: f = 0 \wedge m = 0 \\\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}}{f} & \text{for}\: m = 0 \\0^{m - 1} \left(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}\right) & \text{for}\: f = 0 \\\frac{a^{2} f^{m} x^{m}}{f m} + \frac{2 a b f^{m} n x^{m} \log{\left(x \right)}}{f m} + \frac{2 a b f^{m} x^{m} \log{\left(c \right)}}{f m} - \frac{2 a b f^{m} n x^{m}}{f m^{2}} + \frac{b^{2} f^{m} n^{2} x^{m} \log{\left(x \right)}^{2}}{f m} + \frac{2 b^{2} f^{m} n x^{m} \log{\left(c \right)} \log{\left(x \right)}}{f m} + \frac{b^{2} f^{m} x^{m} \log{\left(c \right)}^{2}}{f m} - \frac{2 b^{2} f^{m} n^{2} x^{m} \log{\left(x \right)}}{f m^{2}} - \frac{2 b^{2} f^{m} n x^{m} \log{\left(c \right)}}{f m^{2}} + \frac{2 b^{2} f^{m} n^{2} x^{m}}{f m^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(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), Eq(f, 0) & Eq(m, 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))/f, Eq(m, 0)), (0**(m - 1)*(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), Eq(f, 0)), (a**2*f**m*x**m/(f*m) + 2*a*b*f**m*n*x**m*log(x)/(f*m) + 2*a*b*f**m*x**m*log(c)/(f*m) - 2*a*b*f**m*n*x**m/(f*m**2) + b**2*f**m*n**2*x**m*log(x)**2/(f*m) + 2*b**2*f**m*n*x**m*log(c)*log(x)/(f*m) + b**2*f**m*x**m*log(c)**2/(f*m) - 2*b**2*f**m*n**2*x**m*log(x)/(f*m**2) - 2*b**2*f**m*n*x**m*log(c)/(f*m**2) + 2*b**2*f**m*n**2*x**m/(f*m**3), True))","A",0
363,0,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))**2/(d+e*x**m),x)","\int \frac{\left(f x\right)^{m - 1} \left(a + b \log{\left(c x^{n} \right)}\right)^{2}}{d + e x^{m}}\, dx"," ",0,"Integral((f*x)**(m - 1)*(a + b*log(c*x**n))**2/(d + e*x**m), x)","F",0
364,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))**2/(d+e*x**m)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))**2/(d+e*x**m)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate((f*x)**(-1+m)*(a+b*ln(c*x**n))**2/(d+e*x**m)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,1,525,0,141.141541," ","integrate(x**5*(d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{6 a d r^{2} x^{6}}{36 r^{2} + 432 r + 1296} + \frac{72 a d r x^{6}}{36 r^{2} + 432 r + 1296} + \frac{216 a d x^{6}}{36 r^{2} + 432 r + 1296} + \frac{36 a e r x^{6} x^{r}}{36 r^{2} + 432 r + 1296} + \frac{216 a e x^{6} x^{r}}{36 r^{2} + 432 r + 1296} + \frac{6 b d n r^{2} x^{6} \log{\left(x \right)}}{36 r^{2} + 432 r + 1296} - \frac{b d n r^{2} x^{6}}{36 r^{2} + 432 r + 1296} + \frac{72 b d n r x^{6} \log{\left(x \right)}}{36 r^{2} + 432 r + 1296} - \frac{12 b d n r x^{6}}{36 r^{2} + 432 r + 1296} + \frac{216 b d n x^{6} \log{\left(x \right)}}{36 r^{2} + 432 r + 1296} - \frac{36 b d n x^{6}}{36 r^{2} + 432 r + 1296} + \frac{6 b d r^{2} x^{6} \log{\left(c \right)}}{36 r^{2} + 432 r + 1296} + \frac{72 b d r x^{6} \log{\left(c \right)}}{36 r^{2} + 432 r + 1296} + \frac{216 b d x^{6} \log{\left(c \right)}}{36 r^{2} + 432 r + 1296} + \frac{36 b e n r x^{6} x^{r} \log{\left(x \right)}}{36 r^{2} + 432 r + 1296} + \frac{216 b e n x^{6} x^{r} \log{\left(x \right)}}{36 r^{2} + 432 r + 1296} - \frac{36 b e n x^{6} x^{r}}{36 r^{2} + 432 r + 1296} + \frac{36 b e r x^{6} x^{r} \log{\left(c \right)}}{36 r^{2} + 432 r + 1296} + \frac{216 b e x^{6} x^{r} \log{\left(c \right)}}{36 r^{2} + 432 r + 1296} & \text{for}\: r \neq -6 \\\frac{a d x^{6}}{6} + a e \log{\left(x \right)} + \frac{b d n x^{6} \log{\left(x \right)}}{6} - \frac{b d n x^{6}}{36} + \frac{b d x^{6} \log{\left(c \right)}}{6} + \frac{b e n \log{\left(x \right)}^{2}}{2} + b e \log{\left(c \right)} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*a*d*r**2*x**6/(36*r**2 + 432*r + 1296) + 72*a*d*r*x**6/(36*r**2 + 432*r + 1296) + 216*a*d*x**6/(36*r**2 + 432*r + 1296) + 36*a*e*r*x**6*x**r/(36*r**2 + 432*r + 1296) + 216*a*e*x**6*x**r/(36*r**2 + 432*r + 1296) + 6*b*d*n*r**2*x**6*log(x)/(36*r**2 + 432*r + 1296) - b*d*n*r**2*x**6/(36*r**2 + 432*r + 1296) + 72*b*d*n*r*x**6*log(x)/(36*r**2 + 432*r + 1296) - 12*b*d*n*r*x**6/(36*r**2 + 432*r + 1296) + 216*b*d*n*x**6*log(x)/(36*r**2 + 432*r + 1296) - 36*b*d*n*x**6/(36*r**2 + 432*r + 1296) + 6*b*d*r**2*x**6*log(c)/(36*r**2 + 432*r + 1296) + 72*b*d*r*x**6*log(c)/(36*r**2 + 432*r + 1296) + 216*b*d*x**6*log(c)/(36*r**2 + 432*r + 1296) + 36*b*e*n*r*x**6*x**r*log(x)/(36*r**2 + 432*r + 1296) + 216*b*e*n*x**6*x**r*log(x)/(36*r**2 + 432*r + 1296) - 36*b*e*n*x**6*x**r/(36*r**2 + 432*r + 1296) + 36*b*e*r*x**6*x**r*log(c)/(36*r**2 + 432*r + 1296) + 216*b*e*x**6*x**r*log(c)/(36*r**2 + 432*r + 1296), Ne(r, -6)), (a*d*x**6/6 + a*e*log(x) + b*d*n*x**6*log(x)/6 - b*d*n*x**6/36 + b*d*x**6*log(c)/6 + b*e*n*log(x)**2/2 + b*e*log(c)*log(x), True))","A",0
368,1,525,0,30.316953," ","integrate(x**3*(d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{4 a d r^{2} x^{4}}{16 r^{2} + 128 r + 256} + \frac{32 a d r x^{4}}{16 r^{2} + 128 r + 256} + \frac{64 a d x^{4}}{16 r^{2} + 128 r + 256} + \frac{16 a e r x^{4} x^{r}}{16 r^{2} + 128 r + 256} + \frac{64 a e x^{4} x^{r}}{16 r^{2} + 128 r + 256} + \frac{4 b d n r^{2} x^{4} \log{\left(x \right)}}{16 r^{2} + 128 r + 256} - \frac{b d n r^{2} x^{4}}{16 r^{2} + 128 r + 256} + \frac{32 b d n r x^{4} \log{\left(x \right)}}{16 r^{2} + 128 r + 256} - \frac{8 b d n r x^{4}}{16 r^{2} + 128 r + 256} + \frac{64 b d n x^{4} \log{\left(x \right)}}{16 r^{2} + 128 r + 256} - \frac{16 b d n x^{4}}{16 r^{2} + 128 r + 256} + \frac{4 b d r^{2} x^{4} \log{\left(c \right)}}{16 r^{2} + 128 r + 256} + \frac{32 b d r x^{4} \log{\left(c \right)}}{16 r^{2} + 128 r + 256} + \frac{64 b d x^{4} \log{\left(c \right)}}{16 r^{2} + 128 r + 256} + \frac{16 b e n r x^{4} x^{r} \log{\left(x \right)}}{16 r^{2} + 128 r + 256} + \frac{64 b e n x^{4} x^{r} \log{\left(x \right)}}{16 r^{2} + 128 r + 256} - \frac{16 b e n x^{4} x^{r}}{16 r^{2} + 128 r + 256} + \frac{16 b e r x^{4} x^{r} \log{\left(c \right)}}{16 r^{2} + 128 r + 256} + \frac{64 b e x^{4} x^{r} \log{\left(c \right)}}{16 r^{2} + 128 r + 256} & \text{for}\: r \neq -4 \\\frac{a d x^{4}}{4} + a e \log{\left(x \right)} + \frac{b d n x^{4} \log{\left(x \right)}}{4} - \frac{b d n x^{4}}{16} + \frac{b d x^{4} \log{\left(c \right)}}{4} + \frac{b e n \log{\left(x \right)}^{2}}{2} + b e \log{\left(c \right)} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a*d*r**2*x**4/(16*r**2 + 128*r + 256) + 32*a*d*r*x**4/(16*r**2 + 128*r + 256) + 64*a*d*x**4/(16*r**2 + 128*r + 256) + 16*a*e*r*x**4*x**r/(16*r**2 + 128*r + 256) + 64*a*e*x**4*x**r/(16*r**2 + 128*r + 256) + 4*b*d*n*r**2*x**4*log(x)/(16*r**2 + 128*r + 256) - b*d*n*r**2*x**4/(16*r**2 + 128*r + 256) + 32*b*d*n*r*x**4*log(x)/(16*r**2 + 128*r + 256) - 8*b*d*n*r*x**4/(16*r**2 + 128*r + 256) + 64*b*d*n*x**4*log(x)/(16*r**2 + 128*r + 256) - 16*b*d*n*x**4/(16*r**2 + 128*r + 256) + 4*b*d*r**2*x**4*log(c)/(16*r**2 + 128*r + 256) + 32*b*d*r*x**4*log(c)/(16*r**2 + 128*r + 256) + 64*b*d*x**4*log(c)/(16*r**2 + 128*r + 256) + 16*b*e*n*r*x**4*x**r*log(x)/(16*r**2 + 128*r + 256) + 64*b*e*n*x**4*x**r*log(x)/(16*r**2 + 128*r + 256) - 16*b*e*n*x**4*x**r/(16*r**2 + 128*r + 256) + 16*b*e*r*x**4*x**r*log(c)/(16*r**2 + 128*r + 256) + 64*b*e*x**4*x**r*log(c)/(16*r**2 + 128*r + 256), Ne(r, -4)), (a*d*x**4/4 + a*e*log(x) + b*d*n*x**4*log(x)/4 - b*d*n*x**4/16 + b*d*x**4*log(c)/4 + b*e*n*log(x)**2/2 + b*e*log(c)*log(x), True))","A",0
369,1,525,0,5.849465," ","integrate(x*(d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{2 a d r^{2} x^{2}}{4 r^{2} + 16 r + 16} + \frac{8 a d r x^{2}}{4 r^{2} + 16 r + 16} + \frac{8 a d x^{2}}{4 r^{2} + 16 r + 16} + \frac{4 a e r x^{2} x^{r}}{4 r^{2} + 16 r + 16} + \frac{8 a e x^{2} x^{r}}{4 r^{2} + 16 r + 16} + \frac{2 b d n r^{2} x^{2} \log{\left(x \right)}}{4 r^{2} + 16 r + 16} - \frac{b d n r^{2} x^{2}}{4 r^{2} + 16 r + 16} + \frac{8 b d n r x^{2} \log{\left(x \right)}}{4 r^{2} + 16 r + 16} - \frac{4 b d n r x^{2}}{4 r^{2} + 16 r + 16} + \frac{8 b d n x^{2} \log{\left(x \right)}}{4 r^{2} + 16 r + 16} - \frac{4 b d n x^{2}}{4 r^{2} + 16 r + 16} + \frac{2 b d r^{2} x^{2} \log{\left(c \right)}}{4 r^{2} + 16 r + 16} + \frac{8 b d r x^{2} \log{\left(c \right)}}{4 r^{2} + 16 r + 16} + \frac{8 b d x^{2} \log{\left(c \right)}}{4 r^{2} + 16 r + 16} + \frac{4 b e n r x^{2} x^{r} \log{\left(x \right)}}{4 r^{2} + 16 r + 16} + \frac{8 b e n x^{2} x^{r} \log{\left(x \right)}}{4 r^{2} + 16 r + 16} - \frac{4 b e n x^{2} x^{r}}{4 r^{2} + 16 r + 16} + \frac{4 b e r x^{2} x^{r} \log{\left(c \right)}}{4 r^{2} + 16 r + 16} + \frac{8 b e x^{2} x^{r} \log{\left(c \right)}}{4 r^{2} + 16 r + 16} & \text{for}\: r \neq -2 \\\frac{a d x^{2}}{2} + a e \log{\left(x \right)} + \frac{b d n x^{2} \log{\left(x \right)}}{2} - \frac{b d n x^{2}}{4} + \frac{b d x^{2} \log{\left(c \right)}}{2} + \frac{b e n \log{\left(x \right)}^{2}}{2} + b e \log{\left(c \right)} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*d*r**2*x**2/(4*r**2 + 16*r + 16) + 8*a*d*r*x**2/(4*r**2 + 16*r + 16) + 8*a*d*x**2/(4*r**2 + 16*r + 16) + 4*a*e*r*x**2*x**r/(4*r**2 + 16*r + 16) + 8*a*e*x**2*x**r/(4*r**2 + 16*r + 16) + 2*b*d*n*r**2*x**2*log(x)/(4*r**2 + 16*r + 16) - b*d*n*r**2*x**2/(4*r**2 + 16*r + 16) + 8*b*d*n*r*x**2*log(x)/(4*r**2 + 16*r + 16) - 4*b*d*n*r*x**2/(4*r**2 + 16*r + 16) + 8*b*d*n*x**2*log(x)/(4*r**2 + 16*r + 16) - 4*b*d*n*x**2/(4*r**2 + 16*r + 16) + 2*b*d*r**2*x**2*log(c)/(4*r**2 + 16*r + 16) + 8*b*d*r*x**2*log(c)/(4*r**2 + 16*r + 16) + 8*b*d*x**2*log(c)/(4*r**2 + 16*r + 16) + 4*b*e*n*r*x**2*x**r*log(x)/(4*r**2 + 16*r + 16) + 8*b*e*n*x**2*x**r*log(x)/(4*r**2 + 16*r + 16) - 4*b*e*n*x**2*x**r/(4*r**2 + 16*r + 16) + 4*b*e*r*x**2*x**r*log(c)/(4*r**2 + 16*r + 16) + 8*b*e*x**2*x**r*log(c)/(4*r**2 + 16*r + 16), Ne(r, -2)), (a*d*x**2/2 + a*e*log(x) + b*d*n*x**2*log(x)/2 - b*d*n*x**2/4 + b*d*x**2*log(c)/2 + b*e*n*log(x)**2/2 + b*e*log(c)*log(x), True))","A",0
370,1,112,0,9.855113," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x,x)","\begin{cases} a d \log{\left(x \right)} + \frac{a e x^{r}}{r} + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + \frac{b e n x^{r} \log{\left(x \right)}}{r} - \frac{b e n x^{r}}{r^{2}} + \frac{b e x^{r} \log{\left(c \right)}}{r} & \text{for}\: r \neq 0 \\\left(d + e\right) \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*log(x) + a*e*x**r/r + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x**r*log(x)/r - b*e*n*x**r/r**2 + b*e*x**r*log(c)/r, Ne(r, 0)), ((d + e)*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)), True))","A",0
371,1,644,0,8.938955," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x**3,x)","\begin{cases} - \frac{2 a d r^{2}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{8 a d r}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{8 a d}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{4 a e r x^{r}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{8 a e x^{r}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{2 b d n r^{2} \log{\left(x \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{b d n r^{2}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{8 b d n r \log{\left(x \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{4 b d n r}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{8 b d n \log{\left(x \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{4 b d n}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{2 b d r^{2} \log{\left(c \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{8 b d r \log{\left(c \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{8 b d \log{\left(c \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{4 b e n r x^{r} \log{\left(x \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{8 b e n x^{r} \log{\left(x \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{4 b e n x^{r}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} + \frac{4 b e r x^{r} \log{\left(c \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} - \frac{8 b e x^{r} \log{\left(c \right)}}{4 r^{2} x^{2} - 16 r x^{2} + 16 x^{2}} & \text{for}\: r \neq 2 \\- \frac{a d}{2 x^{2}} + a e \log{\left(x \right)} + b d \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a*d*r**2/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 8*a*d*r/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 8*a*d/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 4*a*e*r*x**r/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 8*a*e*x**r/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 2*b*d*n*r**2*log(x)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - b*d*n*r**2/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 8*b*d*n*r*log(x)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 4*b*d*n*r/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 8*b*d*n*log(x)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 4*b*d*n/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 2*b*d*r**2*log(c)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 8*b*d*r*log(c)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 8*b*d*log(c)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 4*b*e*n*r*x**r*log(x)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 8*b*e*n*x**r*log(x)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 4*b*e*n*x**r/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) + 4*b*e*r*x**r*log(c)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2) - 8*b*e*x**r*log(c)/(4*r**2*x**2 - 16*r*x**2 + 16*x**2), Ne(r, 2)), (-a*d/(2*x**2) + a*e*log(x) + b*d*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), True))","A",0
372,1,644,0,27.558994," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x**5,x)","\begin{cases} - \frac{4 a d r^{2}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{32 a d r}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{64 a d}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{16 a e r x^{r}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{64 a e x^{r}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{4 b d n r^{2} \log{\left(x \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{b d n r^{2}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{32 b d n r \log{\left(x \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{8 b d n r}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{64 b d n \log{\left(x \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{16 b d n}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{4 b d r^{2} \log{\left(c \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{32 b d r \log{\left(c \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{64 b d \log{\left(c \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{16 b e n r x^{r} \log{\left(x \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{64 b e n x^{r} \log{\left(x \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{16 b e n x^{r}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} + \frac{16 b e r x^{r} \log{\left(c \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} - \frac{64 b e x^{r} \log{\left(c \right)}}{16 r^{2} x^{4} - 128 r x^{4} + 256 x^{4}} & \text{for}\: r \neq 4 \\- \frac{a d}{4 x^{4}} + a e \log{\left(x \right)} + b d \left(- \frac{n}{16 x^{4}} - \frac{\log{\left(c x^{n} \right)}}{4 x^{4}}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a*d*r**2/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 32*a*d*r/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 64*a*d/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 16*a*e*r*x**r/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 64*a*e*x**r/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 4*b*d*n*r**2*log(x)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - b*d*n*r**2/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 32*b*d*n*r*log(x)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 8*b*d*n*r/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 64*b*d*n*log(x)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 16*b*d*n/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 4*b*d*r**2*log(c)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 32*b*d*r*log(c)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 64*b*d*log(c)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 16*b*e*n*r*x**r*log(x)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 64*b*e*n*x**r*log(x)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 16*b*e*n*x**r/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) + 16*b*e*r*x**r*log(c)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4) - 64*b*e*x**r*log(c)/(16*r**2*x**4 - 128*r*x**4 + 256*x**4), Ne(r, 4)), (-a*d/(4*x**4) + a*e*log(x) + b*d*(-n/(16*x**4) - log(c*x**n)/(4*x**4)) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), True))","A",0
373,1,525,0,69.726406," ","integrate(x**4*(d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{5 a d r^{2} x^{5}}{25 r^{2} + 250 r + 625} + \frac{50 a d r x^{5}}{25 r^{2} + 250 r + 625} + \frac{125 a d x^{5}}{25 r^{2} + 250 r + 625} + \frac{25 a e r x^{5} x^{r}}{25 r^{2} + 250 r + 625} + \frac{125 a e x^{5} x^{r}}{25 r^{2} + 250 r + 625} + \frac{5 b d n r^{2} x^{5} \log{\left(x \right)}}{25 r^{2} + 250 r + 625} - \frac{b d n r^{2} x^{5}}{25 r^{2} + 250 r + 625} + \frac{50 b d n r x^{5} \log{\left(x \right)}}{25 r^{2} + 250 r + 625} - \frac{10 b d n r x^{5}}{25 r^{2} + 250 r + 625} + \frac{125 b d n x^{5} \log{\left(x \right)}}{25 r^{2} + 250 r + 625} - \frac{25 b d n x^{5}}{25 r^{2} + 250 r + 625} + \frac{5 b d r^{2} x^{5} \log{\left(c \right)}}{25 r^{2} + 250 r + 625} + \frac{50 b d r x^{5} \log{\left(c \right)}}{25 r^{2} + 250 r + 625} + \frac{125 b d x^{5} \log{\left(c \right)}}{25 r^{2} + 250 r + 625} + \frac{25 b e n r x^{5} x^{r} \log{\left(x \right)}}{25 r^{2} + 250 r + 625} + \frac{125 b e n x^{5} x^{r} \log{\left(x \right)}}{25 r^{2} + 250 r + 625} - \frac{25 b e n x^{5} x^{r}}{25 r^{2} + 250 r + 625} + \frac{25 b e r x^{5} x^{r} \log{\left(c \right)}}{25 r^{2} + 250 r + 625} + \frac{125 b e x^{5} x^{r} \log{\left(c \right)}}{25 r^{2} + 250 r + 625} & \text{for}\: r \neq -5 \\\frac{a d x^{5}}{5} + a e \log{\left(x \right)} + \frac{b d n x^{5} \log{\left(x \right)}}{5} - \frac{b d n x^{5}}{25} + \frac{b d x^{5} \log{\left(c \right)}}{5} + \frac{b e n \log{\left(x \right)}^{2}}{2} + b e \log{\left(c \right)} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a*d*r**2*x**5/(25*r**2 + 250*r + 625) + 50*a*d*r*x**5/(25*r**2 + 250*r + 625) + 125*a*d*x**5/(25*r**2 + 250*r + 625) + 25*a*e*r*x**5*x**r/(25*r**2 + 250*r + 625) + 125*a*e*x**5*x**r/(25*r**2 + 250*r + 625) + 5*b*d*n*r**2*x**5*log(x)/(25*r**2 + 250*r + 625) - b*d*n*r**2*x**5/(25*r**2 + 250*r + 625) + 50*b*d*n*r*x**5*log(x)/(25*r**2 + 250*r + 625) - 10*b*d*n*r*x**5/(25*r**2 + 250*r + 625) + 125*b*d*n*x**5*log(x)/(25*r**2 + 250*r + 625) - 25*b*d*n*x**5/(25*r**2 + 250*r + 625) + 5*b*d*r**2*x**5*log(c)/(25*r**2 + 250*r + 625) + 50*b*d*r*x**5*log(c)/(25*r**2 + 250*r + 625) + 125*b*d*x**5*log(c)/(25*r**2 + 250*r + 625) + 25*b*e*n*r*x**5*x**r*log(x)/(25*r**2 + 250*r + 625) + 125*b*e*n*x**5*x**r*log(x)/(25*r**2 + 250*r + 625) - 25*b*e*n*x**5*x**r/(25*r**2 + 250*r + 625) + 25*b*e*r*x**5*x**r*log(c)/(25*r**2 + 250*r + 625) + 125*b*e*x**5*x**r*log(c)/(25*r**2 + 250*r + 625), Ne(r, -5)), (a*d*x**5/5 + a*e*log(x) + b*d*n*x**5*log(x)/5 - b*d*n*x**5/25 + b*d*x**5*log(c)/5 + b*e*n*log(x)**2/2 + b*e*log(c)*log(x), True))","A",0
374,1,525,0,13.461172," ","integrate(x**2*(d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{3 a d r^{2} x^{3}}{9 r^{2} + 54 r + 81} + \frac{18 a d r x^{3}}{9 r^{2} + 54 r + 81} + \frac{27 a d x^{3}}{9 r^{2} + 54 r + 81} + \frac{9 a e r x^{3} x^{r}}{9 r^{2} + 54 r + 81} + \frac{27 a e x^{3} x^{r}}{9 r^{2} + 54 r + 81} + \frac{3 b d n r^{2} x^{3} \log{\left(x \right)}}{9 r^{2} + 54 r + 81} - \frac{b d n r^{2} x^{3}}{9 r^{2} + 54 r + 81} + \frac{18 b d n r x^{3} \log{\left(x \right)}}{9 r^{2} + 54 r + 81} - \frac{6 b d n r x^{3}}{9 r^{2} + 54 r + 81} + \frac{27 b d n x^{3} \log{\left(x \right)}}{9 r^{2} + 54 r + 81} - \frac{9 b d n x^{3}}{9 r^{2} + 54 r + 81} + \frac{3 b d r^{2} x^{3} \log{\left(c \right)}}{9 r^{2} + 54 r + 81} + \frac{18 b d r x^{3} \log{\left(c \right)}}{9 r^{2} + 54 r + 81} + \frac{27 b d x^{3} \log{\left(c \right)}}{9 r^{2} + 54 r + 81} + \frac{9 b e n r x^{3} x^{r} \log{\left(x \right)}}{9 r^{2} + 54 r + 81} + \frac{27 b e n x^{3} x^{r} \log{\left(x \right)}}{9 r^{2} + 54 r + 81} - \frac{9 b e n x^{3} x^{r}}{9 r^{2} + 54 r + 81} + \frac{9 b e r x^{3} x^{r} \log{\left(c \right)}}{9 r^{2} + 54 r + 81} + \frac{27 b e x^{3} x^{r} \log{\left(c \right)}}{9 r^{2} + 54 r + 81} & \text{for}\: r \neq -3 \\\frac{a d x^{3}}{3} + a e \log{\left(x \right)} + \frac{b d n x^{3} \log{\left(x \right)}}{3} - \frac{b d n x^{3}}{9} + \frac{b d x^{3} \log{\left(c \right)}}{3} + \frac{b e n \log{\left(x \right)}^{2}}{2} + b e \log{\left(c \right)} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*d*r**2*x**3/(9*r**2 + 54*r + 81) + 18*a*d*r*x**3/(9*r**2 + 54*r + 81) + 27*a*d*x**3/(9*r**2 + 54*r + 81) + 9*a*e*r*x**3*x**r/(9*r**2 + 54*r + 81) + 27*a*e*x**3*x**r/(9*r**2 + 54*r + 81) + 3*b*d*n*r**2*x**3*log(x)/(9*r**2 + 54*r + 81) - b*d*n*r**2*x**3/(9*r**2 + 54*r + 81) + 18*b*d*n*r*x**3*log(x)/(9*r**2 + 54*r + 81) - 6*b*d*n*r*x**3/(9*r**2 + 54*r + 81) + 27*b*d*n*x**3*log(x)/(9*r**2 + 54*r + 81) - 9*b*d*n*x**3/(9*r**2 + 54*r + 81) + 3*b*d*r**2*x**3*log(c)/(9*r**2 + 54*r + 81) + 18*b*d*r*x**3*log(c)/(9*r**2 + 54*r + 81) + 27*b*d*x**3*log(c)/(9*r**2 + 54*r + 81) + 9*b*e*n*r*x**3*x**r*log(x)/(9*r**2 + 54*r + 81) + 27*b*e*n*x**3*x**r*log(x)/(9*r**2 + 54*r + 81) - 9*b*e*n*x**3*x**r/(9*r**2 + 54*r + 81) + 9*b*e*r*x**3*x**r*log(c)/(9*r**2 + 54*r + 81) + 27*b*e*x**3*x**r*log(c)/(9*r**2 + 54*r + 81), Ne(r, -3)), (a*d*x**3/3 + a*e*log(x) + b*d*n*x**3*log(x)/3 - b*d*n*x**3/9 + b*d*x**3*log(c)/3 + b*e*n*log(x)**2/2 + b*e*log(c)*log(x), True))","A",0
375,1,423,0,2.370169," ","integrate((d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a d r^{2} x}{r^{2} + 2 r + 1} + \frac{2 a d r x}{r^{2} + 2 r + 1} + \frac{a d x}{r^{2} + 2 r + 1} + \frac{a e r x x^{r}}{r^{2} + 2 r + 1} + \frac{a e x x^{r}}{r^{2} + 2 r + 1} + \frac{b d n r^{2} x \log{\left(x \right)}}{r^{2} + 2 r + 1} - \frac{b d n r^{2} x}{r^{2} + 2 r + 1} + \frac{2 b d n r x \log{\left(x \right)}}{r^{2} + 2 r + 1} - \frac{2 b d n r x}{r^{2} + 2 r + 1} + \frac{b d n x \log{\left(x \right)}}{r^{2} + 2 r + 1} - \frac{b d n x}{r^{2} + 2 r + 1} + \frac{b d r^{2} x \log{\left(c \right)}}{r^{2} + 2 r + 1} + \frac{2 b d r x \log{\left(c \right)}}{r^{2} + 2 r + 1} + \frac{b d x \log{\left(c \right)}}{r^{2} + 2 r + 1} + \frac{b e n r x x^{r} \log{\left(x \right)}}{r^{2} + 2 r + 1} + \frac{b e n x x^{r} \log{\left(x \right)}}{r^{2} + 2 r + 1} - \frac{b e n x x^{r}}{r^{2} + 2 r + 1} + \frac{b e r x x^{r} \log{\left(c \right)}}{r^{2} + 2 r + 1} + \frac{b e x x^{r} \log{\left(c \right)}}{r^{2} + 2 r + 1} & \text{for}\: r \neq -1 \\a d x + a e \log{\left(x \right)} + b d n x \log{\left(x \right)} - b d n x + b d x \log{\left(c \right)} + \frac{b e n \log{\left(x \right)}^{2}}{2} + b e \log{\left(c \right)} \log{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*r**2*x/(r**2 + 2*r + 1) + 2*a*d*r*x/(r**2 + 2*r + 1) + a*d*x/(r**2 + 2*r + 1) + a*e*r*x*x**r/(r**2 + 2*r + 1) + a*e*x*x**r/(r**2 + 2*r + 1) + b*d*n*r**2*x*log(x)/(r**2 + 2*r + 1) - b*d*n*r**2*x/(r**2 + 2*r + 1) + 2*b*d*n*r*x*log(x)/(r**2 + 2*r + 1) - 2*b*d*n*r*x/(r**2 + 2*r + 1) + b*d*n*x*log(x)/(r**2 + 2*r + 1) - b*d*n*x/(r**2 + 2*r + 1) + b*d*r**2*x*log(c)/(r**2 + 2*r + 1) + 2*b*d*r*x*log(c)/(r**2 + 2*r + 1) + b*d*x*log(c)/(r**2 + 2*r + 1) + b*e*n*r*x*x**r*log(x)/(r**2 + 2*r + 1) + b*e*n*x*x**r*log(x)/(r**2 + 2*r + 1) - b*e*n*x*x**r/(r**2 + 2*r + 1) + b*e*r*x*x**r*log(c)/(r**2 + 2*r + 1) + b*e*x*x**r*log(c)/(r**2 + 2*r + 1), Ne(r, -1)), (a*d*x + a*e*log(x) + b*d*n*x*log(x) - b*d*n*x + b*d*x*log(c) + b*e*n*log(x)**2/2 + b*e*log(c)*log(x), True))","A",0
376,1,449,0,6.861905," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x**2,x)","\begin{cases} - \frac{a d r^{2}}{r^{2} x - 2 r x + x} + \frac{2 a d r}{r^{2} x - 2 r x + x} - \frac{a d}{r^{2} x - 2 r x + x} + \frac{a e r x^{r}}{r^{2} x - 2 r x + x} - \frac{a e x^{r}}{r^{2} x - 2 r x + x} - \frac{b d n r^{2} \log{\left(x \right)}}{r^{2} x - 2 r x + x} - \frac{b d n r^{2}}{r^{2} x - 2 r x + x} + \frac{2 b d n r \log{\left(x \right)}}{r^{2} x - 2 r x + x} + \frac{2 b d n r}{r^{2} x - 2 r x + x} - \frac{b d n \log{\left(x \right)}}{r^{2} x - 2 r x + x} - \frac{b d n}{r^{2} x - 2 r x + x} - \frac{b d r^{2} \log{\left(c \right)}}{r^{2} x - 2 r x + x} + \frac{2 b d r \log{\left(c \right)}}{r^{2} x - 2 r x + x} - \frac{b d \log{\left(c \right)}}{r^{2} x - 2 r x + x} + \frac{b e n r x^{r} \log{\left(x \right)}}{r^{2} x - 2 r x + x} - \frac{b e n x^{r} \log{\left(x \right)}}{r^{2} x - 2 r x + x} - \frac{b e n x^{r}}{r^{2} x - 2 r x + x} + \frac{b e r x^{r} \log{\left(c \right)}}{r^{2} x - 2 r x + x} - \frac{b e x^{r} \log{\left(c \right)}}{r^{2} x - 2 r x + x} & \text{for}\: r \neq 1 \\- \frac{a d}{x} + a e \log{\left(x \right)} + b d \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d*r**2/(r**2*x - 2*r*x + x) + 2*a*d*r/(r**2*x - 2*r*x + x) - a*d/(r**2*x - 2*r*x + x) + a*e*r*x**r/(r**2*x - 2*r*x + x) - a*e*x**r/(r**2*x - 2*r*x + x) - b*d*n*r**2*log(x)/(r**2*x - 2*r*x + x) - b*d*n*r**2/(r**2*x - 2*r*x + x) + 2*b*d*n*r*log(x)/(r**2*x - 2*r*x + x) + 2*b*d*n*r/(r**2*x - 2*r*x + x) - b*d*n*log(x)/(r**2*x - 2*r*x + x) - b*d*n/(r**2*x - 2*r*x + x) - b*d*r**2*log(c)/(r**2*x - 2*r*x + x) + 2*b*d*r*log(c)/(r**2*x - 2*r*x + x) - b*d*log(c)/(r**2*x - 2*r*x + x) + b*e*n*r*x**r*log(x)/(r**2*x - 2*r*x + x) - b*e*n*x**r*log(x)/(r**2*x - 2*r*x + x) - b*e*n*x**r/(r**2*x - 2*r*x + x) + b*e*r*x**r*log(c)/(r**2*x - 2*r*x + x) - b*e*x**r*log(c)/(r**2*x - 2*r*x + x), Ne(r, 1)), (-a*d/x + a*e*log(x) + b*d*(-n/x - log(c*x**n)/x) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), True))","A",0
377,1,644,0,14.945312," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x**4,x)","\begin{cases} - \frac{3 a d r^{2}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{18 a d r}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{27 a d}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{9 a e r x^{r}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{27 a e x^{r}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{3 b d n r^{2} \log{\left(x \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{b d n r^{2}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{18 b d n r \log{\left(x \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{6 b d n r}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{27 b d n \log{\left(x \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{9 b d n}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{3 b d r^{2} \log{\left(c \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{18 b d r \log{\left(c \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{27 b d \log{\left(c \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{9 b e n r x^{r} \log{\left(x \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{27 b e n x^{r} \log{\left(x \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{9 b e n x^{r}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} + \frac{9 b e r x^{r} \log{\left(c \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} - \frac{27 b e x^{r} \log{\left(c \right)}}{9 r^{2} x^{3} - 54 r x^{3} + 81 x^{3}} & \text{for}\: r \neq 3 \\- \frac{a d}{3 x^{3}} + a e \log{\left(x \right)} + b d \left(- \frac{n}{9 x^{3}} - \frac{\log{\left(c x^{n} \right)}}{3 x^{3}}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a*d*r**2/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 18*a*d*r/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 27*a*d/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 9*a*e*r*x**r/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 27*a*e*x**r/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 3*b*d*n*r**2*log(x)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - b*d*n*r**2/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 18*b*d*n*r*log(x)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 6*b*d*n*r/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 27*b*d*n*log(x)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 9*b*d*n/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 3*b*d*r**2*log(c)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 18*b*d*r*log(c)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 27*b*d*log(c)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 9*b*e*n*r*x**r*log(x)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 27*b*e*n*x**r*log(x)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 9*b*e*n*x**r/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) + 9*b*e*r*x**r*log(c)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3) - 27*b*e*x**r*log(c)/(9*r**2*x**3 - 54*r*x**3 + 81*x**3), Ne(r, 3)), (-a*d/(3*x**3) + a*e*log(x) + b*d*(-n/(9*x**3) - log(c*x**n)/(3*x**3)) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), True))","A",0
378,1,644,0,53.332007," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x**6,x)","\begin{cases} - \frac{5 a d r^{2}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{50 a d r}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{125 a d}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{25 a e r x^{r}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{125 a e x^{r}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{5 b d n r^{2} \log{\left(x \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{b d n r^{2}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{50 b d n r \log{\left(x \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{10 b d n r}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{125 b d n \log{\left(x \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{25 b d n}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{5 b d r^{2} \log{\left(c \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{50 b d r \log{\left(c \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{125 b d \log{\left(c \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{25 b e n r x^{r} \log{\left(x \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{125 b e n x^{r} \log{\left(x \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{25 b e n x^{r}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} + \frac{25 b e r x^{r} \log{\left(c \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} - \frac{125 b e x^{r} \log{\left(c \right)}}{25 r^{2} x^{5} - 250 r x^{5} + 625 x^{5}} & \text{for}\: r \neq 5 \\- \frac{a d}{5 x^{5}} + a e \log{\left(x \right)} + b d \left(- \frac{n}{25 x^{5}} - \frac{\log{\left(c x^{n} \right)}}{5 x^{5}}\right) - b e \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a*d*r**2/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 50*a*d*r/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 125*a*d/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 25*a*e*r*x**r/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 125*a*e*x**r/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 5*b*d*n*r**2*log(x)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - b*d*n*r**2/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 50*b*d*n*r*log(x)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 10*b*d*n*r/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 125*b*d*n*log(x)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 25*b*d*n/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 5*b*d*r**2*log(c)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 50*b*d*r*log(c)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 125*b*d*log(c)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 25*b*e*n*r*x**r*log(x)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 125*b*e*n*x**r*log(x)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 25*b*e*n*x**r/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) + 25*b*e*r*x**r*log(c)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5) - 125*b*e*x**r*log(c)/(25*r**2*x**5 - 250*r*x**5 + 625*x**5), Ne(r, 5)), (-a*d/(5*x**5) + a*e*log(x) + b*d*(-n/(25*x**5) - log(c*x**n)/(5*x**5)) - b*e*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), True))","A",0
379,-1,0,0,0.000000," ","integrate(x**5*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,1,2162,0,116.276485," ","integrate(x**3*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a d^{2} x^{4}}{4} + 2 a d e \log{\left(x \right)} - \frac{a e^{2}}{4 x^{4}} + \frac{b d^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b d^{2} n x^{4}}{16} + \frac{b d^{2} x^{4} \log{\left(c \right)}}{4} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} - \frac{b e^{2} n \log{\left(x \right)}}{4 x^{4}} - \frac{b e^{2} n}{16 x^{4}} - \frac{b e^{2} \log{\left(c \right)}}{4 x^{4}} & \text{for}\: r = -4 \\\frac{a d^{2} x^{4}}{4} + a d e x^{2} + a e^{2} \log{\left(x \right)} + \frac{b d^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b d^{2} n x^{4}}{16} + \frac{b d^{2} x^{4} \log{\left(c \right)}}{4} + b d e n x^{2} \log{\left(x \right)} - \frac{b d e n x^{2}}{2} + b d e x^{2} \log{\left(c \right)} + \frac{b e^{2} n \log{\left(x \right)}^{2}}{2} + b e^{2} \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: r = -2 \\\frac{4 a d^{2} r^{4} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{48 a d^{2} r^{3} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{208 a d^{2} r^{2} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{384 a d^{2} r x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 a d^{2} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{32 a d e r^{3} x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 a d e r^{2} x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{640 a d e r x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{512 a d e x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{8 a e^{2} r^{3} x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{80 a e^{2} r^{2} x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 a e^{2} r x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 a e^{2} x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{4 b d^{2} n r^{4} x^{4} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{b d^{2} n r^{4} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{48 b d^{2} n r^{3} x^{4} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{12 b d^{2} n r^{3} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{208 b d^{2} n r^{2} x^{4} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{52 b d^{2} n r^{2} x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{384 b d^{2} n r x^{4} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{96 b d^{2} n r x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b d^{2} n x^{4} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{64 b d^{2} n x^{4}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{4 b d^{2} r^{4} x^{4} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{48 b d^{2} r^{3} x^{4} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{208 b d^{2} r^{2} x^{4} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{384 b d^{2} r x^{4} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b d^{2} x^{4} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{32 b d e n r^{3} x^{4} x^{r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b d e n r^{2} x^{4} x^{r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{32 b d e n r^{2} x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{640 b d e n r x^{4} x^{r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{128 b d e n r x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{512 b d e n x^{4} x^{r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{128 b d e n x^{4} x^{r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{32 b d e r^{3} x^{4} x^{r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b d e r^{2} x^{4} x^{r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{640 b d e r x^{4} x^{r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{512 b d e x^{4} x^{r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{8 b e^{2} n r^{3} x^{4} x^{2 r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{80 b e^{2} n r^{2} x^{4} x^{2 r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{4 b e^{2} n r^{2} x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b e^{2} n r x^{4} x^{2 r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{32 b e^{2} n r x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b e^{2} n x^{4} x^{2 r} \log{\left(x \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} - \frac{64 b e^{2} n x^{4} x^{2 r}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{8 b e^{2} r^{3} x^{4} x^{2 r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{80 b e^{2} r^{2} x^{4} x^{2 r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b e^{2} r x^{4} x^{2 r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} + \frac{256 b e^{2} x^{4} x^{2 r} \log{\left(c \right)}}{16 r^{4} + 192 r^{3} + 832 r^{2} + 1536 r + 1024} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x**4/4 + 2*a*d*e*log(x) - a*e**2/(4*x**4) + b*d**2*n*x**4*log(x)/4 - b*d**2*n*x**4/16 + b*d**2*x**4*log(c)/4 + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) - b*e**2*n*log(x)/(4*x**4) - b*e**2*n/(16*x**4) - b*e**2*log(c)/(4*x**4), Eq(r, -4)), (a*d**2*x**4/4 + a*d*e*x**2 + a*e**2*log(x) + b*d**2*n*x**4*log(x)/4 - b*d**2*n*x**4/16 + b*d**2*x**4*log(c)/4 + b*d*e*n*x**2*log(x) - b*d*e*n*x**2/2 + b*d*e*x**2*log(c) + b*e**2*n*log(x)**2/2 + b*e**2*log(c)*log(x), Eq(r, -2)), (4*a*d**2*r**4*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 48*a*d**2*r**3*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 208*a*d**2*r**2*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 384*a*d**2*r*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*a*d**2*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 32*a*d*e*r**3*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*a*d*e*r**2*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 640*a*d*e*r*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 512*a*d*e*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 8*a*e**2*r**3*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 80*a*e**2*r**2*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*a*e**2*r*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*a*e**2*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 4*b*d**2*n*r**4*x**4*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - b*d**2*n*r**4*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 48*b*d**2*n*r**3*x**4*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 12*b*d**2*n*r**3*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 208*b*d**2*n*r**2*x**4*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 52*b*d**2*n*r**2*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 384*b*d**2*n*r*x**4*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 96*b*d**2*n*r*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*d**2*n*x**4*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 64*b*d**2*n*x**4/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 4*b*d**2*r**4*x**4*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 48*b*d**2*r**3*x**4*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 208*b*d**2*r**2*x**4*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 384*b*d**2*r*x**4*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*d**2*x**4*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 32*b*d*e*n*r**3*x**4*x**r*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*d*e*n*r**2*x**4*x**r*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 32*b*d*e*n*r**2*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 640*b*d*e*n*r*x**4*x**r*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 128*b*d*e*n*r*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 512*b*d*e*n*x**4*x**r*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 128*b*d*e*n*x**4*x**r/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 32*b*d*e*r**3*x**4*x**r*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*d*e*r**2*x**4*x**r*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 640*b*d*e*r*x**4*x**r*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 512*b*d*e*x**4*x**r*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 8*b*e**2*n*r**3*x**4*x**(2*r)*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 80*b*e**2*n*r**2*x**4*x**(2*r)*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 4*b*e**2*n*r**2*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*e**2*n*r*x**4*x**(2*r)*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 32*b*e**2*n*r*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*e**2*n*x**4*x**(2*r)*log(x)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) - 64*b*e**2*n*x**4*x**(2*r)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 8*b*e**2*r**3*x**4*x**(2*r)*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 80*b*e**2*r**2*x**4*x**(2*r)*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*e**2*r*x**4*x**(2*r)*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024) + 256*b*e**2*x**4*x**(2*r)*log(c)/(16*r**4 + 192*r**3 + 832*r**2 + 1536*r + 1024), True))","A",0
381,1,2159,0,18.567863," ","integrate(x*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a d^{2} x^{2}}{2} + 2 a d e \log{\left(x \right)} - \frac{a e^{2}}{2 x^{2}} + \frac{b d^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b d^{2} n x^{2}}{4} + \frac{b d^{2} x^{2} \log{\left(c \right)}}{2} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} - \frac{b e^{2} n \log{\left(x \right)}}{2 x^{2}} - \frac{b e^{2} n}{4 x^{2}} - \frac{b e^{2} \log{\left(c \right)}}{2 x^{2}} & \text{for}\: r = -2 \\\frac{a d^{2} x^{2}}{2} + 2 a d e x + a e^{2} \log{\left(x \right)} + \frac{b d^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b d^{2} n x^{2}}{4} + \frac{b d^{2} x^{2} \log{\left(c \right)}}{2} + 2 b d e n x \log{\left(x \right)} - 2 b d e n x + 2 b d e x \log{\left(c \right)} + \frac{b e^{2} n \log{\left(x \right)}^{2}}{2} + b e^{2} \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: r = -1 \\\frac{2 a d^{2} r^{4} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{12 a d^{2} r^{3} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{26 a d^{2} r^{2} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{24 a d^{2} r x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 a d^{2} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 a d e r^{3} x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{32 a d e r^{2} x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{40 a d e r x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{16 a d e x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{2 a e^{2} r^{3} x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{10 a e^{2} r^{2} x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{16 a e^{2} r x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 a e^{2} x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{2 b d^{2} n r^{4} x^{2} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{b d^{2} n r^{4} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{12 b d^{2} n r^{3} x^{2} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{6 b d^{2} n r^{3} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{26 b d^{2} n r^{2} x^{2} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{13 b d^{2} n r^{2} x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{24 b d^{2} n r x^{2} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{12 b d^{2} n r x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 b d^{2} n x^{2} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{4 b d^{2} n x^{2}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{2 b d^{2} r^{4} x^{2} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{12 b d^{2} r^{3} x^{2} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{26 b d^{2} r^{2} x^{2} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{24 b d^{2} r x^{2} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 b d^{2} x^{2} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 b d e n r^{3} x^{2} x^{r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{32 b d e n r^{2} x^{2} x^{r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{8 b d e n r^{2} x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{40 b d e n r x^{2} x^{r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{16 b d e n r x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{16 b d e n x^{2} x^{r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{8 b d e n x^{2} x^{r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 b d e r^{3} x^{2} x^{r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{32 b d e r^{2} x^{2} x^{r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{40 b d e r x^{2} x^{r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{16 b d e x^{2} x^{r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{2 b e^{2} n r^{3} x^{2} x^{2 r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{10 b e^{2} n r^{2} x^{2} x^{2 r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{b e^{2} n r^{2} x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{16 b e^{2} n r x^{2} x^{2 r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{4 b e^{2} n r x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 b e^{2} n x^{2} x^{2 r} \log{\left(x \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} - \frac{4 b e^{2} n x^{2} x^{2 r}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{2 b e^{2} r^{3} x^{2} x^{2 r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{10 b e^{2} r^{2} x^{2} x^{2 r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{16 b e^{2} r x^{2} x^{2 r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} + \frac{8 b e^{2} x^{2} x^{2 r} \log{\left(c \right)}}{4 r^{4} + 24 r^{3} + 52 r^{2} + 48 r + 16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x**2/2 + 2*a*d*e*log(x) - a*e**2/(2*x**2) + b*d**2*n*x**2*log(x)/2 - b*d**2*n*x**2/4 + b*d**2*x**2*log(c)/2 + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) - b*e**2*n*log(x)/(2*x**2) - b*e**2*n/(4*x**2) - b*e**2*log(c)/(2*x**2), Eq(r, -2)), (a*d**2*x**2/2 + 2*a*d*e*x + a*e**2*log(x) + b*d**2*n*x**2*log(x)/2 - b*d**2*n*x**2/4 + b*d**2*x**2*log(c)/2 + 2*b*d*e*n*x*log(x) - 2*b*d*e*n*x + 2*b*d*e*x*log(c) + b*e**2*n*log(x)**2/2 + b*e**2*log(c)*log(x), Eq(r, -1)), (2*a*d**2*r**4*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 12*a*d**2*r**3*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 26*a*d**2*r**2*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 24*a*d**2*r*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*a*d**2*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*a*d*e*r**3*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 32*a*d*e*r**2*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 40*a*d*e*r*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 16*a*d*e*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 2*a*e**2*r**3*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 10*a*e**2*r**2*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 16*a*e**2*r*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*a*e**2*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 2*b*d**2*n*r**4*x**2*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - b*d**2*n*r**4*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 12*b*d**2*n*r**3*x**2*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 6*b*d**2*n*r**3*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 26*b*d**2*n*r**2*x**2*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 13*b*d**2*n*r**2*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 24*b*d**2*n*r*x**2*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 12*b*d**2*n*r*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*b*d**2*n*x**2*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 4*b*d**2*n*x**2/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 2*b*d**2*r**4*x**2*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 12*b*d**2*r**3*x**2*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 26*b*d**2*r**2*x**2*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 24*b*d**2*r*x**2*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*b*d**2*x**2*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*b*d*e*n*r**3*x**2*x**r*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 32*b*d*e*n*r**2*x**2*x**r*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 8*b*d*e*n*r**2*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 40*b*d*e*n*r*x**2*x**r*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 16*b*d*e*n*r*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 16*b*d*e*n*x**2*x**r*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 8*b*d*e*n*x**2*x**r/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*b*d*e*r**3*x**2*x**r*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 32*b*d*e*r**2*x**2*x**r*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 40*b*d*e*r*x**2*x**r*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 16*b*d*e*x**2*x**r*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 2*b*e**2*n*r**3*x**2*x**(2*r)*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 10*b*e**2*n*r**2*x**2*x**(2*r)*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - b*e**2*n*r**2*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 16*b*e**2*n*r*x**2*x**(2*r)*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 4*b*e**2*n*r*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*b*e**2*n*x**2*x**(2*r)*log(x)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) - 4*b*e**2*n*x**2*x**(2*r)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 2*b*e**2*r**3*x**2*x**(2*r)*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 10*b*e**2*r**2*x**2*x**(2*r)*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 16*b*e**2*r*x**2*x**(2*r)*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16) + 8*b*e**2*x**2*x**(2*r)*log(c)/(4*r**4 + 24*r**3 + 52*r**2 + 48*r + 16), True))","A",0
382,1,199,0,13.998277," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x,x)","\begin{cases} a d^{2} \log{\left(x \right)} + \frac{2 a d e x^{r}}{r} + \frac{a e^{2} x^{2 r}}{2 r} + \frac{b d^{2} n \log{\left(x \right)}^{2}}{2} + b d^{2} \log{\left(c \right)} \log{\left(x \right)} + \frac{2 b d e n x^{r} \log{\left(x \right)}}{r} - \frac{2 b d e n x^{r}}{r^{2}} + \frac{2 b d e x^{r} \log{\left(c \right)}}{r} + \frac{b e^{2} n x^{2 r} \log{\left(x \right)}}{2 r} - \frac{b e^{2} n x^{2 r}}{4 r^{2}} + \frac{b e^{2} x^{2 r} \log{\left(c \right)}}{2 r} & \text{for}\: r \neq 0 \\\left(d + e\right)^{2} \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*log(x) + 2*a*d*e*x**r/r + a*e**2*x**(2*r)/(2*r) + b*d**2*n*log(x)**2/2 + b*d**2*log(c)*log(x) + 2*b*d*e*n*x**r*log(x)/r - 2*b*d*e*n*x**r/r**2 + 2*b*d*e*x**r*log(c)/r + b*e**2*n*x**(2*r)*log(x)/(2*r) - b*e**2*n*x**(2*r)/(4*r**2) + b*e**2*x**(2*r)*log(c)/(2*r), Ne(r, 0)), ((d + e)**2*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)), True))","A",0
383,1,2807,0,15.654723," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x**3,x)","\begin{cases} - \frac{a d^{2}}{2 x^{2}} - \frac{2 a d e}{x} + a e^{2} \log{\left(x \right)} + b d^{2} \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) + 2 b d e \left(- \frac{n}{x} - \frac{\log{\left(c x^{n} \right)}}{x}\right) - b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{for}\: r = 1 \\- \frac{a d^{2}}{2 x^{2}} + 2 a d e \log{\left(x \right)} + \frac{a e^{2} x^{2}}{2} - \frac{b d^{2} n \log{\left(x \right)}}{2 x^{2}} - \frac{b d^{2} n}{4 x^{2}} - \frac{b d^{2} \log{\left(c \right)}}{2 x^{2}} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} + \frac{b e^{2} n x^{2} \log{\left(x \right)}}{2} - \frac{b e^{2} n x^{2}}{4} + \frac{b e^{2} x^{2} \log{\left(c \right)}}{2} & \text{for}\: r = 2 \\- \frac{2 a d^{2} r^{4}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{12 a d^{2} r^{3}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{26 a d^{2} r^{2}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{24 a d^{2} r}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 a d^{2}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{8 a d e r^{3} x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{32 a d e r^{2} x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{40 a d e r x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{16 a d e x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{2 a e^{2} r^{3} x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{10 a e^{2} r^{2} x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{16 a e^{2} r x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 a e^{2} x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{2 b d^{2} n r^{4} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{b d^{2} n r^{4}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{12 b d^{2} n r^{3} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{6 b d^{2} n r^{3}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{26 b d^{2} n r^{2} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{13 b d^{2} n r^{2}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{24 b d^{2} n r \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{12 b d^{2} n r}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 b d^{2} n \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{4 b d^{2} n}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{2 b d^{2} r^{4} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{12 b d^{2} r^{3} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{26 b d^{2} r^{2} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{24 b d^{2} r \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 b d^{2} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{8 b d e n r^{3} x^{r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{32 b d e n r^{2} x^{r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 b d e n r^{2} x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{40 b d e n r x^{r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{16 b d e n r x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{16 b d e n x^{r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 b d e n x^{r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{8 b d e r^{3} x^{r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{32 b d e r^{2} x^{r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{40 b d e r x^{r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{16 b d e x^{r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{2 b e^{2} n r^{3} x^{2 r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{10 b e^{2} n r^{2} x^{2 r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{b e^{2} n r^{2} x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{16 b e^{2} n r x^{2 r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{4 b e^{2} n r x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 b e^{2} n x^{2 r} \log{\left(x \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{4 b e^{2} n x^{2 r}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{2 b e^{2} r^{3} x^{2 r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{10 b e^{2} r^{2} x^{2 r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} + \frac{16 b e^{2} r x^{2 r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} - \frac{8 b e^{2} x^{2 r} \log{\left(c \right)}}{4 r^{4} x^{2} - 24 r^{3} x^{2} + 52 r^{2} x^{2} - 48 r x^{2} + 16 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2/(2*x**2) - 2*a*d*e/x + a*e**2*log(x) + b*d**2*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) + 2*b*d*e*(-n/x - log(c*x**n)/x) - b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), Eq(r, 1)), (-a*d**2/(2*x**2) + 2*a*d*e*log(x) + a*e**2*x**2/2 - b*d**2*n*log(x)/(2*x**2) - b*d**2*n/(4*x**2) - b*d**2*log(c)/(2*x**2) + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) + b*e**2*n*x**2*log(x)/2 - b*e**2*n*x**2/4 + b*e**2*x**2*log(c)/2, Eq(r, 2)), (-2*a*d**2*r**4/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 12*a*d**2*r**3/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 26*a*d**2*r**2/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 24*a*d**2*r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*a*d**2/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 8*a*d*e*r**3*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 32*a*d*e*r**2*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 40*a*d*e*r*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 16*a*d*e*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 2*a*e**2*r**3*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 10*a*e**2*r**2*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 16*a*e**2*r*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*a*e**2*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 2*b*d**2*n*r**4*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - b*d**2*n*r**4/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 12*b*d**2*n*r**3*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 6*b*d**2*n*r**3/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 26*b*d**2*n*r**2*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 13*b*d**2*n*r**2/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 24*b*d**2*n*r*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 12*b*d**2*n*r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*b*d**2*n*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 4*b*d**2*n/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 2*b*d**2*r**4*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 12*b*d**2*r**3*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 26*b*d**2*r**2*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 24*b*d**2*r*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*b*d**2*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 8*b*d*e*n*r**3*x**r*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 32*b*d*e*n*r**2*x**r*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*b*d*e*n*r**2*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 40*b*d*e*n*r*x**r*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 16*b*d*e*n*r*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 16*b*d*e*n*x**r*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*b*d*e*n*x**r/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 8*b*d*e*r**3*x**r*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 32*b*d*e*r**2*x**r*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 40*b*d*e*r*x**r*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 16*b*d*e*x**r*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 2*b*e**2*n*r**3*x**(2*r)*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 10*b*e**2*n*r**2*x**(2*r)*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - b*e**2*n*r**2*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 16*b*e**2*n*r*x**(2*r)*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 4*b*e**2*n*r*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*b*e**2*n*x**(2*r)*log(x)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 4*b*e**2*n*x**(2*r)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 2*b*e**2*r**3*x**(2*r)*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 10*b*e**2*r**2*x**(2*r)*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) + 16*b*e**2*r*x**(2*r)*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2) - 8*b*e**2*x**(2*r)*log(c)/(4*r**4*x**2 - 24*r**3*x**2 + 52*r**2*x**2 - 48*r*x**2 + 16*x**2), True))","A",0
384,1,2815,0,49.702992," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x**5,x)","\begin{cases} - \frac{a d^{2}}{4 x^{4}} - \frac{a d e}{x^{2}} + a e^{2} \log{\left(x \right)} + b d^{2} \left(- \frac{n}{16 x^{4}} - \frac{\log{\left(c x^{n} \right)}}{4 x^{4}}\right) + 2 b d e \left(- \frac{n}{4 x^{2}} - \frac{\log{\left(c x^{n} \right)}}{2 x^{2}}\right) - b e^{2} \left(\begin{cases} - \log{\left(c \right)} \log{\left(x \right)} & \text{for}\: n = 0 \\- \frac{\log{\left(c x^{n} \right)}^{2}}{2 n} & \text{otherwise} \end{cases}\right) & \text{for}\: r = 2 \\- \frac{a d^{2}}{4 x^{4}} + 2 a d e \log{\left(x \right)} + \frac{a e^{2} x^{4}}{4} - \frac{b d^{2} n \log{\left(x \right)}}{4 x^{4}} - \frac{b d^{2} n}{16 x^{4}} - \frac{b d^{2} \log{\left(c \right)}}{4 x^{4}} + b d e n \log{\left(x \right)}^{2} + 2 b d e \log{\left(c \right)} \log{\left(x \right)} + \frac{b e^{2} n x^{4} \log{\left(x \right)}}{4} - \frac{b e^{2} n x^{4}}{16} + \frac{b e^{2} x^{4} \log{\left(c \right)}}{4} & \text{for}\: r = 4 \\- \frac{4 a d^{2} r^{4}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{48 a d^{2} r^{3}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{208 a d^{2} r^{2}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{384 a d^{2} r}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 a d^{2}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{32 a d e r^{3} x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 a d e r^{2} x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{640 a d e r x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{512 a d e x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{8 a e^{2} r^{3} x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{80 a e^{2} r^{2} x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{256 a e^{2} r x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 a e^{2} x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{4 b d^{2} n r^{4} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{b d^{2} n r^{4}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{48 b d^{2} n r^{3} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{12 b d^{2} n r^{3}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{208 b d^{2} n r^{2} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{52 b d^{2} n r^{2}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{384 b d^{2} n r \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{96 b d^{2} n r}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 b d^{2} n \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{64 b d^{2} n}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{4 b d^{2} r^{4} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{48 b d^{2} r^{3} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{208 b d^{2} r^{2} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{384 b d^{2} r \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 b d^{2} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{32 b d e n r^{3} x^{r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 b d e n r^{2} x^{r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{32 b d e n r^{2} x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{640 b d e n r x^{r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{128 b d e n r x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{512 b d e n x^{r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{128 b d e n x^{r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{32 b d e r^{3} x^{r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 b d e r^{2} x^{r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{640 b d e r x^{r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{512 b d e x^{r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{8 b e^{2} n r^{3} x^{2 r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{80 b e^{2} n r^{2} x^{2 r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{4 b e^{2} n r^{2} x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{256 b e^{2} n r x^{2 r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{32 b e^{2} n r x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 b e^{2} n x^{2 r} \log{\left(x \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{64 b e^{2} n x^{2 r}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{8 b e^{2} r^{3} x^{2 r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{80 b e^{2} r^{2} x^{2 r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} + \frac{256 b e^{2} r x^{2 r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} - \frac{256 b e^{2} x^{2 r} \log{\left(c \right)}}{16 r^{4} x^{4} - 192 r^{3} x^{4} + 832 r^{2} x^{4} - 1536 r x^{4} + 1024 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*d**2/(4*x**4) - a*d*e/x**2 + a*e**2*log(x) + b*d**2*(-n/(16*x**4) - log(c*x**n)/(4*x**4)) + 2*b*d*e*(-n/(4*x**2) - log(c*x**n)/(2*x**2)) - b*e**2*Piecewise((-log(c)*log(x), Eq(n, 0)), (-log(c*x**n)**2/(2*n), True)), Eq(r, 2)), (-a*d**2/(4*x**4) + 2*a*d*e*log(x) + a*e**2*x**4/4 - b*d**2*n*log(x)/(4*x**4) - b*d**2*n/(16*x**4) - b*d**2*log(c)/(4*x**4) + b*d*e*n*log(x)**2 + 2*b*d*e*log(c)*log(x) + b*e**2*n*x**4*log(x)/4 - b*e**2*n*x**4/16 + b*e**2*x**4*log(c)/4, Eq(r, 4)), (-4*a*d**2*r**4/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 48*a*d**2*r**3/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 208*a*d**2*r**2/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 384*a*d**2*r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*a*d**2/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 32*a*d*e*r**3*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*a*d*e*r**2*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 640*a*d*e*r*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 512*a*d*e*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 8*a*e**2*r**3*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 80*a*e**2*r**2*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 256*a*e**2*r*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*a*e**2*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 4*b*d**2*n*r**4*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - b*d**2*n*r**4/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 48*b*d**2*n*r**3*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 12*b*d**2*n*r**3/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 208*b*d**2*n*r**2*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 52*b*d**2*n*r**2/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 384*b*d**2*n*r*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 96*b*d**2*n*r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*b*d**2*n*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 64*b*d**2*n/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 4*b*d**2*r**4*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 48*b*d**2*r**3*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 208*b*d**2*r**2*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 384*b*d**2*r*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*b*d**2*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 32*b*d*e*n*r**3*x**r*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*b*d*e*n*r**2*x**r*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 32*b*d*e*n*r**2*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 640*b*d*e*n*r*x**r*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 128*b*d*e*n*r*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 512*b*d*e*n*x**r*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 128*b*d*e*n*x**r/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 32*b*d*e*r**3*x**r*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*b*d*e*r**2*x**r*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 640*b*d*e*r*x**r*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 512*b*d*e*x**r*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 8*b*e**2*n*r**3*x**(2*r)*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 80*b*e**2*n*r**2*x**(2*r)*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 4*b*e**2*n*r**2*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 256*b*e**2*n*r*x**(2*r)*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 32*b*e**2*n*r*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*b*e**2*n*x**(2*r)*log(x)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 64*b*e**2*n*x**(2*r)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 8*b*e**2*r**3*x**(2*r)*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 80*b*e**2*r**2*x**(2*r)*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) + 256*b*e**2*r*x**(2*r)*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4) - 256*b*e**2*x**(2*r)*log(c)/(16*r**4*x**4 - 192*r**3*x**4 + 832*r**2*x**4 - 1536*r*x**4 + 1024*x**4), True))","A",0
385,-1,0,0,0.000000," ","integrate(x**4*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(x**2*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,1,211,0,13.916962," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n)),x)","a d^{2} x + 2 a d e \left(\begin{cases} \frac{x^{r + 1}}{r + 1} & \text{for}\: r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{2} \left(\begin{cases} \frac{x^{2 r + 1}}{2 r + 1} & \text{for}\: 2 r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - b d^{2} n x + b d^{2} x \log{\left(c x^{n} \right)} - 2 b d e n \left(\begin{cases} \frac{\begin{cases} \frac{x x^{r}}{r + 1} & \text{for}\: r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r + 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq -1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 2 b d e \left(\begin{cases} \frac{x^{r + 1}}{r + 1} & \text{for}\: r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x x^{2 r}}{2 r + 1} & \text{for}\: r \neq - \frac{1}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r + 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq - \frac{1}{2} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{2} \left(\begin{cases} \frac{x^{2 r + 1}}{2 r + 1} & \text{for}\: 2 r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"a*d**2*x + 2*a*d*e*Piecewise((x**(r + 1)/(r + 1), Ne(r, -1)), (log(x), True)) + a*e**2*Piecewise((x**(2*r + 1)/(2*r + 1), Ne(2*r, -1)), (log(x), True)) - b*d**2*n*x + b*d**2*x*log(c*x**n) - 2*b*d*e*n*Piecewise((Piecewise((x*x**r/(r + 1), Ne(r, -1)), (log(x), True))/(r + 1), (r > -oo) & (r < oo) & Ne(r, -1)), (log(x)**2/2, True)) + 2*b*d*e*Piecewise((x**(r + 1)/(r + 1), Ne(r, -1)), (log(x), True))*log(c*x**n) - b*e**2*n*Piecewise((Piecewise((x*x**(2*r)/(2*r + 1), Ne(r, -1/2)), (log(x), True))/(2*r + 1), (r > -oo) & (r < oo) & Ne(r, -1/2)), (log(x)**2/2, True)) + b*e**2*Piecewise((x**(2*r + 1)/(2*r + 1), Ne(2*r, -1)), (log(x), True))*log(c*x**n)","A",0
388,1,204,0,36.633782," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d^{2}}{x} + 2 a d e \left(\begin{cases} \frac{x^{r}}{r x - x} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{2} \left(\begin{cases} \frac{x^{2 r}}{2 r x - x} & \text{for}\: r \neq \frac{1}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - \frac{b d^{2} n}{x} - \frac{b d^{2} \log{\left(c x^{n} \right)}}{x} - 2 b d e n \left(\begin{cases} \frac{\begin{cases} \frac{x^{r}}{r x - x} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r - 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 2 b d e \left(\begin{cases} \frac{x^{r - 1}}{r - 1} & \text{for}\: r - 2 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{2 r}}{2 r x - x} & \text{for}\: r \neq \frac{1}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r - 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq \frac{1}{2} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{2} \left(\begin{cases} \frac{x^{2 r - 1}}{2 r - 1} & \text{for}\: 2 r - 2 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-a*d**2/x + 2*a*d*e*Piecewise((x**r/(r*x - x), Ne(r, 1)), (log(x), True)) + a*e**2*Piecewise((x**(2*r)/(2*r*x - x), Ne(r, 1/2)), (log(x), True)) - b*d**2*n/x - b*d**2*log(c*x**n)/x - 2*b*d*e*n*Piecewise((Piecewise((x**r/(r*x - x), Ne(r, 1)), (log(x), True))/(r - 1), (r > -oo) & (r < oo) & Ne(r, 1)), (log(x)**2/2, True)) + 2*b*d*e*Piecewise((x**(r - 1)/(r - 1), Ne(r - 2, -1)), (log(x), True))*log(c*x**n) - b*e**2*n*Piecewise((Piecewise((x**(2*r)/(2*r*x - x), Ne(r, 1/2)), (log(x), True))/(2*r - 1), (r > -oo) & (r < oo) & Ne(r, 1/2)), (log(x)**2/2, True)) + b*e**2*Piecewise((x**(2*r - 1)/(2*r - 1), Ne(2*r - 2, -1)), (log(x), True))*log(c*x**n)","A",0
389,1,235,0,93.826971," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d^{2}}{3 x^{3}} + 2 a d e \left(\begin{cases} \frac{x^{r}}{r x^{3} - 3 x^{3}} & \text{for}\: r \neq 3 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{2} \left(\begin{cases} \frac{x^{2 r}}{2 r x^{3} - 3 x^{3}} & \text{for}\: r \neq \frac{3}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - \frac{b d^{2} n}{9 x^{3}} - \frac{b d^{2} \log{\left(c x^{n} \right)}}{3 x^{3}} - 2 b d e n \left(\begin{cases} \frac{\begin{cases} \frac{x^{r}}{r x^{3} - 3 x^{3}} & \text{for}\: r \neq 3 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r - 3} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 3 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 2 b d e \left(\begin{cases} \frac{x^{r - 3}}{r - 3} & \text{for}\: r - 4 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{2 r}}{2 r x^{3} - 3 x^{3}} & \text{for}\: r \neq \frac{3}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r - 3} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq \frac{3}{2} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{2} \left(\begin{cases} \frac{x^{2 r - 3}}{2 r - 3} & \text{for}\: 2 r - 4 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-a*d**2/(3*x**3) + 2*a*d*e*Piecewise((x**r/(r*x**3 - 3*x**3), Ne(r, 3)), (log(x), True)) + a*e**2*Piecewise((x**(2*r)/(2*r*x**3 - 3*x**3), Ne(r, 3/2)), (log(x), True)) - b*d**2*n/(9*x**3) - b*d**2*log(c*x**n)/(3*x**3) - 2*b*d*e*n*Piecewise((Piecewise((x**r/(r*x**3 - 3*x**3), Ne(r, 3)), (log(x), True))/(r - 3), (r > -oo) & (r < oo) & Ne(r, 3)), (log(x)**2/2, True)) + 2*b*d*e*Piecewise((x**(r - 3)/(r - 3), Ne(r - 4, -1)), (log(x), True))*log(c*x**n) - b*e**2*n*Piecewise((Piecewise((x**(2*r)/(2*r*x**3 - 3*x**3), Ne(r, 3/2)), (log(x), True))/(2*r - 3), (r > -oo) & (r < oo) & Ne(r, 3/2)), (log(x)**2/2, True)) + b*e**2*Piecewise((x**(2*r - 3)/(2*r - 3), Ne(2*r - 4, -1)), (log(x), True))*log(c*x**n)","A",0
390,-1,0,0,0.000000," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate(x**5*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(x**3*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(x*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,1,286,0,19.732964," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x,x)","\begin{cases} a d^{3} \log{\left(x \right)} + \frac{3 a d^{2} e x^{r}}{r} + \frac{3 a d e^{2} x^{2 r}}{2 r} + \frac{a e^{3} x^{3 r}}{3 r} + \frac{b d^{3} n \log{\left(x \right)}^{2}}{2} + b d^{3} \log{\left(c \right)} \log{\left(x \right)} + \frac{3 b d^{2} e n x^{r} \log{\left(x \right)}}{r} - \frac{3 b d^{2} e n x^{r}}{r^{2}} + \frac{3 b d^{2} e x^{r} \log{\left(c \right)}}{r} + \frac{3 b d e^{2} n x^{2 r} \log{\left(x \right)}}{2 r} - \frac{3 b d e^{2} n x^{2 r}}{4 r^{2}} + \frac{3 b d e^{2} x^{2 r} \log{\left(c \right)}}{2 r} + \frac{b e^{3} n x^{3 r} \log{\left(x \right)}}{3 r} - \frac{b e^{3} n x^{3 r}}{9 r^{2}} + \frac{b e^{3} x^{3 r} \log{\left(c \right)}}{3 r} & \text{for}\: r \neq 0 \\\left(d + e\right)^{3} \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*log(x) + 3*a*d**2*e*x**r/r + 3*a*d*e**2*x**(2*r)/(2*r) + a*e**3*x**(3*r)/(3*r) + b*d**3*n*log(x)**2/2 + b*d**3*log(c)*log(x) + 3*b*d**2*e*n*x**r*log(x)/r - 3*b*d**2*e*n*x**r/r**2 + 3*b*d**2*e*x**r*log(c)/r + 3*b*d*e**2*n*x**(2*r)*log(x)/(2*r) - 3*b*d*e**2*n*x**(2*r)/(4*r**2) + 3*b*d*e**2*x**(2*r)*log(c)/(2*r) + b*e**3*n*x**(3*r)*log(x)/(3*r) - b*e**3*n*x**(3*r)/(9*r**2) + b*e**3*x**(3*r)*log(c)/(3*r), Ne(r, 0)), ((d + e)**3*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)), True))","A",0
396,1,350,0,141.142630," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**3,x)","- \frac{a d^{3}}{2 x^{2}} + 3 a d^{2} e \left(\begin{cases} \frac{x^{r}}{r x^{2} - 2 x^{2}} & \text{for}\: r \neq 2 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 3 a d e^{2} \left(\begin{cases} \frac{x^{2 r}}{2 r x^{2} - 2 x^{2}} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{3} \left(\begin{cases} \frac{x^{3 r}}{3 r x^{2} - 2 x^{2}} & \text{for}\: r \neq \frac{2}{3} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - \frac{b d^{3} n}{4 x^{2}} - \frac{b d^{3} \log{\left(c x^{n} \right)}}{2 x^{2}} - 3 b d^{2} e n \left(\begin{cases} \frac{\begin{cases} \frac{x^{r}}{r x^{2} - 2 x^{2}} & \text{for}\: r \neq 2 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r - 2} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 2 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d^{2} e \left(\begin{cases} \frac{x^{r - 2}}{r - 2} & \text{for}\: r - 3 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - 3 b d e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{2 r}}{2 r x^{2} - 2 x^{2}} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r - 2} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d e^{2} \left(\begin{cases} \frac{x^{2 r - 2}}{2 r - 2} & \text{for}\: 2 r - 3 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{3} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{3 r}}{3 r x^{2} - 2 x^{2}} & \text{for}\: r \neq \frac{2}{3} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{3 r - 2} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq \frac{2}{3} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{3} \left(\begin{cases} \frac{x^{3 r - 2}}{3 r - 2} & \text{for}\: 3 r - 3 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-a*d**3/(2*x**2) + 3*a*d**2*e*Piecewise((x**r/(r*x**2 - 2*x**2), Ne(r, 2)), (log(x), True)) + 3*a*d*e**2*Piecewise((x**(2*r)/(2*r*x**2 - 2*x**2), Ne(r, 1)), (log(x), True)) + a*e**3*Piecewise((x**(3*r)/(3*r*x**2 - 2*x**2), Ne(r, 2/3)), (log(x), True)) - b*d**3*n/(4*x**2) - b*d**3*log(c*x**n)/(2*x**2) - 3*b*d**2*e*n*Piecewise((Piecewise((x**r/(r*x**2 - 2*x**2), Ne(r, 2)), (log(x), True))/(r - 2), (r > -oo) & (r < oo) & Ne(r, 2)), (log(x)**2/2, True)) + 3*b*d**2*e*Piecewise((x**(r - 2)/(r - 2), Ne(r - 3, -1)), (log(x), True))*log(c*x**n) - 3*b*d*e**2*n*Piecewise((Piecewise((x**(2*r)/(2*r*x**2 - 2*x**2), Ne(r, 1)), (log(x), True))/(2*r - 2), (r > -oo) & (r < oo) & Ne(r, 1)), (log(x)**2/2, True)) + 3*b*d*e**2*Piecewise((x**(2*r - 2)/(2*r - 2), Ne(2*r - 3, -1)), (log(x), True))*log(c*x**n) - b*e**3*n*Piecewise((Piecewise((x**(3*r)/(3*r*x**2 - 2*x**2), Ne(r, 2/3)), (log(x), True))/(3*r - 2), (r > -oo) & (r < oo) & Ne(r, 2/3)), (log(x)**2/2, True)) + b*e**3*Piecewise((x**(3*r - 2)/(3*r - 2), Ne(3*r - 3, -1)), (log(x), True))*log(c*x**n)","A",0
397,-1,0,0,0.000000," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate(x**4*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate(x**2*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,1,325,0,22.758474," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n)),x)","a d^{3} x + 3 a d^{2} e \left(\begin{cases} \frac{x^{r + 1}}{r + 1} & \text{for}\: r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 3 a d e^{2} \left(\begin{cases} \frac{x^{2 r + 1}}{2 r + 1} & \text{for}\: 2 r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{3} \left(\begin{cases} \frac{x^{3 r + 1}}{3 r + 1} & \text{for}\: 3 r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - b d^{3} n x + b d^{3} x \log{\left(c x^{n} \right)} - 3 b d^{2} e n \left(\begin{cases} \frac{\begin{cases} \frac{x x^{r}}{r + 1} & \text{for}\: r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r + 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq -1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d^{2} e \left(\begin{cases} \frac{x^{r + 1}}{r + 1} & \text{for}\: r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - 3 b d e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x x^{2 r}}{2 r + 1} & \text{for}\: r \neq - \frac{1}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r + 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq - \frac{1}{2} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d e^{2} \left(\begin{cases} \frac{x^{2 r + 1}}{2 r + 1} & \text{for}\: 2 r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{3} n \left(\begin{cases} \frac{\begin{cases} \frac{x x^{3 r}}{3 r + 1} & \text{for}\: r \neq - \frac{1}{3} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{3 r + 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq - \frac{1}{3} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{3} \left(\begin{cases} \frac{x^{3 r + 1}}{3 r + 1} & \text{for}\: 3 r \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"a*d**3*x + 3*a*d**2*e*Piecewise((x**(r + 1)/(r + 1), Ne(r, -1)), (log(x), True)) + 3*a*d*e**2*Piecewise((x**(2*r + 1)/(2*r + 1), Ne(2*r, -1)), (log(x), True)) + a*e**3*Piecewise((x**(3*r + 1)/(3*r + 1), Ne(3*r, -1)), (log(x), True)) - b*d**3*n*x + b*d**3*x*log(c*x**n) - 3*b*d**2*e*n*Piecewise((Piecewise((x*x**r/(r + 1), Ne(r, -1)), (log(x), True))/(r + 1), (r > -oo) & (r < oo) & Ne(r, -1)), (log(x)**2/2, True)) + 3*b*d**2*e*Piecewise((x**(r + 1)/(r + 1), Ne(r, -1)), (log(x), True))*log(c*x**n) - 3*b*d*e**2*n*Piecewise((Piecewise((x*x**(2*r)/(2*r + 1), Ne(r, -1/2)), (log(x), True))/(2*r + 1), (r > -oo) & (r < oo) & Ne(r, -1/2)), (log(x)**2/2, True)) + 3*b*d*e**2*Piecewise((x**(2*r + 1)/(2*r + 1), Ne(2*r, -1)), (log(x), True))*log(c*x**n) - b*e**3*n*Piecewise((Piecewise((x*x**(3*r)/(3*r + 1), Ne(r, -1/3)), (log(x), True))/(3*r + 1), (r > -oo) & (r < oo) & Ne(r, -1/3)), (log(x)**2/2, True)) + b*e**3*Piecewise((x**(3*r + 1)/(3*r + 1), Ne(3*r, -1)), (log(x), True))*log(c*x**n)","A",0
401,1,314,0,62.803344," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**2,x)","- \frac{a d^{3}}{x} + 3 a d^{2} e \left(\begin{cases} \frac{x^{r}}{r x - x} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 3 a d e^{2} \left(\begin{cases} \frac{x^{2 r}}{2 r x - x} & \text{for}\: r \neq \frac{1}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{3} \left(\begin{cases} \frac{x^{3 r}}{3 r x - x} & \text{for}\: r \neq \frac{1}{3} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - \frac{b d^{3} n}{x} - \frac{b d^{3} \log{\left(c x^{n} \right)}}{x} - 3 b d^{2} e n \left(\begin{cases} \frac{\begin{cases} \frac{x^{r}}{r x - x} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r - 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d^{2} e \left(\begin{cases} \frac{x^{r - 1}}{r - 1} & \text{for}\: r - 2 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - 3 b d e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{2 r}}{2 r x - x} & \text{for}\: r \neq \frac{1}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r - 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq \frac{1}{2} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d e^{2} \left(\begin{cases} \frac{x^{2 r - 1}}{2 r - 1} & \text{for}\: 2 r - 2 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{3} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{3 r}}{3 r x - x} & \text{for}\: r \neq \frac{1}{3} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{3 r - 1} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq \frac{1}{3} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{3} \left(\begin{cases} \frac{x^{3 r - 1}}{3 r - 1} & \text{for}\: 3 r - 2 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-a*d**3/x + 3*a*d**2*e*Piecewise((x**r/(r*x - x), Ne(r, 1)), (log(x), True)) + 3*a*d*e**2*Piecewise((x**(2*r)/(2*r*x - x), Ne(r, 1/2)), (log(x), True)) + a*e**3*Piecewise((x**(3*r)/(3*r*x - x), Ne(r, 1/3)), (log(x), True)) - b*d**3*n/x - b*d**3*log(c*x**n)/x - 3*b*d**2*e*n*Piecewise((Piecewise((x**r/(r*x - x), Ne(r, 1)), (log(x), True))/(r - 1), (r > -oo) & (r < oo) & Ne(r, 1)), (log(x)**2/2, True)) + 3*b*d**2*e*Piecewise((x**(r - 1)/(r - 1), Ne(r - 2, -1)), (log(x), True))*log(c*x**n) - 3*b*d*e**2*n*Piecewise((Piecewise((x**(2*r)/(2*r*x - x), Ne(r, 1/2)), (log(x), True))/(2*r - 1), (r > -oo) & (r < oo) & Ne(r, 1/2)), (log(x)**2/2, True)) + 3*b*d*e**2*Piecewise((x**(2*r - 1)/(2*r - 1), Ne(2*r - 2, -1)), (log(x), True))*log(c*x**n) - b*e**3*n*Piecewise((Piecewise((x**(3*r)/(3*r*x - x), Ne(r, 1/3)), (log(x), True))/(3*r - 1), (r > -oo) & (r < oo) & Ne(r, 1/3)), (log(x)**2/2, True)) + b*e**3*Piecewise((x**(3*r - 1)/(3*r - 1), Ne(3*r - 2, -1)), (log(x), True))*log(c*x**n)","A",0
402,1,350,0,178.893735," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**4,x)","- \frac{a d^{3}}{3 x^{3}} + 3 a d^{2} e \left(\begin{cases} \frac{x^{r}}{r x^{3} - 3 x^{3}} & \text{for}\: r \neq 3 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + 3 a d e^{2} \left(\begin{cases} \frac{x^{2 r}}{2 r x^{3} - 3 x^{3}} & \text{for}\: r \neq \frac{3}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) + a e^{3} \left(\begin{cases} \frac{x^{3 r}}{3 r x^{3} - 3 x^{3}} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) - \frac{b d^{3} n}{9 x^{3}} - \frac{b d^{3} \log{\left(c x^{n} \right)}}{3 x^{3}} - 3 b d^{2} e n \left(\begin{cases} \frac{\begin{cases} \frac{x^{r}}{r x^{3} - 3 x^{3}} & \text{for}\: r \neq 3 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{r - 3} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 3 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d^{2} e \left(\begin{cases} \frac{x^{r - 3}}{r - 3} & \text{for}\: r - 4 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - 3 b d e^{2} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{2 r}}{2 r x^{3} - 3 x^{3}} & \text{for}\: r \neq \frac{3}{2} \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{2 r - 3} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq \frac{3}{2} \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + 3 b d e^{2} \left(\begin{cases} \frac{x^{2 r - 3}}{2 r - 3} & \text{for}\: 2 r - 4 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)} - b e^{3} n \left(\begin{cases} \frac{\begin{cases} \frac{x^{3 r}}{3 r x^{3} - 3 x^{3}} & \text{for}\: r \neq 1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}}{3 r - 3} & \text{for}\: r > -\infty \wedge r < \infty \wedge r \neq 1 \\\frac{\log{\left(x \right)}^{2}}{2} & \text{otherwise} \end{cases}\right) + b e^{3} \left(\begin{cases} \frac{x^{3 r - 3}}{3 r - 3} & \text{for}\: 3 r - 4 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right) \log{\left(c x^{n} \right)}"," ",0,"-a*d**3/(3*x**3) + 3*a*d**2*e*Piecewise((x**r/(r*x**3 - 3*x**3), Ne(r, 3)), (log(x), True)) + 3*a*d*e**2*Piecewise((x**(2*r)/(2*r*x**3 - 3*x**3), Ne(r, 3/2)), (log(x), True)) + a*e**3*Piecewise((x**(3*r)/(3*r*x**3 - 3*x**3), Ne(r, 1)), (log(x), True)) - b*d**3*n/(9*x**3) - b*d**3*log(c*x**n)/(3*x**3) - 3*b*d**2*e*n*Piecewise((Piecewise((x**r/(r*x**3 - 3*x**3), Ne(r, 3)), (log(x), True))/(r - 3), (r > -oo) & (r < oo) & Ne(r, 3)), (log(x)**2/2, True)) + 3*b*d**2*e*Piecewise((x**(r - 3)/(r - 3), Ne(r - 4, -1)), (log(x), True))*log(c*x**n) - 3*b*d*e**2*n*Piecewise((Piecewise((x**(2*r)/(2*r*x**3 - 3*x**3), Ne(r, 3/2)), (log(x), True))/(2*r - 3), (r > -oo) & (r < oo) & Ne(r, 3/2)), (log(x)**2/2, True)) + 3*b*d*e**2*Piecewise((x**(2*r - 3)/(2*r - 3), Ne(2*r - 4, -1)), (log(x), True))*log(c*x**n) - b*e**3*n*Piecewise((Piecewise((x**(3*r)/(3*r*x**3 - 3*x**3), Ne(r, 1)), (log(x), True))/(3*r - 3), (r > -oo) & (r < oo) & Ne(r, 1)), (log(x)**2/2, True)) + b*e**3*Piecewise((x**(3*r - 3)/(3*r - 3), Ne(3*r - 4, -1)), (log(x), True))*log(c*x**n)","A",0
403,-1,0,0,0.000000," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(d+e*x**r),x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{r}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))/(d + e*x**r), x)","F",0
407,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(d+e*x**r),x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{r}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))/(d + e*x**r), x)","F",0
408,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(d+e*x**r),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{3} \left(d + e x^{r}\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**3*(d + e*x**r)), x)","F",0
410,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(d+e*x**r),x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{r}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/(d + e*x**r), x)","F",0
411,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(d+e*x**r),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{d + e x^{r}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d + e*x**r), x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(d+e*x**r),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \left(d + e x^{r}\right)}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*(d + e*x**r)), x)","F",0
413,0,0,0,0.000000," ","integrate(x**3*(a+b*ln(c*x**n))/(d+e*x**r)**2,x)","\int \frac{x^{3} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{r}\right)^{2}}\, dx"," ",0,"Integral(x**3*(a + b*log(c*x**n))/(d + e*x**r)**2, x)","F",0
414,0,0,0,0.000000," ","integrate(x*(a+b*ln(c*x**n))/(d+e*x**r)**2,x)","\int \frac{x \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{r}\right)^{2}}\, dx"," ",0,"Integral(x*(a + b*log(c*x**n))/(d + e*x**r)**2, x)","F",0
415,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**3/(d+e*x**r)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,0,0,0,0.000000," ","integrate(x**2*(a+b*ln(c*x**n))/(d+e*x**r)**2,x)","\int \frac{x^{2} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{r}\right)^{2}}\, dx"," ",0,"Integral(x**2*(a + b*log(c*x**n))/(d + e*x**r)**2, x)","F",0
418,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/(d+e*x**r)**2,x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{\left(d + e x^{r}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(d + e*x**r)**2, x)","F",0
419,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x**2/(d+e*x**r)**2,x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x^{2} \left(d + e x^{r}\right)^{2}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x**2*(d + e*x**r)**2), x)","F",0
420,-2,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(c-1/(x**n)),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
421,1,286,0,20.729416," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))/x,x)","\begin{cases} a d^{3} \log{\left(x \right)} + \frac{3 a d^{2} e x^{r}}{r} + \frac{3 a d e^{2} x^{2 r}}{2 r} + \frac{a e^{3} x^{3 r}}{3 r} + \frac{b d^{3} n \log{\left(x \right)}^{2}}{2} + b d^{3} \log{\left(c \right)} \log{\left(x \right)} + \frac{3 b d^{2} e n x^{r} \log{\left(x \right)}}{r} - \frac{3 b d^{2} e n x^{r}}{r^{2}} + \frac{3 b d^{2} e x^{r} \log{\left(c \right)}}{r} + \frac{3 b d e^{2} n x^{2 r} \log{\left(x \right)}}{2 r} - \frac{3 b d e^{2} n x^{2 r}}{4 r^{2}} + \frac{3 b d e^{2} x^{2 r} \log{\left(c \right)}}{2 r} + \frac{b e^{3} n x^{3 r} \log{\left(x \right)}}{3 r} - \frac{b e^{3} n x^{3 r}}{9 r^{2}} + \frac{b e^{3} x^{3 r} \log{\left(c \right)}}{3 r} & \text{for}\: r \neq 0 \\\left(d + e\right)^{3} \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*log(x) + 3*a*d**2*e*x**r/r + 3*a*d*e**2*x**(2*r)/(2*r) + a*e**3*x**(3*r)/(3*r) + b*d**3*n*log(x)**2/2 + b*d**3*log(c)*log(x) + 3*b*d**2*e*n*x**r*log(x)/r - 3*b*d**2*e*n*x**r/r**2 + 3*b*d**2*e*x**r*log(c)/r + 3*b*d*e**2*n*x**(2*r)*log(x)/(2*r) - 3*b*d*e**2*n*x**(2*r)/(4*r**2) + 3*b*d*e**2*x**(2*r)*log(c)/(2*r) + b*e**3*n*x**(3*r)*log(x)/(3*r) - b*e**3*n*x**(3*r)/(9*r**2) + b*e**3*x**(3*r)*log(c)/(3*r), Ne(r, 0)), ((d + e)**3*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)), True))","A",0
422,1,199,0,13.251501," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))/x,x)","\begin{cases} a d^{2} \log{\left(x \right)} + \frac{2 a d e x^{r}}{r} + \frac{a e^{2} x^{2 r}}{2 r} + \frac{b d^{2} n \log{\left(x \right)}^{2}}{2} + b d^{2} \log{\left(c \right)} \log{\left(x \right)} + \frac{2 b d e n x^{r} \log{\left(x \right)}}{r} - \frac{2 b d e n x^{r}}{r^{2}} + \frac{2 b d e x^{r} \log{\left(c \right)}}{r} + \frac{b e^{2} n x^{2 r} \log{\left(x \right)}}{2 r} - \frac{b e^{2} n x^{2 r}}{4 r^{2}} + \frac{b e^{2} x^{2 r} \log{\left(c \right)}}{2 r} & \text{for}\: r \neq 0 \\\left(d + e\right)^{2} \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*log(x) + 2*a*d*e*x**r/r + a*e**2*x**(2*r)/(2*r) + b*d**2*n*log(x)**2/2 + b*d**2*log(c)*log(x) + 2*b*d*e*n*x**r*log(x)/r - 2*b*d*e*n*x**r/r**2 + 2*b*d*e*x**r*log(c)/r + b*e**2*n*x**(2*r)*log(x)/(2*r) - b*e**2*n*x**(2*r)/(4*r**2) + b*e**2*x**(2*r)*log(c)/(2*r), Ne(r, 0)), ((d + e)**2*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)), True))","A",0
423,1,112,0,10.086972," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))/x,x)","\begin{cases} a d \log{\left(x \right)} + \frac{a e x^{r}}{r} + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + \frac{b e n x^{r} \log{\left(x \right)}}{r} - \frac{b e n x^{r}}{r^{2}} + \frac{b e x^{r} \log{\left(c \right)}}{r} & \text{for}\: r \neq 0 \\\left(d + e\right) \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*log(x) + a*e*x**r/r + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x**r*log(x)/r - b*e*n*x**r/r**2 + b*e*x**r*log(c)/r, Ne(r, 0)), ((d + e)*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)), True))","A",0
424,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,1,816,0,50.700786," ","integrate((d+e*x**r)**3*(a+b*ln(c*x**n))**2/x,x)","\begin{cases} a^{2} d^{3} \log{\left(x \right)} + \frac{3 a^{2} d^{2} e x^{r}}{r} + \frac{3 a^{2} d e^{2} x^{2 r}}{2 r} + \frac{a^{2} e^{3} x^{3 r}}{3 r} + a b d^{3} n \log{\left(x \right)}^{2} + 2 a b d^{3} \log{\left(c \right)} \log{\left(x \right)} + \frac{6 a b d^{2} e n x^{r} \log{\left(x \right)}}{r} - \frac{6 a b d^{2} e n x^{r}}{r^{2}} + \frac{6 a b d^{2} e x^{r} \log{\left(c \right)}}{r} + \frac{3 a b d e^{2} n x^{2 r} \log{\left(x \right)}}{r} - \frac{3 a b d e^{2} n x^{2 r}}{2 r^{2}} + \frac{3 a b d e^{2} x^{2 r} \log{\left(c \right)}}{r} + \frac{2 a b e^{3} n x^{3 r} \log{\left(x \right)}}{3 r} - \frac{2 a b e^{3} n x^{3 r}}{9 r^{2}} + \frac{2 a b e^{3} x^{3 r} \log{\left(c \right)}}{3 r} + \frac{b^{2} d^{3} n^{2} \log{\left(x \right)}^{3}}{3} + b^{2} d^{3} n \log{\left(c \right)} \log{\left(x \right)}^{2} + b^{2} d^{3} \log{\left(c \right)}^{2} \log{\left(x \right)} + \frac{3 b^{2} d^{2} e n^{2} x^{r} \log{\left(x \right)}^{2}}{r} - \frac{6 b^{2} d^{2} e n^{2} x^{r} \log{\left(x \right)}}{r^{2}} + \frac{6 b^{2} d^{2} e n^{2} x^{r}}{r^{3}} + \frac{6 b^{2} d^{2} e n x^{r} \log{\left(c \right)} \log{\left(x \right)}}{r} - \frac{6 b^{2} d^{2} e n x^{r} \log{\left(c \right)}}{r^{2}} + \frac{3 b^{2} d^{2} e x^{r} \log{\left(c \right)}^{2}}{r} + \frac{3 b^{2} d e^{2} n^{2} x^{2 r} \log{\left(x \right)}^{2}}{2 r} - \frac{3 b^{2} d e^{2} n^{2} x^{2 r} \log{\left(x \right)}}{2 r^{2}} + \frac{3 b^{2} d e^{2} n^{2} x^{2 r}}{4 r^{3}} + \frac{3 b^{2} d e^{2} n x^{2 r} \log{\left(c \right)} \log{\left(x \right)}}{r} - \frac{3 b^{2} d e^{2} n x^{2 r} \log{\left(c \right)}}{2 r^{2}} + \frac{3 b^{2} d e^{2} x^{2 r} \log{\left(c \right)}^{2}}{2 r} + \frac{b^{2} e^{3} n^{2} x^{3 r} \log{\left(x \right)}^{2}}{3 r} - \frac{2 b^{2} e^{3} n^{2} x^{3 r} \log{\left(x \right)}}{9 r^{2}} + \frac{2 b^{2} e^{3} n^{2} x^{3 r}}{27 r^{3}} + \frac{2 b^{2} e^{3} n x^{3 r} \log{\left(c \right)} \log{\left(x \right)}}{3 r} - \frac{2 b^{2} e^{3} n x^{3 r} \log{\left(c \right)}}{9 r^{2}} + \frac{b^{2} e^{3} x^{3 r} \log{\left(c \right)}^{2}}{3 r} & \text{for}\: r \neq 0 \\\left(d + e\right)^{3} \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**3*log(x) + 3*a**2*d**2*e*x**r/r + 3*a**2*d*e**2*x**(2*r)/(2*r) + a**2*e**3*x**(3*r)/(3*r) + a*b*d**3*n*log(x)**2 + 2*a*b*d**3*log(c)*log(x) + 6*a*b*d**2*e*n*x**r*log(x)/r - 6*a*b*d**2*e*n*x**r/r**2 + 6*a*b*d**2*e*x**r*log(c)/r + 3*a*b*d*e**2*n*x**(2*r)*log(x)/r - 3*a*b*d*e**2*n*x**(2*r)/(2*r**2) + 3*a*b*d*e**2*x**(2*r)*log(c)/r + 2*a*b*e**3*n*x**(3*r)*log(x)/(3*r) - 2*a*b*e**3*n*x**(3*r)/(9*r**2) + 2*a*b*e**3*x**(3*r)*log(c)/(3*r) + b**2*d**3*n**2*log(x)**3/3 + b**2*d**3*n*log(c)*log(x)**2 + b**2*d**3*log(c)**2*log(x) + 3*b**2*d**2*e*n**2*x**r*log(x)**2/r - 6*b**2*d**2*e*n**2*x**r*log(x)/r**2 + 6*b**2*d**2*e*n**2*x**r/r**3 + 6*b**2*d**2*e*n*x**r*log(c)*log(x)/r - 6*b**2*d**2*e*n*x**r*log(c)/r**2 + 3*b**2*d**2*e*x**r*log(c)**2/r + 3*b**2*d*e**2*n**2*x**(2*r)*log(x)**2/(2*r) - 3*b**2*d*e**2*n**2*x**(2*r)*log(x)/(2*r**2) + 3*b**2*d*e**2*n**2*x**(2*r)/(4*r**3) + 3*b**2*d*e**2*n*x**(2*r)*log(c)*log(x)/r - 3*b**2*d*e**2*n*x**(2*r)*log(c)/(2*r**2) + 3*b**2*d*e**2*x**(2*r)*log(c)**2/(2*r) + b**2*e**3*n**2*x**(3*r)*log(x)**2/(3*r) - 2*b**2*e**3*n**2*x**(3*r)*log(x)/(9*r**2) + 2*b**2*e**3*n**2*x**(3*r)/(27*r**3) + 2*b**2*e**3*n*x**(3*r)*log(c)*log(x)/(3*r) - 2*b**2*e**3*n*x**(3*r)*log(c)/(9*r**2) + b**2*e**3*x**(3*r)*log(c)**2/(3*r), Ne(r, 0)), ((d + e)**3*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)), True))","A",0
428,1,546,0,33.782130," ","integrate((d+e*x**r)**2*(a+b*ln(c*x**n))**2/x,x)","\begin{cases} a^{2} d^{2} \log{\left(x \right)} + \frac{2 a^{2} d e x^{r}}{r} + \frac{a^{2} e^{2} x^{2 r}}{2 r} + a b d^{2} n \log{\left(x \right)}^{2} + 2 a b d^{2} \log{\left(c \right)} \log{\left(x \right)} + \frac{4 a b d e n x^{r} \log{\left(x \right)}}{r} - \frac{4 a b d e n x^{r}}{r^{2}} + \frac{4 a b d e x^{r} \log{\left(c \right)}}{r} + \frac{a b e^{2} n x^{2 r} \log{\left(x \right)}}{r} - \frac{a b e^{2} n x^{2 r}}{2 r^{2}} + \frac{a b e^{2} x^{2 r} \log{\left(c \right)}}{r} + \frac{b^{2} d^{2} n^{2} \log{\left(x \right)}^{3}}{3} + b^{2} d^{2} n \log{\left(c \right)} \log{\left(x \right)}^{2} + b^{2} d^{2} \log{\left(c \right)}^{2} \log{\left(x \right)} + \frac{2 b^{2} d e n^{2} x^{r} \log{\left(x \right)}^{2}}{r} - \frac{4 b^{2} d e n^{2} x^{r} \log{\left(x \right)}}{r^{2}} + \frac{4 b^{2} d e n^{2} x^{r}}{r^{3}} + \frac{4 b^{2} d e n x^{r} \log{\left(c \right)} \log{\left(x \right)}}{r} - \frac{4 b^{2} d e n x^{r} \log{\left(c \right)}}{r^{2}} + \frac{2 b^{2} d e x^{r} \log{\left(c \right)}^{2}}{r} + \frac{b^{2} e^{2} n^{2} x^{2 r} \log{\left(x \right)}^{2}}{2 r} - \frac{b^{2} e^{2} n^{2} x^{2 r} \log{\left(x \right)}}{2 r^{2}} + \frac{b^{2} e^{2} n^{2} x^{2 r}}{4 r^{3}} + \frac{b^{2} e^{2} n x^{2 r} \log{\left(c \right)} \log{\left(x \right)}}{r} - \frac{b^{2} e^{2} n x^{2 r} \log{\left(c \right)}}{2 r^{2}} + \frac{b^{2} e^{2} x^{2 r} \log{\left(c \right)}^{2}}{2 r} & \text{for}\: r \neq 0 \\\left(d + e\right)^{2} \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*log(x) + 2*a**2*d*e*x**r/r + a**2*e**2*x**(2*r)/(2*r) + a*b*d**2*n*log(x)**2 + 2*a*b*d**2*log(c)*log(x) + 4*a*b*d*e*n*x**r*log(x)/r - 4*a*b*d*e*n*x**r/r**2 + 4*a*b*d*e*x**r*log(c)/r + a*b*e**2*n*x**(2*r)*log(x)/r - a*b*e**2*n*x**(2*r)/(2*r**2) + a*b*e**2*x**(2*r)*log(c)/r + b**2*d**2*n**2*log(x)**3/3 + b**2*d**2*n*log(c)*log(x)**2 + b**2*d**2*log(c)**2*log(x) + 2*b**2*d*e*n**2*x**r*log(x)**2/r - 4*b**2*d*e*n**2*x**r*log(x)/r**2 + 4*b**2*d*e*n**2*x**r/r**3 + 4*b**2*d*e*n*x**r*log(c)*log(x)/r - 4*b**2*d*e*n*x**r*log(c)/r**2 + 2*b**2*d*e*x**r*log(c)**2/r + b**2*e**2*n**2*x**(2*r)*log(x)**2/(2*r) - b**2*e**2*n**2*x**(2*r)*log(x)/(2*r**2) + b**2*e**2*n**2*x**(2*r)/(4*r**3) + b**2*e**2*n*x**(2*r)*log(c)*log(x)/r - b**2*e**2*n*x**(2*r)*log(c)/(2*r**2) + b**2*e**2*x**(2*r)*log(c)**2/(2*r), Ne(r, 0)), ((d + e)**2*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)), True))","A",0
429,1,309,0,25.982871," ","integrate((d+e*x**r)*(a+b*ln(c*x**n))**2/x,x)","\begin{cases} a^{2} d \log{\left(x \right)} + \frac{a^{2} e x^{r}}{r} + a b d n \log{\left(x \right)}^{2} + 2 a b d \log{\left(c \right)} \log{\left(x \right)} + \frac{2 a b e n x^{r} \log{\left(x \right)}}{r} - \frac{2 a b e n x^{r}}{r^{2}} + \frac{2 a b e x^{r} \log{\left(c \right)}}{r} + \frac{b^{2} d n^{2} \log{\left(x \right)}^{3}}{3} + b^{2} d n \log{\left(c \right)} \log{\left(x \right)}^{2} + b^{2} d \log{\left(c \right)}^{2} \log{\left(x \right)} + \frac{b^{2} e n^{2} x^{r} \log{\left(x \right)}^{2}}{r} - \frac{2 b^{2} e n^{2} x^{r} \log{\left(x \right)}}{r^{2}} + \frac{2 b^{2} e n^{2} x^{r}}{r^{3}} + \frac{2 b^{2} e n x^{r} \log{\left(c \right)} \log{\left(x \right)}}{r} - \frac{2 b^{2} e n x^{r} \log{\left(c \right)}}{r^{2}} + \frac{b^{2} e x^{r} \log{\left(c \right)}^{2}}{r} & \text{for}\: r \neq 0 \\\left(d + e\right) \left(\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}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*log(x) + a**2*e*x**r/r + a*b*d*n*log(x)**2 + 2*a*b*d*log(c)*log(x) + 2*a*b*e*n*x**r*log(x)/r - 2*a*b*e*n*x**r/r**2 + 2*a*b*e*x**r*log(c)/r + b**2*d*n**2*log(x)**3/3 + b**2*d*n*log(c)*log(x)**2 + b**2*d*log(c)**2*log(x) + b**2*e*n**2*x**r*log(x)**2/r - 2*b**2*e*n**2*x**r*log(x)/r**2 + 2*b**2*e*n**2*x**r/r**3 + 2*b**2*e*n*x**r*log(c)*log(x)/r - 2*b**2*e*n*x**r*log(c)/r**2 + b**2*e*x**r*log(c)**2/r, Ne(r, 0)), ((d + e)*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)), True))","A",0
430,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(d+e*x**r),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(d+e*x**r)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))**2/x/(d+e*x**r)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((d+e*x**r)**(5/2)*(a+b*ln(c*x**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate((d+e*x**r)**(3/2)*(a+b*ln(c*x**n))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,0,0,0,0.000000," ","integrate((d+e*x**r)**(1/2)*(a+b*ln(c*x**n))/x,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right) \sqrt{d + e x^{r}}}{x}\, dx"," ",0,"Integral((a + b*log(c*x**n))*sqrt(d + e*x**r)/x, x)","F",0
436,0,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**(1/2),x)","\int \frac{a + b \log{\left(c x^{n} \right)}}{x \sqrt{d + e x^{r}}}\, dx"," ",0,"Integral((a + b*log(c*x**n))/(x*sqrt(d + e*x**r)), x)","F",0
437,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate((a+b*ln(c*x**n))/x/(d+e*x**r)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate((f*x)**m*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate((f*x)**m*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,1,6356,0,116.666832," ","integrate((f*x)**m*(d+e*x**r)*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{\left(d + e\right) \left(\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}\right)}{f} & \text{for}\: m = -1 \wedge r = 0 \\\frac{a d \log{\left(x \right)} + \frac{a e x^{r}}{r} + \frac{b d n \log{\left(x \right)}^{2}}{2} + b d \log{\left(c \right)} \log{\left(x \right)} + \frac{b e n x^{r} \log{\left(x \right)}}{r} - \frac{b e n x^{r}}{r^{2}} + \frac{b e x^{r} \log{\left(c \right)}}{r}}{f} & \text{for}\: m = -1 \\- \frac{2 a d n r^{3}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{4 a d n r^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 a d n r}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 a e n r^{4} x^{r} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{4 a e n r^{3} x^{r} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 a e n r^{3} x^{r}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 a e n r^{2} x^{r} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 a e n r^{2} x^{r}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 a e r^{4} x^{r} \log{\left(c \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{4 a e r^{3} x^{r} \log{\left(c \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 a e r^{2} x^{r} \log{\left(c \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b d n^{2} r^{3} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{4 b d n^{2} r^{2} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b d n^{2} r^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b d n^{2} r \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{4 b d n^{2} r}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b d n^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b d n r^{3} \log{\left(c \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{4 b d n r^{2} \log{\left(c \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b d n r \log{\left(c \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{b e n^{2} r^{4} x^{r} \log{\left(x \right)}^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 b e n^{2} r^{3} x^{r} \log{\left(x \right)}^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{b e n^{2} r^{2} x^{r} \log{\left(x \right)}^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} - \frac{2 b e n^{2} r^{2} x^{r}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 b e n r^{4} x^{r} \log{\left(c \right)} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{4 b e n r^{3} x^{r} \log{\left(c \right)} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 b e n r^{2} x^{r} \log{\left(c \right)} \log{\left(x \right)}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{b e r^{4} x^{r} \log{\left(c \right)}^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{2 b e r^{3} x^{r} \log{\left(c \right)}^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} + \frac{b e r^{2} x^{r} \log{\left(c \right)}^{2}}{2 f f^{r} n r^{4} x^{r} + 4 f f^{r} n r^{3} x^{r} + 2 f f^{r} n r^{2} x^{r}} & \text{for}\: m = - r - 1 \\\frac{a d f^{m} m^{3} x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 a d f^{m} m^{2} r x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 a d f^{m} m^{2} x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a d f^{m} m r^{2} x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{4 a d f^{m} m r x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 a d f^{m} m x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a d f^{m} r^{2} x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 a d f^{m} r x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a d f^{m} x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a e f^{m} m^{3} x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a e f^{m} m^{2} r x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 a e f^{m} m^{2} x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 a e f^{m} m r x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 a e f^{m} m x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a e f^{m} r x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{a e f^{m} x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} m^{3} n x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} m^{3} x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 b d f^{m} m^{2} n r x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b d f^{m} m^{2} n x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{b d f^{m} m^{2} n x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 b d f^{m} m^{2} r x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b d f^{m} m^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} m n r^{2} x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{4 b d f^{m} m n r x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{2 b d f^{m} m n r x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b d f^{m} m n x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{2 b d f^{m} m n x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} m r^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{4 b d f^{m} m r x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b d f^{m} m x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} n r^{2} x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{b d f^{m} n r^{2} x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 b d f^{m} n r x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{2 b d f^{m} n r x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} n x x^{m} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{b d f^{m} n x x^{m}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} r^{2} x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 b d f^{m} r x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b d f^{m} x x^{m} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} m^{3} n x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} m^{3} x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} m^{2} n r x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b e f^{m} m^{2} n x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{b e f^{m} m^{2} n x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} m^{2} r x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b e f^{m} m^{2} x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 b e f^{m} m n r x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b e f^{m} m n x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{2 b e f^{m} m n x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{2 b e f^{m} m r x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{3 b e f^{m} m x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} n r x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} n x x^{m} x^{r} \log{\left(x \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} - \frac{b e f^{m} n x x^{m} x^{r}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} r x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} + \frac{b e f^{m} x x^{m} x^{r} \log{\left(c \right)}}{m^{4} + 2 m^{3} r + 4 m^{3} + m^{2} r^{2} + 6 m^{2} r + 6 m^{2} + 2 m r^{2} + 6 m r + 4 m + r^{2} + 2 r + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((d + e)*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))/f, Eq(m, -1) & Eq(r, 0)), ((a*d*log(x) + a*e*x**r/r + b*d*n*log(x)**2/2 + b*d*log(c)*log(x) + b*e*n*x**r*log(x)/r - b*e*n*x**r/r**2 + b*e*x**r*log(c)/r)/f, Eq(m, -1)), (-2*a*d*n*r**3/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 4*a*d*n*r**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*a*d*n*r/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*a*e*n*r**4*x**r*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 4*a*e*n*r**3*x**r*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*a*e*n*r**3*x**r/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*a*e*n*r**2*x**r*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*a*e*n*r**2*x**r/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*a*e*r**4*x**r*log(c)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 4*a*e*r**3*x**r*log(c)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*a*e*r**2*x**r*log(c)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*d*n**2*r**3*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 4*b*d*n**2*r**2*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*d*n**2*r**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*d*n**2*r*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 4*b*d*n**2*r/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*d*n**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*d*n*r**3*log(c)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 4*b*d*n*r**2*log(c)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*d*n*r*log(c)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + b*e*n**2*r**4*x**r*log(x)**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*b*e*n**2*r**3*x**r*log(x)**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + b*e*n**2*r**2*x**r*log(x)**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) - 2*b*e*n**2*r**2*x**r/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*b*e*n*r**4*x**r*log(c)*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 4*b*e*n*r**3*x**r*log(c)*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*b*e*n*r**2*x**r*log(c)*log(x)/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + b*e*r**4*x**r*log(c)**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + 2*b*e*r**3*x**r*log(c)**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r) + b*e*r**2*x**r*log(c)**2/(2*f*f**r*n*r**4*x**r + 4*f*f**r*n*r**3*x**r + 2*f*f**r*n*r**2*x**r), Eq(m, -r - 1)), (a*d*f**m*m**3*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*a*d*f**m*m**2*r*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*a*d*f**m*m**2*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*d*f**m*m*r**2*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 4*a*d*f**m*m*r*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*a*d*f**m*m*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*d*f**m*r**2*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*a*d*f**m*r*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*d*f**m*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*e*f**m*m**3*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*e*f**m*m**2*r*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*a*e*f**m*m**2*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*a*e*f**m*m*r*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*a*e*f**m*m*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*e*f**m*r*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + a*e*f**m*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*m**3*n*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*m**3*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*b*d*f**m*m**2*n*r*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*d*f**m*m**2*n*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - b*d*f**m*m**2*n*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*b*d*f**m*m**2*r*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*d*f**m*m**2*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*m*n*r**2*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 4*b*d*f**m*m*n*r*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - 2*b*d*f**m*m*n*r*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*d*f**m*m*n*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - 2*b*d*f**m*m*n*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*m*r**2*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 4*b*d*f**m*m*r*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*d*f**m*m*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*n*r**2*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - b*d*f**m*n*r**2*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*b*d*f**m*n*r*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - 2*b*d*f**m*n*r*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*n*x*x**m*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - b*d*f**m*n*x*x**m/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*r**2*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*b*d*f**m*r*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*d*f**m*x*x**m*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*m**3*n*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*m**3*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*m**2*n*r*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*e*f**m*m**2*n*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - b*e*f**m*m**2*n*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*m**2*r*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*e*f**m*m**2*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*b*e*f**m*m*n*r*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*e*f**m*m*n*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - 2*b*e*f**m*m*n*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 2*b*e*f**m*m*r*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + 3*b*e*f**m*m*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*n*r*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*n*x*x**m*x**r*log(x)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) - b*e*f**m*n*x*x**m*x**r/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*r*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1) + b*e*f**m*x*x**m*x**r*log(c)/(m**4 + 2*m**3*r + 4*m**3 + m**2*r**2 + 6*m**2*r + 6*m**2 + 2*m*r**2 + 6*m*r + 4*m + r**2 + 2*r + 1), True))","A",0
443,1,192,0,10.366624," ","integrate((f*x)**m*(a+b*ln(c*x**n)),x)","\begin{cases} \frac{a f^{m} m x x^{m}}{m^{2} + 2 m + 1} + \frac{a f^{m} x x^{m}}{m^{2} + 2 m + 1} + \frac{b f^{m} m n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} + \frac{b f^{m} m x x^{m} \log{\left(c \right)}}{m^{2} + 2 m + 1} + \frac{b f^{m} n x x^{m} \log{\left(x \right)}}{m^{2} + 2 m + 1} - \frac{b f^{m} n x x^{m}}{m^{2} + 2 m + 1} + \frac{b f^{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}}{f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*f**m*m*x*x**m/(m**2 + 2*m + 1) + a*f**m*x*x**m/(m**2 + 2*m + 1) + b*f**m*m*n*x*x**m*log(x)/(m**2 + 2*m + 1) + b*f**m*m*x*x**m*log(c)/(m**2 + 2*m + 1) + b*f**m*n*x*x**m*log(x)/(m**2 + 2*m + 1) - b*f**m*n*x*x**m/(m**2 + 2*m + 1) + b*f**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))/f, True))","A",0
444,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))/(d+e*x**r),x)","\int \frac{\left(f x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)}{d + e x^{r}}\, dx"," ",0,"Integral((f*x)**m*(a + b*log(c*x**n))/(d + e*x**r), x)","F",0
445,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))/(d+e*x**r)**2,x)","\int \frac{\left(f x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)}{\left(d + e x^{r}\right)^{2}}\, dx"," ",0,"Integral((f*x)**m*(a + b*log(c*x**n))/(d + e*x**r)**2, x)","F",0
446,-1,0,0,0.000000," ","integrate((d+e/(x**(1/(1+q))))**q*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate((f*x)**(-1-(1+q)*r)*(d+e*x**r)**q*(a+b*ln(c*x**n)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((f*x)**m*(d+e*x**r)**3*(a+b*ln(c*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((f*x)**m*(d+e*x**r)**2*(a+b*ln(c*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((f*x)**m*(d+e*x**r)*(a+b*ln(c*x**n))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,0,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))**p,x)","\int \left(f x\right)^{m} \left(a + b \log{\left(c x^{n} \right)}\right)^{p}\, dx"," ",0,"Integral((f*x)**m*(a + b*log(c*x**n))**p, x)","F",0
452,-1,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))**p/(d+e*x**r),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,-1,0,0,0.000000," ","integrate((f*x)**m*(a+b*ln(c*x**n))**p/(d+e*x**r)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
454,1,1090,0,8.298775," ","integrate((g*x+f)*(a+b*ln(c*x**n))/(e*x+d)**3,x)","\begin{cases} \tilde{\infty} \left(- \frac{a f}{2 x^{2}} - \frac{a g}{x} - \frac{b f n \log{\left(x \right)}}{2 x^{2}} - \frac{b f n}{4 x^{2}} - \frac{b f \log{\left(c \right)}}{2 x^{2}} - \frac{b g n \log{\left(x \right)}}{x} - \frac{b g n}{x} - \frac{b g \log{\left(c \right)}}{x}\right) & \text{for}\: d = 0 \wedge e = 0 \\\frac{- \frac{a f}{2 x^{2}} - \frac{a g}{x} - \frac{b f n \log{\left(x \right)}}{2 x^{2}} - \frac{b f n}{4 x^{2}} - \frac{b f \log{\left(c \right)}}{2 x^{2}} - \frac{b g n \log{\left(x \right)}}{x} - \frac{b g n}{x} - \frac{b g \log{\left(c \right)}}{x}}{e^{3}} & \text{for}\: d = 0 \\\frac{a f x + \frac{a g x^{2}}{2} + b f n x \log{\left(x \right)} - b f n x + b f x \log{\left(c \right)} + \frac{b g n x^{2} \log{\left(x \right)}}{2} - \frac{b g n x^{2}}{4} + \frac{b g x^{2} \log{\left(c \right)}}{2}}{d^{3}} & \text{for}\: e = 0 \\- \frac{a d^{3} g}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{a d^{2} e f}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{2 a d^{2} e g x}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{b d^{3} g n \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{b d^{3} g n}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{b d^{2} e f n \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{b d^{2} e f n}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{2 b d^{2} e g n x \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{b d^{2} e g n x}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{2 b d e^{2} f n x \log{\left(x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{2 b d e^{2} f n x \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{b d e^{2} f n x}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{2 b d e^{2} f x \log{\left(c \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{b d e^{2} g n x^{2} \log{\left(x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{b d e^{2} g n x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{b d e^{2} g x^{2} \log{\left(c \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{b e^{3} f n x^{2} \log{\left(x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} - \frac{b e^{3} f n x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} + \frac{b e^{3} f x^{2} \log{\left(c \right)}}{2 d^{4} e^{2} + 4 d^{3} e^{3} x + 2 d^{2} e^{4} x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-a*f/(2*x**2) - a*g/x - b*f*n*log(x)/(2*x**2) - b*f*n/(4*x**2) - b*f*log(c)/(2*x**2) - b*g*n*log(x)/x - b*g*n/x - b*g*log(c)/x), Eq(d, 0) & Eq(e, 0)), ((-a*f/(2*x**2) - a*g/x - b*f*n*log(x)/(2*x**2) - b*f*n/(4*x**2) - b*f*log(c)/(2*x**2) - b*g*n*log(x)/x - b*g*n/x - b*g*log(c)/x)/e**3, Eq(d, 0)), ((a*f*x + a*g*x**2/2 + b*f*n*x*log(x) - b*f*n*x + b*f*x*log(c) + b*g*n*x**2*log(x)/2 - b*g*n*x**2/4 + b*g*x**2*log(c)/2)/d**3, Eq(e, 0)), (-a*d**3*g/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - a*d**2*e*f/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - 2*a*d**2*e*g*x/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - b*d**3*g*n*log(d/e + x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - b*d**3*g*n/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - b*d**2*e*f*n*log(d/e + x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + b*d**2*e*f*n/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - 2*b*d**2*e*g*n*x*log(d/e + x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - b*d**2*e*g*n*x/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + 2*b*d*e**2*f*n*x*log(x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - 2*b*d*e**2*f*n*x*log(d/e + x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + b*d*e**2*f*n*x/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + 2*b*d*e**2*f*x*log(c)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + b*d*e**2*g*n*x**2*log(x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - b*d*e**2*g*n*x**2*log(d/e + x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + b*d*e**2*g*x**2*log(c)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + b*e**3*f*n*x**2*log(x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) - b*e**3*f*n*x**2*log(d/e + x)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2) + b*e**3*f*x**2*log(c)/(2*d**4*e**2 + 4*d**3*e**3*x + 2*d**2*e**4*x**2), True))","A",0
455,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*x**n))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{2} \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**2*(f + g*x)/(d + e*x)**3, x)","F",0
456,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*ln(c*x**n))**3/(e*x+d)**3,x)","\int \frac{\left(a + b \log{\left(c x^{n} \right)}\right)^{3} \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*log(c*x**n))**3*(f + g*x)/(d + e*x)**3, x)","F",0
