1,1,124,0,1.532937," ","integrate(x**3*(c*d*x+d)*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c d x^{5}}{5} + \frac{a d x^{4}}{4} + \frac{b c d x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b d x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b d x^{4}}{20} + \frac{b d x^{3}}{12 c} + \frac{b d x^{2}}{10 c^{2}} + \frac{b d x}{4 c^{3}} + \frac{b d \log{\left(x - \frac{1}{c} \right)}}{5 c^{4}} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{20 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*d*x**5/5 + a*d*x**4/4 + b*c*d*x**5*atanh(c*x)/5 + b*d*x**4*atanh(c*x)/4 + b*d*x**4/20 + b*d*x**3/(12*c) + b*d*x**2/(10*c**2) + b*d*x/(4*c**3) + b*d*log(x - 1/c)/(5*c**4) - b*d*atanh(c*x)/(20*c**4), Ne(c, 0)), (a*d*x**4/4, True))","A",0
2,1,112,0,1.201492," ","integrate(x**2*(c*d*x+d)*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c d x^{4}}{4} + \frac{a d x^{3}}{3} + \frac{b c d x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b d x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b d x^{3}}{12} + \frac{b d x^{2}}{6 c} + \frac{b d x}{4 c^{2}} + \frac{b d \log{\left(x - \frac{1}{c} \right)}}{3 c^{3}} + \frac{b d \operatorname{atanh}{\left(c x \right)}}{12 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*d*x**4/4 + a*d*x**3/3 + b*c*d*x**4*atanh(c*x)/4 + b*d*x**3*atanh(c*x)/3 + b*d*x**3/12 + b*d*x**2/(6*c) + b*d*x/(4*c**2) + b*d*log(x - 1/c)/(3*c**3) + b*d*atanh(c*x)/(12*c**3), Ne(c, 0)), (a*d*x**3/3, True))","A",0
3,1,100,0,0.923599," ","integrate(x*(c*d*x+d)*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c d x^{3}}{3} + \frac{a d x^{2}}{2} + \frac{b c d x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b d x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b d x^{2}}{6} + \frac{b d x}{2 c} + \frac{b d \log{\left(x - \frac{1}{c} \right)}}{3 c^{2}} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{6 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*d*x**3/3 + a*d*x**2/2 + b*c*d*x**3*atanh(c*x)/3 + b*d*x**2*atanh(c*x)/2 + b*d*x**2/6 + b*d*x/(2*c) + b*d*log(x - 1/c)/(3*c**2) - b*d*atanh(c*x)/(6*c**2), Ne(c, 0)), (a*d*x**2/2, True))","A",0
4,1,75,0,0.577436," ","integrate((c*d*x+d)*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c d x^{2}}{2} + a d x + \frac{b c d x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + b d x \operatorname{atanh}{\left(c x \right)} + \frac{b d x}{2} + \frac{b d \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b d \operatorname{atanh}{\left(c x \right)}}{2 c} & \text{for}\: c \neq 0 \\a d x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*d*x**2/2 + a*d*x + b*c*d*x**2*atanh(c*x)/2 + b*d*x*atanh(c*x) + b*d*x/2 + b*d*log(x - 1/c)/c + b*d*atanh(c*x)/(2*c), Ne(c, 0)), (a*d*x, True))","A",0
5,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))/x,x)","d \left(\int a c\, dx + \int \frac{a}{x}\, dx + \int b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d*(Integral(a*c, x) + Integral(a/x, x) + Integral(b*c*atanh(c*x), x) + Integral(b*atanh(c*x)/x, x))","F",0
6,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))/x**2,x)","d \left(\int \frac{a}{x^{2}}\, dx + \int \frac{a c}{x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d*(Integral(a/x**2, x) + Integral(a*c/x, x) + Integral(b*atanh(c*x)/x**2, x) + Integral(b*c*atanh(c*x)/x, x))","F",0
7,1,95,0,1.076193," ","integrate((c*d*x+d)*(a+b*atanh(c*x))/x**3,x)","\begin{cases} - \frac{a c d}{x} - \frac{a d}{2 x^{2}} + b c^{2} d \log{\left(x \right)} - b c^{2} d \log{\left(x - \frac{1}{c} \right)} - \frac{b c^{2} d \operatorname{atanh}{\left(c x \right)}}{2} - \frac{b c d \operatorname{atanh}{\left(c x \right)}}{x} - \frac{b c d}{2 x} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{2 x^{2}} & \text{for}\: c \neq 0 \\- \frac{a d}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c*d/x - a*d/(2*x**2) + b*c**2*d*log(x) - b*c**2*d*log(x - 1/c) - b*c**2*d*atanh(c*x)/2 - b*c*d*atanh(c*x)/x - b*c*d/(2*x) - b*d*atanh(c*x)/(2*x**2), Ne(c, 0)), (-a*d/(2*x**2), True))","A",0
8,1,117,0,1.422487," ","integrate((c*d*x+d)*(a+b*atanh(c*x))/x**4,x)","\begin{cases} - \frac{a c d}{2 x^{2}} - \frac{a d}{3 x^{3}} + \frac{b c^{3} d \log{\left(x \right)}}{3} - \frac{b c^{3} d \log{\left(x - \frac{1}{c} \right)}}{3} + \frac{b c^{3} d \operatorname{atanh}{\left(c x \right)}}{6} - \frac{b c^{2} d}{2 x} - \frac{b c d \operatorname{atanh}{\left(c x \right)}}{2 x^{2}} - \frac{b c d}{6 x^{2}} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\- \frac{a d}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c*d/(2*x**2) - a*d/(3*x**3) + b*c**3*d*log(x)/3 - b*c**3*d*log(x - 1/c)/3 + b*c**3*d*atanh(c*x)/6 - b*c**2*d/(2*x) - b*c*d*atanh(c*x)/(2*x**2) - b*c*d/(6*x**2) - b*d*atanh(c*x)/(3*x**3), Ne(c, 0)), (-a*d/(3*x**3), True))","A",0
9,1,129,0,1.881330," ","integrate((c*d*x+d)*(a+b*atanh(c*x))/x**5,x)","\begin{cases} - \frac{a c d}{3 x^{3}} - \frac{a d}{4 x^{4}} + \frac{b c^{4} d \log{\left(x \right)}}{3} - \frac{b c^{4} d \log{\left(x - \frac{1}{c} \right)}}{3} - \frac{b c^{4} d \operatorname{atanh}{\left(c x \right)}}{12} - \frac{b c^{3} d}{4 x} - \frac{b c^{2} d}{6 x^{2}} - \frac{b c d \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} - \frac{b c d}{12 x^{3}} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a d}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c*d/(3*x**3) - a*d/(4*x**4) + b*c**4*d*log(x)/3 - b*c**4*d*log(x - 1/c)/3 - b*c**4*d*atanh(c*x)/12 - b*c**3*d/(4*x) - b*c**2*d/(6*x**2) - b*c*d*atanh(c*x)/(3*x**3) - b*c*d/(12*x**3) - b*d*atanh(c*x)/(4*x**4), Ne(c, 0)), (-a*d/(4*x**4), True))","A",0
10,1,196,0,2.155403," ","integrate(x**3*(c*d*x+d)**2*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{2} d^{2} x^{6}}{6} + \frac{2 a c d^{2} x^{5}}{5} + \frac{a d^{2} x^{4}}{4} + \frac{b c^{2} d^{2} x^{6} \operatorname{atanh}{\left(c x \right)}}{6} + \frac{2 b c d^{2} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b c d^{2} x^{5}}{30} + \frac{b d^{2} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b d^{2} x^{4}}{10} + \frac{5 b d^{2} x^{3}}{36 c} + \frac{b d^{2} x^{2}}{5 c^{2}} + \frac{5 b d^{2} x}{12 c^{3}} + \frac{2 b d^{2} \log{\left(x - \frac{1}{c} \right)}}{5 c^{4}} - \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{60 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d**2*x**6/6 + 2*a*c*d**2*x**5/5 + a*d**2*x**4/4 + b*c**2*d**2*x**6*atanh(c*x)/6 + 2*b*c*d**2*x**5*atanh(c*x)/5 + b*c*d**2*x**5/30 + b*d**2*x**4*atanh(c*x)/4 + b*d**2*x**4/10 + 5*b*d**2*x**3/(36*c) + b*d**2*x**2/(5*c**2) + 5*b*d**2*x/(12*c**3) + 2*b*d**2*log(x - 1/c)/(5*c**4) - b*d**2*atanh(c*x)/(60*c**4), Ne(c, 0)), (a*d**2*x**4/4, True))","A",0
11,1,177,0,1.712597," ","integrate(x**2*(c*d*x+d)**2*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{2} d^{2} x^{5}}{5} + \frac{a c d^{2} x^{4}}{2} + \frac{a d^{2} x^{3}}{3} + \frac{b c^{2} d^{2} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b c d^{2} x^{4} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b c d^{2} x^{4}}{20} + \frac{b d^{2} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b d^{2} x^{3}}{6} + \frac{4 b d^{2} x^{2}}{15 c} + \frac{b d^{2} x}{2 c^{2}} + \frac{8 b d^{2} \log{\left(x - \frac{1}{c} \right)}}{15 c^{3}} + \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{30 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d**2*x**5/5 + a*c*d**2*x**4/2 + a*d**2*x**3/3 + b*c**2*d**2*x**5*atanh(c*x)/5 + b*c*d**2*x**4*atanh(c*x)/2 + b*c*d**2*x**4/20 + b*d**2*x**3*atanh(c*x)/3 + b*d**2*x**3/6 + 4*b*d**2*x**2/(15*c) + b*d**2*x/(2*c**2) + 8*b*d**2*log(x - 1/c)/(15*c**3) + b*d**2*atanh(c*x)/(30*c**3), Ne(c, 0)), (a*d**2*x**3/3, True))","A",0
12,1,167,0,1.327305," ","integrate(x*(c*d*x+d)**2*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{2} d^{2} x^{4}}{4} + \frac{2 a c d^{2} x^{3}}{3} + \frac{a d^{2} x^{2}}{2} + \frac{b c^{2} d^{2} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{2 b c d^{2} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b c d^{2} x^{3}}{12} + \frac{b d^{2} x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b d^{2} x^{2}}{3} + \frac{3 b d^{2} x}{4 c} + \frac{2 b d^{2} \log{\left(x - \frac{1}{c} \right)}}{3 c^{2}} - \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{12 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d^{2} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d**2*x**4/4 + 2*a*c*d**2*x**3/3 + a*d**2*x**2/2 + b*c**2*d**2*x**4*atanh(c*x)/4 + 2*b*c*d**2*x**3*atanh(c*x)/3 + b*c*d**2*x**3/12 + b*d**2*x**2*atanh(c*x)/2 + b*d**2*x**2/3 + 3*b*d**2*x/(4*c) + 2*b*d**2*log(x - 1/c)/(3*c**2) - b*d**2*atanh(c*x)/(12*c**2), Ne(c, 0)), (a*d**2*x**2/2, True))","A",0
13,1,131,0,0.957767," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{2} d^{2} x^{3}}{3} + a c d^{2} x^{2} + a d^{2} x + \frac{b c^{2} d^{2} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + b c d^{2} x^{2} \operatorname{atanh}{\left(c x \right)} + \frac{b c d^{2} x^{2}}{6} + b d^{2} x \operatorname{atanh}{\left(c x \right)} + b d^{2} x + \frac{4 b d^{2} \log{\left(x - \frac{1}{c} \right)}}{3 c} + \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{3 c} & \text{for}\: c \neq 0 \\a d^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*d**2*x**3/3 + a*c*d**2*x**2 + a*d**2*x + b*c**2*d**2*x**3*atanh(c*x)/3 + b*c*d**2*x**2*atanh(c*x) + b*c*d**2*x**2/6 + b*d**2*x*atanh(c*x) + b*d**2*x + 4*b*d**2*log(x - 1/c)/(3*c) + b*d**2*atanh(c*x)/(3*c), Ne(c, 0)), (a*d**2*x, True))","A",0
14,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))/x,x)","d^{2} \left(\int 2 a c\, dx + \int \frac{a}{x}\, dx + \int a c^{2} x\, dx + \int 2 b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int b c^{2} x \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(2*a*c, x) + Integral(a/x, x) + Integral(a*c**2*x, x) + Integral(2*b*c*atanh(c*x), x) + Integral(b*atanh(c*x)/x, x) + Integral(b*c**2*x*atanh(c*x), x))","F",0
15,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))/x**2,x)","d^{2} \left(\int a c^{2}\, dx + \int \frac{a}{x^{2}}\, dx + \int \frac{2 a c}{x}\, dx + \int b c^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**2*(Integral(a*c**2, x) + Integral(a/x**2, x) + Integral(2*a*c/x, x) + Integral(b*c**2*atanh(c*x), x) + Integral(b*atanh(c*x)/x**2, x) + Integral(2*b*c*atanh(c*x)/x, x))","F",0
16,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))/x**3,x)","d^{2} \left(\int \frac{a}{x^{3}}\, dx + \int \frac{2 a c}{x^{2}}\, dx + \int \frac{a c^{2}}{x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 b c \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b c^{2} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**2*(Integral(a/x**3, x) + Integral(2*a*c/x**2, x) + Integral(a*c**2/x, x) + Integral(b*atanh(c*x)/x**3, x) + Integral(2*b*c*atanh(c*x)/x**2, x) + Integral(b*c**2*atanh(c*x)/x, x))","F",0
17,1,158,0,1.577681," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))/x**4,x)","\begin{cases} - \frac{a c^{2} d^{2}}{x} - \frac{a c d^{2}}{x^{2}} - \frac{a d^{2}}{3 x^{3}} + \frac{4 b c^{3} d^{2} \log{\left(x \right)}}{3} - \frac{4 b c^{3} d^{2} \log{\left(x - \frac{1}{c} \right)}}{3} - \frac{b c^{3} d^{2} \operatorname{atanh}{\left(c x \right)}}{3} - \frac{b c^{2} d^{2} \operatorname{atanh}{\left(c x \right)}}{x} - \frac{b c^{2} d^{2}}{x} - \frac{b c d^{2} \operatorname{atanh}{\left(c x \right)}}{x^{2}} - \frac{b c d^{2}}{6 x^{2}} - \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\- \frac{a d^{2}}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**2*d**2/x - a*c*d**2/x**2 - a*d**2/(3*x**3) + 4*b*c**3*d**2*log(x)/3 - 4*b*c**3*d**2*log(x - 1/c)/3 - b*c**3*d**2*atanh(c*x)/3 - b*c**2*d**2*atanh(c*x)/x - b*c**2*d**2/x - b*c*d**2*atanh(c*x)/x**2 - b*c*d**2/(6*x**2) - b*d**2*atanh(c*x)/(3*x**3), Ne(c, 0)), (-a*d**2/(3*x**3), True))","A",0
18,1,189,0,2.020766," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))/x**5,x)","\begin{cases} - \frac{a c^{2} d^{2}}{2 x^{2}} - \frac{2 a c d^{2}}{3 x^{3}} - \frac{a d^{2}}{4 x^{4}} + \frac{2 b c^{4} d^{2} \log{\left(x \right)}}{3} - \frac{2 b c^{4} d^{2} \log{\left(x - \frac{1}{c} \right)}}{3} + \frac{b c^{4} d^{2} \operatorname{atanh}{\left(c x \right)}}{12} - \frac{3 b c^{3} d^{2}}{4 x} - \frac{b c^{2} d^{2} \operatorname{atanh}{\left(c x \right)}}{2 x^{2}} - \frac{b c^{2} d^{2}}{3 x^{2}} - \frac{2 b c d^{2} \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} - \frac{b c d^{2}}{12 x^{3}} - \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a d^{2}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**2*d**2/(2*x**2) - 2*a*c*d**2/(3*x**3) - a*d**2/(4*x**4) + 2*b*c**4*d**2*log(x)/3 - 2*b*c**4*d**2*log(x - 1/c)/3 + b*c**4*d**2*atanh(c*x)/12 - 3*b*c**3*d**2/(4*x) - b*c**2*d**2*atanh(c*x)/(2*x**2) - b*c**2*d**2/(3*x**2) - 2*b*c*d**2*atanh(c*x)/(3*x**3) - b*c*d**2/(12*x**3) - b*d**2*atanh(c*x)/(4*x**4), Ne(c, 0)), (-a*d**2/(4*x**4), True))","A",0
19,1,199,0,2.563832," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))/x**6,x)","\begin{cases} - \frac{a c^{2} d^{2}}{3 x^{3}} - \frac{a c d^{2}}{2 x^{4}} - \frac{a d^{2}}{5 x^{5}} + \frac{8 b c^{5} d^{2} \log{\left(x \right)}}{15} - \frac{8 b c^{5} d^{2} \log{\left(x - \frac{1}{c} \right)}}{15} - \frac{b c^{5} d^{2} \operatorname{atanh}{\left(c x \right)}}{30} - \frac{b c^{4} d^{2}}{2 x} - \frac{4 b c^{3} d^{2}}{15 x^{2}} - \frac{b c^{2} d^{2} \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} - \frac{b c^{2} d^{2}}{6 x^{3}} - \frac{b c d^{2} \operatorname{atanh}{\left(c x \right)}}{2 x^{4}} - \frac{b c d^{2}}{20 x^{4}} - \frac{b d^{2} \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a d^{2}}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**2*d**2/(3*x**3) - a*c*d**2/(2*x**4) - a*d**2/(5*x**5) + 8*b*c**5*d**2*log(x)/15 - 8*b*c**5*d**2*log(x - 1/c)/15 - b*c**5*d**2*atanh(c*x)/30 - b*c**4*d**2/(2*x) - 4*b*c**3*d**2/(15*x**2) - b*c**2*d**2*atanh(c*x)/(3*x**3) - b*c**2*d**2/(6*x**3) - b*c*d**2*atanh(c*x)/(2*x**4) - b*c*d**2/(20*x**4) - b*d**2*atanh(c*x)/(5*x**5), Ne(c, 0)), (-a*d**2/(5*x**5), True))","A",0
20,1,243,0,2.835222," ","integrate(x**3*(c*d*x+d)**3*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{3} d^{3} x^{7}}{7} + \frac{a c^{2} d^{3} x^{6}}{2} + \frac{3 a c d^{3} x^{5}}{5} + \frac{a d^{3} x^{4}}{4} + \frac{b c^{3} d^{3} x^{7} \operatorname{atanh}{\left(c x \right)}}{7} + \frac{b c^{2} d^{3} x^{6} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b c^{2} d^{3} x^{6}}{42} + \frac{3 b c d^{3} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b c d^{3} x^{5}}{10} + \frac{b d^{3} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{13 b d^{3} x^{4}}{70} + \frac{b d^{3} x^{3}}{4 c} + \frac{13 b d^{3} x^{2}}{35 c^{2}} + \frac{3 b d^{3} x}{4 c^{3}} + \frac{26 b d^{3} \log{\left(x - \frac{1}{c} \right)}}{35 c^{4}} - \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{140 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*d**3*x**7/7 + a*c**2*d**3*x**6/2 + 3*a*c*d**3*x**5/5 + a*d**3*x**4/4 + b*c**3*d**3*x**7*atanh(c*x)/7 + b*c**2*d**3*x**6*atanh(c*x)/2 + b*c**2*d**3*x**6/42 + 3*b*c*d**3*x**5*atanh(c*x)/5 + b*c*d**3*x**5/10 + b*d**3*x**4*atanh(c*x)/4 + 13*b*d**3*x**4/70 + b*d**3*x**3/(4*c) + 13*b*d**3*x**2/(35*c**2) + 3*b*d**3*x/(4*c**3) + 26*b*d**3*log(x - 1/c)/(35*c**4) - b*d**3*atanh(c*x)/(140*c**4), Ne(c, 0)), (a*d**3*x**4/4, True))","A",0
21,1,235,0,2.290753," ","integrate(x**2*(c*d*x+d)**3*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{3} d^{3} x^{6}}{6} + \frac{3 a c^{2} d^{3} x^{5}}{5} + \frac{3 a c d^{3} x^{4}}{4} + \frac{a d^{3} x^{3}}{3} + \frac{b c^{3} d^{3} x^{6} \operatorname{atanh}{\left(c x \right)}}{6} + \frac{3 b c^{2} d^{3} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b c^{2} d^{3} x^{5}}{30} + \frac{3 b c d^{3} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{3 b c d^{3} x^{4}}{20} + \frac{b d^{3} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{11 b d^{3} x^{3}}{36} + \frac{7 b d^{3} x^{2}}{15 c} + \frac{11 b d^{3} x}{12 c^{2}} + \frac{14 b d^{3} \log{\left(x - \frac{1}{c} \right)}}{15 c^{3}} + \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{60 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*d**3*x**6/6 + 3*a*c**2*d**3*x**5/5 + 3*a*c*d**3*x**4/4 + a*d**3*x**3/3 + b*c**3*d**3*x**6*atanh(c*x)/6 + 3*b*c**2*d**3*x**5*atanh(c*x)/5 + b*c**2*d**3*x**5/30 + 3*b*c*d**3*x**4*atanh(c*x)/4 + 3*b*c*d**3*x**4/20 + b*d**3*x**3*atanh(c*x)/3 + 11*b*d**3*x**3/36 + 7*b*d**3*x**2/(15*c) + 11*b*d**3*x/(12*c**2) + 14*b*d**3*log(x - 1/c)/(15*c**3) + b*d**3*atanh(c*x)/(60*c**3), Ne(c, 0)), (a*d**3*x**3/3, True))","A",0
22,1,211,0,1.793339," ","integrate(x*(c*d*x+d)**3*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{3} d^{3} x^{5}}{5} + \frac{3 a c^{2} d^{3} x^{4}}{4} + a c d^{3} x^{3} + \frac{a d^{3} x^{2}}{2} + \frac{b c^{3} d^{3} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{3 b c^{2} d^{3} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b c^{2} d^{3} x^{4}}{20} + b c d^{3} x^{3} \operatorname{atanh}{\left(c x \right)} + \frac{b c d^{3} x^{3}}{4} + \frac{b d^{3} x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{3 b d^{3} x^{2}}{5} + \frac{5 b d^{3} x}{4 c} + \frac{6 b d^{3} \log{\left(x - \frac{1}{c} \right)}}{5 c^{2}} - \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{20 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d^{3} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*d**3*x**5/5 + 3*a*c**2*d**3*x**4/4 + a*c*d**3*x**3 + a*d**3*x**2/2 + b*c**3*d**3*x**5*atanh(c*x)/5 + 3*b*c**2*d**3*x**4*atanh(c*x)/4 + b*c**2*d**3*x**4/20 + b*c*d**3*x**3*atanh(c*x) + b*c*d**3*x**3/4 + b*d**3*x**2*atanh(c*x)/2 + 3*b*d**3*x**2/5 + 5*b*d**3*x/(4*c) + 6*b*d**3*log(x - 1/c)/(5*c**2) - b*d**3*atanh(c*x)/(20*c**2), Ne(c, 0)), (a*d**3*x**2/2, True))","A",0
23,1,182,0,1.314066," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{3} d^{3} x^{4}}{4} + a c^{2} d^{3} x^{3} + \frac{3 a c d^{3} x^{2}}{2} + a d^{3} x + \frac{b c^{3} d^{3} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + b c^{2} d^{3} x^{3} \operatorname{atanh}{\left(c x \right)} + \frac{b c^{2} d^{3} x^{3}}{12} + \frac{3 b c d^{3} x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b c d^{3} x^{2}}{2} + b d^{3} x \operatorname{atanh}{\left(c x \right)} + \frac{7 b d^{3} x}{4} + \frac{2 b d^{3} \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{4 c} & \text{for}\: c \neq 0 \\a d^{3} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*d**3*x**4/4 + a*c**2*d**3*x**3 + 3*a*c*d**3*x**2/2 + a*d**3*x + b*c**3*d**3*x**4*atanh(c*x)/4 + b*c**2*d**3*x**3*atanh(c*x) + b*c**2*d**3*x**3/12 + 3*b*c*d**3*x**2*atanh(c*x)/2 + b*c*d**3*x**2/2 + b*d**3*x*atanh(c*x) + 7*b*d**3*x/4 + 2*b*d**3*log(x - 1/c)/c + b*d**3*atanh(c*x)/(4*c), Ne(c, 0)), (a*d**3*x, True))","A",0
24,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x,x)","d^{3} \left(\int 3 a c\, dx + \int \frac{a}{x}\, dx + \int 3 a c^{2} x\, dx + \int a c^{3} x^{2}\, dx + \int 3 b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int 3 b c^{2} x \operatorname{atanh}{\left(c x \right)}\, dx + \int b c^{3} x^{2} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a*c, x) + Integral(a/x, x) + Integral(3*a*c**2*x, x) + Integral(a*c**3*x**2, x) + Integral(3*b*c*atanh(c*x), x) + Integral(b*atanh(c*x)/x, x) + Integral(3*b*c**2*x*atanh(c*x), x) + Integral(b*c**3*x**2*atanh(c*x), x))","F",0
25,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x**2,x)","d^{3} \left(\int 3 a c^{2}\, dx + \int \frac{a}{x^{2}}\, dx + \int \frac{3 a c}{x}\, dx + \int a c^{3} x\, dx + \int 3 b c^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{3 b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int b c^{3} x \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a*c**2, x) + Integral(a/x**2, x) + Integral(3*a*c/x, x) + Integral(a*c**3*x, x) + Integral(3*b*c**2*atanh(c*x), x) + Integral(b*atanh(c*x)/x**2, x) + Integral(3*b*c*atanh(c*x)/x, x) + Integral(b*c**3*x*atanh(c*x), x))","F",0
26,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x**3,x)","d^{3} \left(\int a c^{3}\, dx + \int \frac{a}{x^{3}}\, dx + \int \frac{3 a c}{x^{2}}\, dx + \int \frac{3 a c^{2}}{x}\, dx + \int b c^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{3 b c \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{3 b c^{2} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**3*(Integral(a*c**3, x) + Integral(a/x**3, x) + Integral(3*a*c/x**2, x) + Integral(3*a*c**2/x, x) + Integral(b*c**3*atanh(c*x), x) + Integral(b*atanh(c*x)/x**3, x) + Integral(3*b*c*atanh(c*x)/x**2, x) + Integral(3*b*c**2*atanh(c*x)/x, x))","F",0
27,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x**4,x)","d^{3} \left(\int \frac{a}{x^{4}}\, dx + \int \frac{3 a c}{x^{3}}\, dx + \int \frac{3 a c^{2}}{x^{2}}\, dx + \int \frac{a c^{3}}{x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{3 b c \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{3 b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b c^{3} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**3*(Integral(a/x**4, x) + Integral(3*a*c/x**3, x) + Integral(3*a*c**2/x**2, x) + Integral(a*c**3/x, x) + Integral(b*atanh(c*x)/x**4, x) + Integral(3*b*c*atanh(c*x)/x**3, x) + Integral(3*b*c**2*atanh(c*x)/x**2, x) + Integral(b*c**3*atanh(c*x)/x, x))","F",0
28,1,207,0,2.021402," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x**5,x)","\begin{cases} - \frac{a c^{3} d^{3}}{x} - \frac{3 a c^{2} d^{3}}{2 x^{2}} - \frac{a c d^{3}}{x^{3}} - \frac{a d^{3}}{4 x^{4}} + 2 b c^{4} d^{3} \log{\left(x \right)} - 2 b c^{4} d^{3} \log{\left(x - \frac{1}{c} \right)} - \frac{b c^{4} d^{3} \operatorname{atanh}{\left(c x \right)}}{4} - \frac{b c^{3} d^{3} \operatorname{atanh}{\left(c x \right)}}{x} - \frac{7 b c^{3} d^{3}}{4 x} - \frac{3 b c^{2} d^{3} \operatorname{atanh}{\left(c x \right)}}{2 x^{2}} - \frac{b c^{2} d^{3}}{2 x^{2}} - \frac{b c d^{3} \operatorname{atanh}{\left(c x \right)}}{x^{3}} - \frac{b c d^{3}}{12 x^{3}} - \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a d^{3}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**3*d**3/x - 3*a*c**2*d**3/(2*x**2) - a*c*d**3/x**3 - a*d**3/(4*x**4) + 2*b*c**4*d**3*log(x) - 2*b*c**4*d**3*log(x - 1/c) - b*c**4*d**3*atanh(c*x)/4 - b*c**3*d**3*atanh(c*x)/x - 7*b*c**3*d**3/(4*x) - 3*b*c**2*d**3*atanh(c*x)/(2*x**2) - b*c**2*d**3/(2*x**2) - b*c*d**3*atanh(c*x)/x**3 - b*c*d**3/(12*x**3) - b*d**3*atanh(c*x)/(4*x**4), Ne(c, 0)), (-a*d**3/(4*x**4), True))","A",0
29,1,233,0,2.624351," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x**6,x)","\begin{cases} - \frac{a c^{3} d^{3}}{2 x^{2}} - \frac{a c^{2} d^{3}}{x^{3}} - \frac{3 a c d^{3}}{4 x^{4}} - \frac{a d^{3}}{5 x^{5}} + \frac{6 b c^{5} d^{3} \log{\left(x \right)}}{5} - \frac{6 b c^{5} d^{3} \log{\left(x - \frac{1}{c} \right)}}{5} + \frac{b c^{5} d^{3} \operatorname{atanh}{\left(c x \right)}}{20} - \frac{5 b c^{4} d^{3}}{4 x} - \frac{b c^{3} d^{3} \operatorname{atanh}{\left(c x \right)}}{2 x^{2}} - \frac{3 b c^{3} d^{3}}{5 x^{2}} - \frac{b c^{2} d^{3} \operatorname{atanh}{\left(c x \right)}}{x^{3}} - \frac{b c^{2} d^{3}}{4 x^{3}} - \frac{3 b c d^{3} \operatorname{atanh}{\left(c x \right)}}{4 x^{4}} - \frac{b c d^{3}}{20 x^{4}} - \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a d^{3}}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**3*d**3/(2*x**2) - a*c**2*d**3/x**3 - 3*a*c*d**3/(4*x**4) - a*d**3/(5*x**5) + 6*b*c**5*d**3*log(x)/5 - 6*b*c**5*d**3*log(x - 1/c)/5 + b*c**5*d**3*atanh(c*x)/20 - 5*b*c**4*d**3/(4*x) - b*c**3*d**3*atanh(c*x)/(2*x**2) - 3*b*c**3*d**3/(5*x**2) - b*c**2*d**3*atanh(c*x)/x**3 - b*c**2*d**3/(4*x**3) - 3*b*c*d**3*atanh(c*x)/(4*x**4) - b*c*d**3/(20*x**4) - b*d**3*atanh(c*x)/(5*x**5), Ne(c, 0)), (-a*d**3/(5*x**5), True))","A",0
30,1,257,0,3.305863," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))/x**7,x)","\begin{cases} - \frac{a c^{3} d^{3}}{3 x^{3}} - \frac{3 a c^{2} d^{3}}{4 x^{4}} - \frac{3 a c d^{3}}{5 x^{5}} - \frac{a d^{3}}{6 x^{6}} + \frac{14 b c^{6} d^{3} \log{\left(x \right)}}{15} - \frac{14 b c^{6} d^{3} \log{\left(x - \frac{1}{c} \right)}}{15} - \frac{b c^{6} d^{3} \operatorname{atanh}{\left(c x \right)}}{60} - \frac{11 b c^{5} d^{3}}{12 x} - \frac{7 b c^{4} d^{3}}{15 x^{2}} - \frac{b c^{3} d^{3} \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} - \frac{11 b c^{3} d^{3}}{36 x^{3}} - \frac{3 b c^{2} d^{3} \operatorname{atanh}{\left(c x \right)}}{4 x^{4}} - \frac{3 b c^{2} d^{3}}{20 x^{4}} - \frac{3 b c d^{3} \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} - \frac{b c d^{3}}{30 x^{5}} - \frac{b d^{3} \operatorname{atanh}{\left(c x \right)}}{6 x^{6}} & \text{for}\: c \neq 0 \\- \frac{a d^{3}}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**3*d**3/(3*x**3) - 3*a*c**2*d**3/(4*x**4) - 3*a*c*d**3/(5*x**5) - a*d**3/(6*x**6) + 14*b*c**6*d**3*log(x)/15 - 14*b*c**6*d**3*log(x - 1/c)/15 - b*c**6*d**3*atanh(c*x)/60 - 11*b*c**5*d**3/(12*x) - 7*b*c**4*d**3/(15*x**2) - b*c**3*d**3*atanh(c*x)/(3*x**3) - 11*b*c**3*d**3/(36*x**3) - 3*b*c**2*d**3*atanh(c*x)/(4*x**4) - 3*b*c**2*d**3/(20*x**4) - 3*b*c*d**3*atanh(c*x)/(5*x**5) - b*c*d**3/(30*x**5) - b*d**3*atanh(c*x)/(6*x**6), Ne(c, 0)), (-a*d**3/(6*x**6), True))","A",0
31,1,294,0,3.755661," ","integrate(x**3*(c*d*x+d)**4*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{4} x^{8}}{8} + \frac{4 a c^{3} d^{4} x^{7}}{7} + a c^{2} d^{4} x^{6} + \frac{4 a c d^{4} x^{5}}{5} + \frac{a d^{4} x^{4}}{4} + \frac{b c^{4} d^{4} x^{8} \operatorname{atanh}{\left(c x \right)}}{8} + \frac{4 b c^{3} d^{4} x^{7} \operatorname{atanh}{\left(c x \right)}}{7} + \frac{b c^{3} d^{4} x^{7}}{56} + b c^{2} d^{4} x^{6} \operatorname{atanh}{\left(c x \right)} + \frac{2 b c^{2} d^{4} x^{6}}{21} + \frac{4 b c d^{4} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{9 b c d^{4} x^{5}}{40} + \frac{b d^{4} x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{12 b d^{4} x^{4}}{35} + \frac{11 b d^{4} x^{3}}{24 c} + \frac{24 b d^{4} x^{2}}{35 c^{2}} + \frac{11 b d^{4} x}{8 c^{3}} + \frac{48 b d^{4} \log{\left(x - \frac{1}{c} \right)}}{35 c^{4}} - \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{280 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d^{4} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**4*x**8/8 + 4*a*c**3*d**4*x**7/7 + a*c**2*d**4*x**6 + 4*a*c*d**4*x**5/5 + a*d**4*x**4/4 + b*c**4*d**4*x**8*atanh(c*x)/8 + 4*b*c**3*d**4*x**7*atanh(c*x)/7 + b*c**3*d**4*x**7/56 + b*c**2*d**4*x**6*atanh(c*x) + 2*b*c**2*d**4*x**6/21 + 4*b*c*d**4*x**5*atanh(c*x)/5 + 9*b*c*d**4*x**5/40 + b*d**4*x**4*atanh(c*x)/4 + 12*b*d**4*x**4/35 + 11*b*d**4*x**3/(24*c) + 24*b*d**4*x**2/(35*c**2) + 11*b*d**4*x/(8*c**3) + 48*b*d**4*log(x - 1/c)/(35*c**4) - b*d**4*atanh(c*x)/(280*c**4), Ne(c, 0)), (a*d**4*x**4/4, True))","A",0
32,1,279,0,2.990052," ","integrate(x**2*(c*d*x+d)**4*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{4} x^{7}}{7} + \frac{2 a c^{3} d^{4} x^{6}}{3} + \frac{6 a c^{2} d^{4} x^{5}}{5} + a c d^{4} x^{4} + \frac{a d^{4} x^{3}}{3} + \frac{b c^{4} d^{4} x^{7} \operatorname{atanh}{\left(c x \right)}}{7} + \frac{2 b c^{3} d^{4} x^{6} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b c^{3} d^{4} x^{6}}{42} + \frac{6 b c^{2} d^{4} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{2 b c^{2} d^{4} x^{5}}{15} + b c d^{4} x^{4} \operatorname{atanh}{\left(c x \right)} + \frac{47 b c d^{4} x^{4}}{140} + \frac{b d^{4} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{5 b d^{4} x^{3}}{9} + \frac{88 b d^{4} x^{2}}{105 c} + \frac{5 b d^{4} x}{3 c^{2}} + \frac{176 b d^{4} \log{\left(x - \frac{1}{c} \right)}}{105 c^{3}} + \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{105 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d^{4} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**4*x**7/7 + 2*a*c**3*d**4*x**6/3 + 6*a*c**2*d**4*x**5/5 + a*c*d**4*x**4 + a*d**4*x**3/3 + b*c**4*d**4*x**7*atanh(c*x)/7 + 2*b*c**3*d**4*x**6*atanh(c*x)/3 + b*c**3*d**4*x**6/42 + 6*b*c**2*d**4*x**5*atanh(c*x)/5 + 2*b*c**2*d**4*x**5/15 + b*c*d**4*x**4*atanh(c*x) + 47*b*c*d**4*x**4/140 + b*d**4*x**3*atanh(c*x)/3 + 5*b*d**4*x**3/9 + 88*b*d**4*x**2/(105*c) + 5*b*d**4*x/(3*c**2) + 176*b*d**4*log(x - 1/c)/(105*c**3) + b*d**4*atanh(c*x)/(105*c**3), Ne(c, 0)), (a*d**4*x**3/3, True))","A",0
33,1,269,0,2.359145," ","integrate(x*(c*d*x+d)**4*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{4} x^{6}}{6} + \frac{4 a c^{3} d^{4} x^{5}}{5} + \frac{3 a c^{2} d^{4} x^{4}}{2} + \frac{4 a c d^{4} x^{3}}{3} + \frac{a d^{4} x^{2}}{2} + \frac{b c^{4} d^{4} x^{6} \operatorname{atanh}{\left(c x \right)}}{6} + \frac{4 b c^{3} d^{4} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b c^{3} d^{4} x^{5}}{30} + \frac{3 b c^{2} d^{4} x^{4} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b c^{2} d^{4} x^{4}}{5} + \frac{4 b c d^{4} x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{5 b c d^{4} x^{3}}{9} + \frac{b d^{4} x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{16 b d^{4} x^{2}}{15} + \frac{13 b d^{4} x}{6 c} + \frac{32 b d^{4} \log{\left(x - \frac{1}{c} \right)}}{15 c^{2}} - \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{30 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d^{4} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**4*x**6/6 + 4*a*c**3*d**4*x**5/5 + 3*a*c**2*d**4*x**4/2 + 4*a*c*d**4*x**3/3 + a*d**4*x**2/2 + b*c**4*d**4*x**6*atanh(c*x)/6 + 4*b*c**3*d**4*x**5*atanh(c*x)/5 + b*c**3*d**4*x**5/30 + 3*b*c**2*d**4*x**4*atanh(c*x)/2 + b*c**2*d**4*x**4/5 + 4*b*c*d**4*x**3*atanh(c*x)/3 + 5*b*c*d**4*x**3/9 + b*d**4*x**2*atanh(c*x)/2 + 16*b*d**4*x**2/15 + 13*b*d**4*x/(6*c) + 32*b*d**4*log(x - 1/c)/(15*c**2) - b*d**4*atanh(c*x)/(30*c**2), Ne(c, 0)), (a*d**4*x**2/2, True))","A",0
34,1,226,0,1.848867," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a c^{4} d^{4} x^{5}}{5} + a c^{3} d^{4} x^{4} + 2 a c^{2} d^{4} x^{3} + 2 a c d^{4} x^{2} + a d^{4} x + \frac{b c^{4} d^{4} x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + b c^{3} d^{4} x^{4} \operatorname{atanh}{\left(c x \right)} + \frac{b c^{3} d^{4} x^{4}}{20} + 2 b c^{2} d^{4} x^{3} \operatorname{atanh}{\left(c x \right)} + \frac{b c^{2} d^{4} x^{3}}{3} + 2 b c d^{4} x^{2} \operatorname{atanh}{\left(c x \right)} + \frac{11 b c d^{4} x^{2}}{10} + b d^{4} x \operatorname{atanh}{\left(c x \right)} + 3 b d^{4} x + \frac{16 b d^{4} \log{\left(x - \frac{1}{c} \right)}}{5 c} + \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{5 c} & \text{for}\: c \neq 0 \\a d^{4} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*d**4*x**5/5 + a*c**3*d**4*x**4 + 2*a*c**2*d**4*x**3 + 2*a*c*d**4*x**2 + a*d**4*x + b*c**4*d**4*x**5*atanh(c*x)/5 + b*c**3*d**4*x**4*atanh(c*x) + b*c**3*d**4*x**4/20 + 2*b*c**2*d**4*x**3*atanh(c*x) + b*c**2*d**4*x**3/3 + 2*b*c*d**4*x**2*atanh(c*x) + 11*b*c*d**4*x**2/10 + b*d**4*x*atanh(c*x) + 3*b*d**4*x + 16*b*d**4*log(x - 1/c)/(5*c) + b*d**4*atanh(c*x)/(5*c), Ne(c, 0)), (a*d**4*x, True))","A",0
35,0,0,0,0.000000," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x,x)","d^{4} \left(\int 4 a c\, dx + \int \frac{a}{x}\, dx + \int 6 a c^{2} x\, dx + \int 4 a c^{3} x^{2}\, dx + \int a c^{4} x^{3}\, dx + \int 4 b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int 6 b c^{2} x \operatorname{atanh}{\left(c x \right)}\, dx + \int 4 b c^{3} x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int b c^{4} x^{3} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**4*(Integral(4*a*c, x) + Integral(a/x, x) + Integral(6*a*c**2*x, x) + Integral(4*a*c**3*x**2, x) + Integral(a*c**4*x**3, x) + Integral(4*b*c*atanh(c*x), x) + Integral(b*atanh(c*x)/x, x) + Integral(6*b*c**2*x*atanh(c*x), x) + Integral(4*b*c**3*x**2*atanh(c*x), x) + Integral(b*c**4*x**3*atanh(c*x), x))","F",0
36,0,0,0,0.000000," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**2,x)","d^{4} \left(\int 6 a c^{2}\, dx + \int \frac{a}{x^{2}}\, dx + \int \frac{4 a c}{x}\, dx + \int 4 a c^{3} x\, dx + \int a c^{4} x^{2}\, dx + \int 6 b c^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{4 b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int 4 b c^{3} x \operatorname{atanh}{\left(c x \right)}\, dx + \int b c^{4} x^{2} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**4*(Integral(6*a*c**2, x) + Integral(a/x**2, x) + Integral(4*a*c/x, x) + Integral(4*a*c**3*x, x) + Integral(a*c**4*x**2, x) + Integral(6*b*c**2*atanh(c*x), x) + Integral(b*atanh(c*x)/x**2, x) + Integral(4*b*c*atanh(c*x)/x, x) + Integral(4*b*c**3*x*atanh(c*x), x) + Integral(b*c**4*x**2*atanh(c*x), x))","F",0
37,0,0,0,0.000000," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**3,x)","d^{4} \left(\int 4 a c^{3}\, dx + \int \frac{a}{x^{3}}\, dx + \int \frac{4 a c}{x^{2}}\, dx + \int \frac{6 a c^{2}}{x}\, dx + \int a c^{4} x\, dx + \int 4 b c^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{4 b c \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{6 b c^{2} \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int b c^{4} x \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**4*(Integral(4*a*c**3, x) + Integral(a/x**3, x) + Integral(4*a*c/x**2, x) + Integral(6*a*c**2/x, x) + Integral(a*c**4*x, x) + Integral(4*b*c**3*atanh(c*x), x) + Integral(b*atanh(c*x)/x**3, x) + Integral(4*b*c*atanh(c*x)/x**2, x) + Integral(6*b*c**2*atanh(c*x)/x, x) + Integral(b*c**4*x*atanh(c*x), x))","F",0
38,0,0,0,0.000000," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**4,x)","d^{4} \left(\int a c^{4}\, dx + \int \frac{a}{x^{4}}\, dx + \int \frac{4 a c}{x^{3}}\, dx + \int \frac{6 a c^{2}}{x^{2}}\, dx + \int \frac{4 a c^{3}}{x}\, dx + \int b c^{4} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{4 b c \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{6 b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{4 b c^{3} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**4*(Integral(a*c**4, x) + Integral(a/x**4, x) + Integral(4*a*c/x**3, x) + Integral(6*a*c**2/x**2, x) + Integral(4*a*c**3/x, x) + Integral(b*c**4*atanh(c*x), x) + Integral(b*atanh(c*x)/x**4, x) + Integral(4*b*c*atanh(c*x)/x**3, x) + Integral(6*b*c**2*atanh(c*x)/x**2, x) + Integral(4*b*c**3*atanh(c*x)/x, x))","F",0
39,0,0,0,0.000000," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**5,x)","d^{4} \left(\int \frac{a}{x^{5}}\, dx + \int \frac{4 a c}{x^{4}}\, dx + \int \frac{6 a c^{2}}{x^{3}}\, dx + \int \frac{4 a c^{3}}{x^{2}}\, dx + \int \frac{a c^{4}}{x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{4 b c \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{6 b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{4 b c^{3} \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b c^{4} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**4*(Integral(a/x**5, x) + Integral(4*a*c/x**4, x) + Integral(6*a*c**2/x**3, x) + Integral(4*a*c**3/x**2, x) + Integral(a*c**4/x, x) + Integral(b*atanh(c*x)/x**5, x) + Integral(4*b*c*atanh(c*x)/x**4, x) + Integral(6*b*c**2*atanh(c*x)/x**3, x) + Integral(4*b*c**3*atanh(c*x)/x**2, x) + Integral(b*c**4*atanh(c*x)/x, x))","F",0
40,1,253,0,2.700738," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**6,x)","\begin{cases} - \frac{a c^{4} d^{4}}{x} - \frac{2 a c^{3} d^{4}}{x^{2}} - \frac{2 a c^{2} d^{4}}{x^{3}} - \frac{a c d^{4}}{x^{4}} - \frac{a d^{4}}{5 x^{5}} + \frac{16 b c^{5} d^{4} \log{\left(x \right)}}{5} - \frac{16 b c^{5} d^{4} \log{\left(x - \frac{1}{c} \right)}}{5} - \frac{b c^{5} d^{4} \operatorname{atanh}{\left(c x \right)}}{5} - \frac{b c^{4} d^{4} \operatorname{atanh}{\left(c x \right)}}{x} - \frac{3 b c^{4} d^{4}}{x} - \frac{2 b c^{3} d^{4} \operatorname{atanh}{\left(c x \right)}}{x^{2}} - \frac{11 b c^{3} d^{4}}{10 x^{2}} - \frac{2 b c^{2} d^{4} \operatorname{atanh}{\left(c x \right)}}{x^{3}} - \frac{b c^{2} d^{4}}{3 x^{3}} - \frac{b c d^{4} \operatorname{atanh}{\left(c x \right)}}{x^{4}} - \frac{b c d^{4}}{20 x^{4}} - \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a d^{4}}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**4*d**4/x - 2*a*c**3*d**4/x**2 - 2*a*c**2*d**4/x**3 - a*c*d**4/x**4 - a*d**4/(5*x**5) + 16*b*c**5*d**4*log(x)/5 - 16*b*c**5*d**4*log(x - 1/c)/5 - b*c**5*d**4*atanh(c*x)/5 - b*c**4*d**4*atanh(c*x)/x - 3*b*c**4*d**4/x - 2*b*c**3*d**4*atanh(c*x)/x**2 - 11*b*c**3*d**4/(10*x**2) - 2*b*c**2*d**4*atanh(c*x)/x**3 - b*c**2*d**4/(3*x**3) - b*c*d**4*atanh(c*x)/x**4 - b*c*d**4/(20*x**4) - b*d**4*atanh(c*x)/(5*x**5), Ne(c, 0)), (-a*d**4/(5*x**5), True))","A",0
41,1,291,0,3.364578," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**7,x)","\begin{cases} - \frac{a c^{4} d^{4}}{2 x^{2}} - \frac{4 a c^{3} d^{4}}{3 x^{3}} - \frac{3 a c^{2} d^{4}}{2 x^{4}} - \frac{4 a c d^{4}}{5 x^{5}} - \frac{a d^{4}}{6 x^{6}} + \frac{32 b c^{6} d^{4} \log{\left(x \right)}}{15} - \frac{32 b c^{6} d^{4} \log{\left(x - \frac{1}{c} \right)}}{15} + \frac{b c^{6} d^{4} \operatorname{atanh}{\left(c x \right)}}{30} - \frac{13 b c^{5} d^{4}}{6 x} - \frac{b c^{4} d^{4} \operatorname{atanh}{\left(c x \right)}}{2 x^{2}} - \frac{16 b c^{4} d^{4}}{15 x^{2}} - \frac{4 b c^{3} d^{4} \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} - \frac{5 b c^{3} d^{4}}{9 x^{3}} - \frac{3 b c^{2} d^{4} \operatorname{atanh}{\left(c x \right)}}{2 x^{4}} - \frac{b c^{2} d^{4}}{5 x^{4}} - \frac{4 b c d^{4} \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} - \frac{b c d^{4}}{30 x^{5}} - \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{6 x^{6}} & \text{for}\: c \neq 0 \\- \frac{a d^{4}}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**4*d**4/(2*x**2) - 4*a*c**3*d**4/(3*x**3) - 3*a*c**2*d**4/(2*x**4) - 4*a*c*d**4/(5*x**5) - a*d**4/(6*x**6) + 32*b*c**6*d**4*log(x)/15 - 32*b*c**6*d**4*log(x - 1/c)/15 + b*c**6*d**4*atanh(c*x)/30 - 13*b*c**5*d**4/(6*x) - b*c**4*d**4*atanh(c*x)/(2*x**2) - 16*b*c**4*d**4/(15*x**2) - 4*b*c**3*d**4*atanh(c*x)/(3*x**3) - 5*b*c**3*d**4/(9*x**3) - 3*b*c**2*d**4*atanh(c*x)/(2*x**4) - b*c**2*d**4/(5*x**4) - 4*b*c*d**4*atanh(c*x)/(5*x**5) - b*c*d**4/(30*x**5) - b*d**4*atanh(c*x)/(6*x**6), Ne(c, 0)), (-a*d**4/(6*x**6), True))","A",0
42,1,301,0,4.187702," ","integrate((c*d*x+d)**4*(a+b*atanh(c*x))/x**8,x)","\begin{cases} - \frac{a c^{4} d^{4}}{3 x^{3}} - \frac{a c^{3} d^{4}}{x^{4}} - \frac{6 a c^{2} d^{4}}{5 x^{5}} - \frac{2 a c d^{4}}{3 x^{6}} - \frac{a d^{4}}{7 x^{7}} + \frac{176 b c^{7} d^{4} \log{\left(x \right)}}{105} - \frac{176 b c^{7} d^{4} \log{\left(x - \frac{1}{c} \right)}}{105} - \frac{b c^{7} d^{4} \operatorname{atanh}{\left(c x \right)}}{105} - \frac{5 b c^{6} d^{4}}{3 x} - \frac{88 b c^{5} d^{4}}{105 x^{2}} - \frac{b c^{4} d^{4} \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} - \frac{5 b c^{4} d^{4}}{9 x^{3}} - \frac{b c^{3} d^{4} \operatorname{atanh}{\left(c x \right)}}{x^{4}} - \frac{47 b c^{3} d^{4}}{140 x^{4}} - \frac{6 b c^{2} d^{4} \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} - \frac{2 b c^{2} d^{4}}{15 x^{5}} - \frac{2 b c d^{4} \operatorname{atanh}{\left(c x \right)}}{3 x^{6}} - \frac{b c d^{4}}{42 x^{6}} - \frac{b d^{4} \operatorname{atanh}{\left(c x \right)}}{7 x^{7}} & \text{for}\: c \neq 0 \\- \frac{a d^{4}}{7 x^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*c**4*d**4/(3*x**3) - a*c**3*d**4/x**4 - 6*a*c**2*d**4/(5*x**5) - 2*a*c*d**4/(3*x**6) - a*d**4/(7*x**7) + 176*b*c**7*d**4*log(x)/105 - 176*b*c**7*d**4*log(x - 1/c)/105 - b*c**7*d**4*atanh(c*x)/105 - 5*b*c**6*d**4/(3*x) - 88*b*c**5*d**4/(105*x**2) - b*c**4*d**4*atanh(c*x)/(3*x**3) - 5*b*c**4*d**4/(9*x**3) - b*c**3*d**4*atanh(c*x)/x**4 - 47*b*c**3*d**4/(140*x**4) - 6*b*c**2*d**4*atanh(c*x)/(5*x**5) - 2*b*c**2*d**4/(15*x**5) - 2*b*c*d**4*atanh(c*x)/(3*x**6) - b*c*d**4/(42*x**6) - b*d**4*atanh(c*x)/(7*x**7), Ne(c, 0)), (-a*d**4/(7*x**7), True))","A",0
43,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))/(c*d*x+d),x)","\frac{\int \frac{a x^{3}}{c x + 1}\, dx + \int \frac{b x^{3} \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a*x**3/(c*x + 1), x) + Integral(b*x**3*atanh(c*x)/(c*x + 1), x))/d","F",0
44,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))/(c*d*x+d),x)","\frac{\int \frac{a x^{2}}{c x + 1}\, dx + \int \frac{b x^{2} \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a*x**2/(c*x + 1), x) + Integral(b*x**2*atanh(c*x)/(c*x + 1), x))/d","F",0
45,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))/(c*d*x+d),x)","\frac{\int \frac{a x}{c x + 1}\, dx + \int \frac{b x \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a*x/(c*x + 1), x) + Integral(b*x*atanh(c*x)/(c*x + 1), x))/d","F",0
46,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(c*d*x+d),x)","\frac{\int \frac{a}{c x + 1}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a/(c*x + 1), x) + Integral(b*atanh(c*x)/(c*x + 1), x))/d","F",0
47,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x/(c*d*x+d),x)","\frac{\int \frac{a}{c x^{2} + x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c x^{2} + x}\, dx}{d}"," ",0,"(Integral(a/(c*x**2 + x), x) + Integral(b*atanh(c*x)/(c*x**2 + x), x))/d","F",0
48,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**2/(c*d*x+d),x)","\frac{\int \frac{a}{c x^{3} + x^{2}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c x^{3} + x^{2}}\, dx}{d}"," ",0,"(Integral(a/(c*x**3 + x**2), x) + Integral(b*atanh(c*x)/(c*x**3 + x**2), x))/d","F",0
49,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**3/(c*d*x+d),x)","\frac{\int \frac{a}{c x^{4} + x^{3}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c x^{4} + x^{3}}\, dx}{d}"," ",0,"(Integral(a/(c*x**4 + x**3), x) + Integral(b*atanh(c*x)/(c*x**4 + x**3), x))/d","F",0
50,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**4/(c*d*x+d),x)","\frac{\int \frac{a}{c x^{5} + x^{4}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c x^{5} + x^{4}}\, dx}{d}"," ",0,"(Integral(a/(c*x**5 + x**4), x) + Integral(b*atanh(c*x)/(c*x**5 + x**4), x))/d","F",0
51,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))/(c*d*x+d)**2,x)","\frac{\int \frac{a x^{3}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b x^{3} \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x**3/(c**2*x**2 + 2*c*x + 1), x) + Integral(b*x**3*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
52,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))/(c*d*x+d)**2,x)","\frac{\int \frac{a x^{2}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b x^{2} \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(b*x**2*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
53,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))/(c*d*x+d)**2,x)","\frac{\int \frac{a x}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b x \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a*x/(c**2*x**2 + 2*c*x + 1), x) + Integral(b*x*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
54,1,121,0,1.385015," ","integrate((a+b*atanh(c*x))/(c*d*x+d)**2,x)","\begin{cases} - \frac{2 a}{2 c^{2} d^{2} x + 2 c d^{2}} + \frac{b c x \operatorname{atanh}{\left(c x \right)}}{2 c^{2} d^{2} x + 2 c d^{2}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{2 c^{2} d^{2} x + 2 c d^{2}} - \frac{b}{2 c^{2} d^{2} x + 2 c d^{2}} & \text{for}\: d \neq 0 \\\tilde{\infty} \left(a x + b x \operatorname{atanh}{\left(c x \right)} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b \operatorname{atanh}{\left(c x \right)}}{c}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a/(2*c**2*d**2*x + 2*c*d**2) + b*c*x*atanh(c*x)/(2*c**2*d**2*x + 2*c*d**2) - b*atanh(c*x)/(2*c**2*d**2*x + 2*c*d**2) - b/(2*c**2*d**2*x + 2*c*d**2), Ne(d, 0)), (zoo*(a*x + b*x*atanh(c*x) + b*log(x - 1/c)/c + b*atanh(c*x)/c), True))","A",0
55,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x/(c*d*x+d)**2,x)","\frac{\int \frac{a}{c^{2} x^{3} + 2 c x^{2} + x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{3} + 2 c x^{2} + x}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**2*x**3 + 2*c*x**2 + x), x) + Integral(b*atanh(c*x)/(c**2*x**3 + 2*c*x**2 + x), x))/d**2","F",0
56,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**2/(c*d*x+d)**2,x)","\frac{\int \frac{a}{c^{2} x^{4} + 2 c x^{3} + x^{2}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{4} + 2 c x^{3} + x^{2}}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**2*x**4 + 2*c*x**3 + x**2), x) + Integral(b*atanh(c*x)/(c**2*x**4 + 2*c*x**3 + x**2), x))/d**2","F",0
57,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**3/(c*d*x+d)**2,x)","\frac{\int \frac{a}{c^{2} x^{5} + 2 c x^{4} + x^{3}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{5} + 2 c x^{4} + x^{3}}\, dx}{d^{2}}"," ",0,"(Integral(a/(c**2*x**5 + 2*c*x**4 + x**3), x) + Integral(b*atanh(c*x)/(c**2*x**5 + 2*c*x**4 + x**3), x))/d**2","F",0
58,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x))/(c*d*x+d)**3,x)","\frac{\int \frac{a x^{4}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b x^{4} \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x**4/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b*x**4*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
59,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))/(c*d*x+d)**3,x)","\frac{\int \frac{a x^{3}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b x^{3} \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x**3/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b*x**3*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
60,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))/(c*d*x+d)**3,x)","\frac{\int \frac{a x^{2}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b x^{2} \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a*x**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b*x**2*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
61,1,306,0,2.259306," ","integrate(x*(a+b*atanh(c*x))/(c*d*x+d)**3,x)","\begin{cases} - \frac{8 a c x}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} - \frac{4 a}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} + \frac{3 b c^{2} x^{2} \operatorname{atanh}{\left(c x \right)}}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} - \frac{2 b c x \operatorname{atanh}{\left(c x \right)}}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} - \frac{3 b c x}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} - \frac{2 b}{8 c^{4} d^{3} x^{2} + 16 c^{3} d^{3} x + 8 c^{2} d^{3}} & \text{for}\: d \neq 0 \\\tilde{\infty} \left(\frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b x}{2 c} - \frac{b \operatorname{atanh}{\left(c x \right)}}{2 c^{2}}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*a*c*x/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3) - 4*a/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3) + 3*b*c**2*x**2*atanh(c*x)/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3) - 2*b*c*x*atanh(c*x)/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3) - 3*b*c*x/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3) - b*atanh(c*x)/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3) - 2*b/(8*c**4*d**3*x**2 + 16*c**3*d**3*x + 8*c**2*d**3), Ne(d, 0)), (zoo*(a*x**2/2 + b*x**2*atanh(c*x)/2 + b*x/(2*c) - b*atanh(c*x)/(2*c**2)), True))","A",0
62,1,250,0,2.154401," ","integrate((a+b*atanh(c*x))/(c*d*x+d)**3,x)","\begin{cases} - \frac{4 a}{8 c^{3} d^{3} x^{2} + 16 c^{2} d^{3} x + 8 c d^{3}} + \frac{b c^{2} x^{2} \operatorname{atanh}{\left(c x \right)}}{8 c^{3} d^{3} x^{2} + 16 c^{2} d^{3} x + 8 c d^{3}} + \frac{2 b c x \operatorname{atanh}{\left(c x \right)}}{8 c^{3} d^{3} x^{2} + 16 c^{2} d^{3} x + 8 c d^{3}} - \frac{b c x}{8 c^{3} d^{3} x^{2} + 16 c^{2} d^{3} x + 8 c d^{3}} - \frac{3 b \operatorname{atanh}{\left(c x \right)}}{8 c^{3} d^{3} x^{2} + 16 c^{2} d^{3} x + 8 c d^{3}} - \frac{2 b}{8 c^{3} d^{3} x^{2} + 16 c^{2} d^{3} x + 8 c d^{3}} & \text{for}\: d \neq 0 \\\tilde{\infty} \left(a x + b x \operatorname{atanh}{\left(c x \right)} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{c} + \frac{b \operatorname{atanh}{\left(c x \right)}}{c}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*a/(8*c**3*d**3*x**2 + 16*c**2*d**3*x + 8*c*d**3) + b*c**2*x**2*atanh(c*x)/(8*c**3*d**3*x**2 + 16*c**2*d**3*x + 8*c*d**3) + 2*b*c*x*atanh(c*x)/(8*c**3*d**3*x**2 + 16*c**2*d**3*x + 8*c*d**3) - b*c*x/(8*c**3*d**3*x**2 + 16*c**2*d**3*x + 8*c*d**3) - 3*b*atanh(c*x)/(8*c**3*d**3*x**2 + 16*c**2*d**3*x + 8*c*d**3) - 2*b/(8*c**3*d**3*x**2 + 16*c**2*d**3*x + 8*c*d**3), Ne(d, 0)), (zoo*(a*x + b*x*atanh(c*x) + b*log(x - 1/c)/c + b*atanh(c*x)/c), True))","A",0
63,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x/(c*d*x+d)**3,x)","\frac{\int \frac{a}{c^{3} x^{4} + 3 c^{2} x^{3} + 3 c x^{2} + x}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{4} + 3 c^{2} x^{3} + 3 c x^{2} + x}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**3*x**4 + 3*c**2*x**3 + 3*c*x**2 + x), x) + Integral(b*atanh(c*x)/(c**3*x**4 + 3*c**2*x**3 + 3*c*x**2 + x), x))/d**3","F",0
64,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**2/(c*d*x+d)**3,x)","\frac{\int \frac{a}{c^{3} x^{5} + 3 c^{2} x^{4} + 3 c x^{3} + x^{2}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{5} + 3 c^{2} x^{4} + 3 c x^{3} + x^{2}}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**3*x**5 + 3*c**2*x**4 + 3*c*x**3 + x**2), x) + Integral(b*atanh(c*x)/(c**3*x**5 + 3*c**2*x**4 + 3*c*x**3 + x**2), x))/d**3","F",0
65,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**3/(c*d*x+d)**3,x)","\frac{\int \frac{a}{c^{3} x^{6} + 3 c^{2} x^{5} + 3 c x^{4} + x^{3}}\, dx + \int \frac{b \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{6} + 3 c^{2} x^{5} + 3 c x^{4} + x^{3}}\, dx}{d^{3}}"," ",0,"(Integral(a/(c**3*x**6 + 3*c**2*x**5 + 3*c*x**4 + x**3), x) + Integral(b*atanh(c*x)/(c**3*x**6 + 3*c**2*x**5 + 3*c*x**4 + x**3), x))/d**3","F",0
66,1,294,0,2.756348," ","integrate((a+b*atanh(c*x))/(c*x+1)**4,x)","\begin{cases} - \frac{24 a}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} + \frac{3 b c^{3} x^{3} \operatorname{atanh}{\left(c x \right)}}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} + \frac{9 b c^{2} x^{2} \operatorname{atanh}{\left(c x \right)}}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} - \frac{3 b c^{2} x^{2}}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} + \frac{9 b c x \operatorname{atanh}{\left(c x \right)}}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} - \frac{9 b c x}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} - \frac{21 b \operatorname{atanh}{\left(c x \right)}}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} - \frac{10 b}{72 c^{4} x^{3} + 216 c^{3} x^{2} + 216 c^{2} x + 72 c} & \text{for}\: c \neq 0 \\a x & \text{otherwise} \end{cases}"," ",0,"Piecewise((-24*a/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) + 3*b*c**3*x**3*atanh(c*x)/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) + 9*b*c**2*x**2*atanh(c*x)/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) - 3*b*c**2*x**2/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) + 9*b*c*x*atanh(c*x)/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) - 9*b*c*x/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) - 21*b*atanh(c*x)/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c) - 10*b/(72*c**4*x**3 + 216*c**3*x**2 + 216*c**2*x + 72*c), Ne(c, 0)), (a*x, True))","A",0
67,0,0,0,0.000000," ","integrate(atanh(a*x)/(a*c*x**2+c*x),x)","\frac{\int \frac{\operatorname{atanh}{\left(a x \right)}}{a x^{2} + x}\, dx}{c}"," ",0,"Integral(atanh(a*x)/(a*x**2 + x), x)/c","F",0
68,0,0,0,0.000000," ","integrate(x**3*(c*d*x+d)*(a+b*atanh(c*x))**2,x)","d \left(\int a^{2} x^{3}\, dx + \int a^{2} c x^{4}\, dx + \int b^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int b^{2} c x^{4} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b c x^{4} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a**2*x**3, x) + Integral(a**2*c*x**4, x) + Integral(b**2*x**3*atanh(c*x)**2, x) + Integral(2*a*b*x**3*atanh(c*x), x) + Integral(b**2*c*x**4*atanh(c*x)**2, x) + Integral(2*a*b*c*x**4*atanh(c*x), x))","F",0
69,0,0,0,0.000000," ","integrate(x**2*(c*d*x+d)*(a+b*atanh(c*x))**2,x)","d \left(\int a^{2} x^{2}\, dx + \int a^{2} c x^{3}\, dx + \int b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int b^{2} c x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b c x^{3} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a**2*x**2, x) + Integral(a**2*c*x**3, x) + Integral(b**2*x**2*atanh(c*x)**2, x) + Integral(2*a*b*x**2*atanh(c*x), x) + Integral(b**2*c*x**3*atanh(c*x)**2, x) + Integral(2*a*b*c*x**3*atanh(c*x), x))","F",0
70,0,0,0,0.000000," ","integrate(x*(c*d*x+d)*(a+b*atanh(c*x))**2,x)","d \left(\int a^{2} x\, dx + \int a^{2} c x^{2}\, dx + \int b^{2} x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x \operatorname{atanh}{\left(c x \right)}\, dx + \int b^{2} c x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b c x^{2} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a**2*x, x) + Integral(a**2*c*x**2, x) + Integral(b**2*x*atanh(c*x)**2, x) + Integral(2*a*b*x*atanh(c*x), x) + Integral(b**2*c*x**2*atanh(c*x)**2, x) + Integral(2*a*b*c*x**2*atanh(c*x), x))","F",0
71,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))**2,x)","d \left(\int a^{2}\, dx + \int b^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b \operatorname{atanh}{\left(c x \right)}\, dx + \int a^{2} c x\, dx + \int b^{2} c x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b c x \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d*(Integral(a**2, x) + Integral(b**2*atanh(c*x)**2, x) + Integral(2*a*b*atanh(c*x), x) + Integral(a**2*c*x, x) + Integral(b**2*c*x*atanh(c*x)**2, x) + Integral(2*a*b*c*x*atanh(c*x), x))","F",0
72,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))**2/x,x)","d \left(\int a^{2} c\, dx + \int \frac{a^{2}}{x}\, dx + \int b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int 2 a b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d*(Integral(a**2*c, x) + Integral(a**2/x, x) + Integral(b**2*c*atanh(c*x)**2, x) + Integral(b**2*atanh(c*x)**2/x, x) + Integral(2*a*b*c*atanh(c*x), x) + Integral(2*a*b*atanh(c*x)/x, x))","F",0
73,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))**2/x**2,x)","d \left(\int \frac{a^{2}}{x^{2}}\, dx + \int \frac{a^{2} c}{x}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{2 a b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d*(Integral(a**2/x**2, x) + Integral(a**2*c/x, x) + Integral(b**2*atanh(c*x)**2/x**2, x) + Integral(2*a*b*atanh(c*x)/x**2, x) + Integral(b**2*c*atanh(c*x)**2/x, x) + Integral(2*a*b*c*atanh(c*x)/x, x))","F",0
74,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))**2/x**3,x)","d \left(\int \frac{a^{2}}{x^{3}}\, dx + \int \frac{a^{2} c}{x^{2}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 a b c \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d*(Integral(a**2/x**3, x) + Integral(a**2*c/x**2, x) + Integral(b**2*atanh(c*x)**2/x**3, x) + Integral(2*a*b*atanh(c*x)/x**3, x) + Integral(b**2*c*atanh(c*x)**2/x**2, x) + Integral(2*a*b*c*atanh(c*x)/x**2, x))","F",0
75,0,0,0,0.000000," ","integrate((c*d*x+d)*(a+b*atanh(c*x))**2/x**4,x)","d \left(\int \frac{a^{2}}{x^{4}}\, dx + \int \frac{a^{2} c}{x^{3}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b c \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx\right)"," ",0,"d*(Integral(a**2/x**4, x) + Integral(a**2*c/x**3, x) + Integral(b**2*atanh(c*x)**2/x**4, x) + Integral(2*a*b*atanh(c*x)/x**4, x) + Integral(b**2*c*atanh(c*x)**2/x**3, x) + Integral(2*a*b*c*atanh(c*x)/x**3, x))","F",0
76,0,0,0,0.000000," ","integrate(x**3*(c*d*x+d)**2*(a+b*atanh(c*x))**2,x)","d^{2} \left(\int a^{2} x^{3}\, dx + \int 2 a^{2} c x^{4}\, dx + \int a^{2} c^{2} x^{5}\, dx + \int b^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 b^{2} c x^{4} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{2} x^{5} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 4 a b c x^{4} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{2} x^{5} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a**2*x**3, x) + Integral(2*a**2*c*x**4, x) + Integral(a**2*c**2*x**5, x) + Integral(b**2*x**3*atanh(c*x)**2, x) + Integral(2*a*b*x**3*atanh(c*x), x) + Integral(2*b**2*c*x**4*atanh(c*x)**2, x) + Integral(b**2*c**2*x**5*atanh(c*x)**2, x) + Integral(4*a*b*c*x**4*atanh(c*x), x) + Integral(2*a*b*c**2*x**5*atanh(c*x), x))","F",0
77,0,0,0,0.000000," ","integrate(x**2*(c*d*x+d)**2*(a+b*atanh(c*x))**2,x)","d^{2} \left(\int a^{2} x^{2}\, dx + \int 2 a^{2} c x^{3}\, dx + \int a^{2} c^{2} x^{4}\, dx + \int b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 b^{2} c x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{2} x^{4} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 4 a b c x^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{2} x^{4} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a**2*x**2, x) + Integral(2*a**2*c*x**3, x) + Integral(a**2*c**2*x**4, x) + Integral(b**2*x**2*atanh(c*x)**2, x) + Integral(2*a*b*x**2*atanh(c*x), x) + Integral(2*b**2*c*x**3*atanh(c*x)**2, x) + Integral(b**2*c**2*x**4*atanh(c*x)**2, x) + Integral(4*a*b*c*x**3*atanh(c*x), x) + Integral(2*a*b*c**2*x**4*atanh(c*x), x))","F",0
78,0,0,0,0.000000," ","integrate(x*(c*d*x+d)**2*(a+b*atanh(c*x))**2,x)","d^{2} \left(\int a^{2} x\, dx + \int 2 a^{2} c x^{2}\, dx + \int a^{2} c^{2} x^{3}\, dx + \int b^{2} x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 b^{2} c x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 4 a b c x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{2} x^{3} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a**2*x, x) + Integral(2*a**2*c*x**2, x) + Integral(a**2*c**2*x**3, x) + Integral(b**2*x*atanh(c*x)**2, x) + Integral(2*a*b*x*atanh(c*x), x) + Integral(2*b**2*c*x**2*atanh(c*x)**2, x) + Integral(b**2*c**2*x**3*atanh(c*x)**2, x) + Integral(4*a*b*c*x**2*atanh(c*x), x) + Integral(2*a*b*c**2*x**3*atanh(c*x), x))","F",0
79,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))**2,x)","d^{2} \left(\int a^{2}\, dx + \int b^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a^{2} c x\, dx + \int a^{2} c^{2} x^{2}\, dx + \int 2 b^{2} c x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 4 a b c x \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{2} x^{2} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(a**2, x) + Integral(b**2*atanh(c*x)**2, x) + Integral(2*a*b*atanh(c*x), x) + Integral(2*a**2*c*x, x) + Integral(a**2*c**2*x**2, x) + Integral(2*b**2*c*x*atanh(c*x)**2, x) + Integral(b**2*c**2*x**2*atanh(c*x)**2, x) + Integral(4*a*b*c*x*atanh(c*x), x) + Integral(2*a*b*c**2*x**2*atanh(c*x), x))","F",0
80,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))**2/x,x)","d^{2} \left(\int 2 a^{2} c\, dx + \int \frac{a^{2}}{x}\, dx + \int a^{2} c^{2} x\, dx + \int 2 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int 4 a b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int b^{2} c^{2} x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b c^{2} x \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**2*(Integral(2*a**2*c, x) + Integral(a**2/x, x) + Integral(a**2*c**2*x, x) + Integral(2*b**2*c*atanh(c*x)**2, x) + Integral(b**2*atanh(c*x)**2/x, x) + Integral(4*a*b*c*atanh(c*x), x) + Integral(2*a*b*atanh(c*x)/x, x) + Integral(b**2*c**2*x*atanh(c*x)**2, x) + Integral(2*a*b*c**2*x*atanh(c*x), x))","F",0
81,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))**2/x**2,x)","d^{2} \left(\int a^{2} c^{2}\, dx + \int \frac{a^{2}}{x^{2}}\, dx + \int \frac{2 a^{2} c}{x}\, dx + \int b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int 2 a b c^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{4 a b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**2*(Integral(a**2*c**2, x) + Integral(a**2/x**2, x) + Integral(2*a**2*c/x, x) + Integral(b**2*c**2*atanh(c*x)**2, x) + Integral(b**2*atanh(c*x)**2/x**2, x) + Integral(2*a*b*c**2*atanh(c*x), x) + Integral(2*a*b*atanh(c*x)/x**2, x) + Integral(2*b**2*c*atanh(c*x)**2/x, x) + Integral(4*a*b*c*atanh(c*x)/x, x))","F",0
82,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))**2/x**3,x)","d^{2} \left(\int \frac{a^{2}}{x^{3}}\, dx + \int \frac{2 a^{2} c}{x^{2}}\, dx + \int \frac{a^{2} c^{2}}{x}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{4 a b c \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**2*(Integral(a**2/x**3, x) + Integral(2*a**2*c/x**2, x) + Integral(a**2*c**2/x, x) + Integral(b**2*atanh(c*x)**2/x**3, x) + Integral(2*a*b*atanh(c*x)/x**3, x) + Integral(2*b**2*c*atanh(c*x)**2/x**2, x) + Integral(b**2*c**2*atanh(c*x)**2/x, x) + Integral(4*a*b*c*atanh(c*x)/x**2, x) + Integral(2*a*b*c**2*atanh(c*x)/x, x))","F",0
83,0,0,0,0.000000," ","integrate((c*d*x+d)**2*(a+b*atanh(c*x))**2/x**4,x)","d^{2} \left(\int \frac{a^{2}}{x^{4}}\, dx + \int \frac{2 a^{2} c}{x^{3}}\, dx + \int \frac{a^{2} c^{2}}{x^{2}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{4 a b c \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d**2*(Integral(a**2/x**4, x) + Integral(2*a**2*c/x**3, x) + Integral(a**2*c**2/x**2, x) + Integral(b**2*atanh(c*x)**2/x**4, x) + Integral(2*a*b*atanh(c*x)/x**4, x) + Integral(2*b**2*c*atanh(c*x)**2/x**3, x) + Integral(b**2*c**2*atanh(c*x)**2/x**2, x) + Integral(4*a*b*c*atanh(c*x)/x**3, x) + Integral(2*a*b*c**2*atanh(c*x)/x**2, x))","F",0
84,0,0,0,0.000000," ","integrate(x**3*(c*d*x+d)**3*(a+b*atanh(c*x))**2,x)","d^{3} \left(\int a^{2} x^{3}\, dx + \int 3 a^{2} c x^{4}\, dx + \int 3 a^{2} c^{2} x^{5}\, dx + \int a^{2} c^{3} x^{6}\, dx + \int b^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int 3 b^{2} c x^{4} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 3 b^{2} c^{2} x^{5} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{3} x^{6} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 6 a b c x^{4} \operatorname{atanh}{\left(c x \right)}\, dx + \int 6 a b c^{2} x^{5} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{3} x^{6} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a**2*x**3, x) + Integral(3*a**2*c*x**4, x) + Integral(3*a**2*c**2*x**5, x) + Integral(a**2*c**3*x**6, x) + Integral(b**2*x**3*atanh(c*x)**2, x) + Integral(2*a*b*x**3*atanh(c*x), x) + Integral(3*b**2*c*x**4*atanh(c*x)**2, x) + Integral(3*b**2*c**2*x**5*atanh(c*x)**2, x) + Integral(b**2*c**3*x**6*atanh(c*x)**2, x) + Integral(6*a*b*c*x**4*atanh(c*x), x) + Integral(6*a*b*c**2*x**5*atanh(c*x), x) + Integral(2*a*b*c**3*x**6*atanh(c*x), x))","F",0
85,0,0,0,0.000000," ","integrate(x**2*(c*d*x+d)**3*(a+b*atanh(c*x))**2,x)","d^{3} \left(\int a^{2} x^{2}\, dx + \int 3 a^{2} c x^{3}\, dx + \int 3 a^{2} c^{2} x^{4}\, dx + \int a^{2} c^{3} x^{5}\, dx + \int b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int 3 b^{2} c x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 3 b^{2} c^{2} x^{4} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{3} x^{5} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 6 a b c x^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int 6 a b c^{2} x^{4} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{3} x^{5} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a**2*x**2, x) + Integral(3*a**2*c*x**3, x) + Integral(3*a**2*c**2*x**4, x) + Integral(a**2*c**3*x**5, x) + Integral(b**2*x**2*atanh(c*x)**2, x) + Integral(2*a*b*x**2*atanh(c*x), x) + Integral(3*b**2*c*x**3*atanh(c*x)**2, x) + Integral(3*b**2*c**2*x**4*atanh(c*x)**2, x) + Integral(b**2*c**3*x**5*atanh(c*x)**2, x) + Integral(6*a*b*c*x**3*atanh(c*x), x) + Integral(6*a*b*c**2*x**4*atanh(c*x), x) + Integral(2*a*b*c**3*x**5*atanh(c*x), x))","F",0
86,0,0,0,0.000000," ","integrate(x*(c*d*x+d)**3*(a+b*atanh(c*x))**2,x)","d^{3} \left(\int a^{2} x\, dx + \int 3 a^{2} c x^{2}\, dx + \int 3 a^{2} c^{2} x^{3}\, dx + \int a^{2} c^{3} x^{4}\, dx + \int b^{2} x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b x \operatorname{atanh}{\left(c x \right)}\, dx + \int 3 b^{2} c x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 3 b^{2} c^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{3} x^{4} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 6 a b c x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int 6 a b c^{2} x^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{3} x^{4} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a**2*x, x) + Integral(3*a**2*c*x**2, x) + Integral(3*a**2*c**2*x**3, x) + Integral(a**2*c**3*x**4, x) + Integral(b**2*x*atanh(c*x)**2, x) + Integral(2*a*b*x*atanh(c*x), x) + Integral(3*b**2*c*x**2*atanh(c*x)**2, x) + Integral(3*b**2*c**2*x**3*atanh(c*x)**2, x) + Integral(b**2*c**3*x**4*atanh(c*x)**2, x) + Integral(6*a*b*c*x**2*atanh(c*x), x) + Integral(6*a*b*c**2*x**3*atanh(c*x), x) + Integral(2*a*b*c**3*x**4*atanh(c*x), x))","F",0
87,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2,x)","d^{3} \left(\int a^{2}\, dx + \int b^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 2 a b \operatorname{atanh}{\left(c x \right)}\, dx + \int 3 a^{2} c x\, dx + \int 3 a^{2} c^{2} x^{2}\, dx + \int a^{2} c^{3} x^{3}\, dx + \int 3 b^{2} c x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 3 b^{2} c^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{3} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 6 a b c x \operatorname{atanh}{\left(c x \right)}\, dx + \int 6 a b c^{2} x^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{3} x^{3} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(a**2, x) + Integral(b**2*atanh(c*x)**2, x) + Integral(2*a*b*atanh(c*x), x) + Integral(3*a**2*c*x, x) + Integral(3*a**2*c**2*x**2, x) + Integral(a**2*c**3*x**3, x) + Integral(3*b**2*c*x*atanh(c*x)**2, x) + Integral(3*b**2*c**2*x**2*atanh(c*x)**2, x) + Integral(b**2*c**3*x**3*atanh(c*x)**2, x) + Integral(6*a*b*c*x*atanh(c*x), x) + Integral(6*a*b*c**2*x**2*atanh(c*x), x) + Integral(2*a*b*c**3*x**3*atanh(c*x), x))","F",0
88,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x,x)","d^{3} \left(\int 3 a^{2} c\, dx + \int \frac{a^{2}}{x}\, dx + \int 3 a^{2} c^{2} x\, dx + \int a^{2} c^{3} x^{2}\, dx + \int 3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int 6 a b c \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int 3 b^{2} c^{2} x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int b^{2} c^{3} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int 6 a b c^{2} x \operatorname{atanh}{\left(c x \right)}\, dx + \int 2 a b c^{3} x^{2} \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a**2*c, x) + Integral(a**2/x, x) + Integral(3*a**2*c**2*x, x) + Integral(a**2*c**3*x**2, x) + Integral(3*b**2*c*atanh(c*x)**2, x) + Integral(b**2*atanh(c*x)**2/x, x) + Integral(6*a*b*c*atanh(c*x), x) + Integral(2*a*b*atanh(c*x)/x, x) + Integral(3*b**2*c**2*x*atanh(c*x)**2, x) + Integral(b**2*c**3*x**2*atanh(c*x)**2, x) + Integral(6*a*b*c**2*x*atanh(c*x), x) + Integral(2*a*b*c**3*x**2*atanh(c*x), x))","F",0
89,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x**2,x)","d^{3} \left(\int 3 a^{2} c^{2}\, dx + \int \frac{a^{2}}{x^{2}}\, dx + \int \frac{3 a^{2} c}{x}\, dx + \int a^{2} c^{3} x\, dx + \int 3 b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int 6 a b c^{2} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int b^{2} c^{3} x \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{6 a b c \operatorname{atanh}{\left(c x \right)}}{x}\, dx + \int 2 a b c^{3} x \operatorname{atanh}{\left(c x \right)}\, dx\right)"," ",0,"d**3*(Integral(3*a**2*c**2, x) + Integral(a**2/x**2, x) + Integral(3*a**2*c/x, x) + Integral(a**2*c**3*x, x) + Integral(3*b**2*c**2*atanh(c*x)**2, x) + Integral(b**2*atanh(c*x)**2/x**2, x) + Integral(6*a*b*c**2*atanh(c*x), x) + Integral(2*a*b*atanh(c*x)/x**2, x) + Integral(3*b**2*c*atanh(c*x)**2/x, x) + Integral(b**2*c**3*x*atanh(c*x)**2, x) + Integral(6*a*b*c*atanh(c*x)/x, x) + Integral(2*a*b*c**3*x*atanh(c*x), x))","F",0
90,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x**3,x)","d^{3} \left(\int a^{2} c^{3}\, dx + \int \frac{a^{2}}{x^{3}}\, dx + \int \frac{3 a^{2} c}{x^{2}}\, dx + \int \frac{3 a^{2} c^{2}}{x}\, dx + \int b^{2} c^{3} \operatorname{atanh}^{2}{\left(c x \right)}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int 2 a b c^{3} \operatorname{atanh}{\left(c x \right)}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{6 a b c \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{6 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**3*(Integral(a**2*c**3, x) + Integral(a**2/x**3, x) + Integral(3*a**2*c/x**2, x) + Integral(3*a**2*c**2/x, x) + Integral(b**2*c**3*atanh(c*x)**2, x) + Integral(b**2*atanh(c*x)**2/x**3, x) + Integral(2*a*b*c**3*atanh(c*x), x) + Integral(2*a*b*atanh(c*x)/x**3, x) + Integral(3*b**2*c*atanh(c*x)**2/x**2, x) + Integral(3*b**2*c**2*atanh(c*x)**2/x, x) + Integral(6*a*b*c*atanh(c*x)/x**2, x) + Integral(6*a*b*c**2*atanh(c*x)/x, x))","F",0
91,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x**4,x)","d^{3} \left(\int \frac{a^{2}}{x^{4}}\, dx + \int \frac{3 a^{2} c}{x^{3}}\, dx + \int \frac{3 a^{2} c^{2}}{x^{2}}\, dx + \int \frac{a^{2} c^{3}}{x}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{b^{2} c^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{x}\, dx + \int \frac{6 a b c \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{6 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{2 a b c^{3} \operatorname{atanh}{\left(c x \right)}}{x}\, dx\right)"," ",0,"d**3*(Integral(a**2/x**4, x) + Integral(3*a**2*c/x**3, x) + Integral(3*a**2*c**2/x**2, x) + Integral(a**2*c**3/x, x) + Integral(b**2*atanh(c*x)**2/x**4, x) + Integral(2*a*b*atanh(c*x)/x**4, x) + Integral(3*b**2*c*atanh(c*x)**2/x**3, x) + Integral(3*b**2*c**2*atanh(c*x)**2/x**2, x) + Integral(b**2*c**3*atanh(c*x)**2/x, x) + Integral(6*a*b*c*atanh(c*x)/x**3, x) + Integral(6*a*b*c**2*atanh(c*x)/x**2, x) + Integral(2*a*b*c**3*atanh(c*x)/x, x))","F",0
92,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x**5,x)","d^{3} \left(\int \frac{a^{2}}{x^{5}}\, dx + \int \frac{3 a^{2} c}{x^{4}}\, dx + \int \frac{3 a^{2} c^{2}}{x^{3}}\, dx + \int \frac{a^{2} c^{3}}{x^{2}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{b^{2} c^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{2}}\, dx + \int \frac{6 a b c \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{6 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{2 a b c^{3} \operatorname{atanh}{\left(c x \right)}}{x^{2}}\, dx\right)"," ",0,"d**3*(Integral(a**2/x**5, x) + Integral(3*a**2*c/x**4, x) + Integral(3*a**2*c**2/x**3, x) + Integral(a**2*c**3/x**2, x) + Integral(b**2*atanh(c*x)**2/x**5, x) + Integral(2*a*b*atanh(c*x)/x**5, x) + Integral(3*b**2*c*atanh(c*x)**2/x**4, x) + Integral(3*b**2*c**2*atanh(c*x)**2/x**3, x) + Integral(b**2*c**3*atanh(c*x)**2/x**2, x) + Integral(6*a*b*c*atanh(c*x)/x**4, x) + Integral(6*a*b*c**2*atanh(c*x)/x**3, x) + Integral(2*a*b*c**3*atanh(c*x)/x**2, x))","F",0
93,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x**6,x)","d^{3} \left(\int \frac{a^{2}}{x^{6}}\, dx + \int \frac{3 a^{2} c}{x^{5}}\, dx + \int \frac{3 a^{2} c^{2}}{x^{4}}\, dx + \int \frac{a^{2} c^{3}}{x^{3}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{6}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{6}}\, dx + \int \frac{3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{b^{2} c^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{3}}\, dx + \int \frac{6 a b c \operatorname{atanh}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{6 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{2 a b c^{3} \operatorname{atanh}{\left(c x \right)}}{x^{3}}\, dx\right)"," ",0,"d**3*(Integral(a**2/x**6, x) + Integral(3*a**2*c/x**5, x) + Integral(3*a**2*c**2/x**4, x) + Integral(a**2*c**3/x**3, x) + Integral(b**2*atanh(c*x)**2/x**6, x) + Integral(2*a*b*atanh(c*x)/x**6, x) + Integral(3*b**2*c*atanh(c*x)**2/x**5, x) + Integral(3*b**2*c**2*atanh(c*x)**2/x**4, x) + Integral(b**2*c**3*atanh(c*x)**2/x**3, x) + Integral(6*a*b*c*atanh(c*x)/x**5, x) + Integral(6*a*b*c**2*atanh(c*x)/x**4, x) + Integral(2*a*b*c**3*atanh(c*x)/x**3, x))","F",0
94,0,0,0,0.000000," ","integrate((c*d*x+d)**3*(a+b*atanh(c*x))**2/x**7,x)","d^{3} \left(\int \frac{a^{2}}{x^{7}}\, dx + \int \frac{3 a^{2} c}{x^{6}}\, dx + \int \frac{3 a^{2} c^{2}}{x^{5}}\, dx + \int \frac{a^{2} c^{3}}{x^{4}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{7}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{x^{7}}\, dx + \int \frac{3 b^{2} c \operatorname{atanh}^{2}{\left(c x \right)}}{x^{6}}\, dx + \int \frac{3 b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{b^{2} c^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{x^{4}}\, dx + \int \frac{6 a b c \operatorname{atanh}{\left(c x \right)}}{x^{6}}\, dx + \int \frac{6 a b c^{2} \operatorname{atanh}{\left(c x \right)}}{x^{5}}\, dx + \int \frac{2 a b c^{3} \operatorname{atanh}{\left(c x \right)}}{x^{4}}\, dx\right)"," ",0,"d**3*(Integral(a**2/x**7, x) + Integral(3*a**2*c/x**6, x) + Integral(3*a**2*c**2/x**5, x) + Integral(a**2*c**3/x**4, x) + Integral(b**2*atanh(c*x)**2/x**7, x) + Integral(2*a*b*atanh(c*x)/x**7, x) + Integral(3*b**2*c*atanh(c*x)**2/x**6, x) + Integral(3*b**2*c**2*atanh(c*x)**2/x**5, x) + Integral(b**2*c**3*atanh(c*x)**2/x**4, x) + Integral(6*a*b*c*atanh(c*x)/x**6, x) + Integral(6*a*b*c**2*atanh(c*x)/x**5, x) + Integral(2*a*b*c**3*atanh(c*x)/x**4, x))","F",0
95,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))**2/(c*d*x+d),x)","\frac{\int \frac{a^{2} x^{3}}{c x + 1}\, dx + \int \frac{b^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{c x + 1}\, dx + \int \frac{2 a b x^{3} \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a**2*x**3/(c*x + 1), x) + Integral(b**2*x**3*atanh(c*x)**2/(c*x + 1), x) + Integral(2*a*b*x**3*atanh(c*x)/(c*x + 1), x))/d","F",0
96,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))**2/(c*d*x+d),x)","\frac{\int \frac{a^{2} x^{2}}{c x + 1}\, dx + \int \frac{b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c x + 1}\, dx + \int \frac{2 a b x^{2} \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a**2*x**2/(c*x + 1), x) + Integral(b**2*x**2*atanh(c*x)**2/(c*x + 1), x) + Integral(2*a*b*x**2*atanh(c*x)/(c*x + 1), x))/d","F",0
97,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))**2/(c*d*x+d),x)","\frac{\int \frac{a^{2} x}{c x + 1}\, dx + \int \frac{b^{2} x \operatorname{atanh}^{2}{\left(c x \right)}}{c x + 1}\, dx + \int \frac{2 a b x \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a**2*x/(c*x + 1), x) + Integral(b**2*x*atanh(c*x)**2/(c*x + 1), x) + Integral(2*a*b*x*atanh(c*x)/(c*x + 1), x))/d","F",0
98,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(c*d*x+d),x)","\frac{\int \frac{a^{2}}{c x + 1}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c x + 1}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c x + 1}\, dx}{d}"," ",0,"(Integral(a**2/(c*x + 1), x) + Integral(b**2*atanh(c*x)**2/(c*x + 1), x) + Integral(2*a*b*atanh(c*x)/(c*x + 1), x))/d","F",0
99,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x/(c*d*x+d),x)","\frac{\int \frac{a^{2}}{c x^{2} + x}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c x^{2} + x}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c x^{2} + x}\, dx}{d}"," ",0,"(Integral(a**2/(c*x**2 + x), x) + Integral(b**2*atanh(c*x)**2/(c*x**2 + x), x) + Integral(2*a*b*atanh(c*x)/(c*x**2 + x), x))/d","F",0
100,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**2/(c*d*x+d),x)","\frac{\int \frac{a^{2}}{c x^{3} + x^{2}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c x^{3} + x^{2}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c x^{3} + x^{2}}\, dx}{d}"," ",0,"(Integral(a**2/(c*x**3 + x**2), x) + Integral(b**2*atanh(c*x)**2/(c*x**3 + x**2), x) + Integral(2*a*b*atanh(c*x)/(c*x**3 + x**2), x))/d","F",0
101,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**3/(c*d*x+d),x)","\frac{\int \frac{a^{2}}{c x^{4} + x^{3}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c x^{4} + x^{3}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c x^{4} + x^{3}}\, dx}{d}"," ",0,"(Integral(a**2/(c*x**4 + x**3), x) + Integral(b**2*atanh(c*x)**2/(c*x**4 + x**3), x) + Integral(2*a*b*atanh(c*x)/(c*x**4 + x**3), x))/d","F",0
102,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**4/(c*d*x+d),x)","\frac{\int \frac{a^{2}}{c x^{5} + x^{4}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c x^{5} + x^{4}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c x^{5} + x^{4}}\, dx}{d}"," ",0,"(Integral(a**2/(c*x**5 + x**4), x) + Integral(b**2*atanh(c*x)**2/(c*x**5 + x**4), x) + Integral(2*a*b*atanh(c*x)/(c*x**5 + x**4), x))/d","F",0
103,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x))**2/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2} x^{4}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b^{2} x^{4} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{2 a b x^{4} \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x**4/(c**2*x**2 + 2*c*x + 1), x) + Integral(b**2*x**4*atanh(c*x)**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(2*a*b*x**4*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
104,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))**2/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2} x^{3}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{2 a b x^{3} \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x**3/(c**2*x**2 + 2*c*x + 1), x) + Integral(b**2*x**3*atanh(c*x)**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(2*a*b*x**3*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
105,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))**2/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2} x^{2}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{2 a b x^{2} \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(b**2*x**2*atanh(c*x)**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(2*a*b*x**2*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
106,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))**2/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2} x}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b^{2} x \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{2 a b x \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2*x/(c**2*x**2 + 2*c*x + 1), x) + Integral(b**2*x*atanh(c*x)**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(2*a*b*x*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
107,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} + 2 c x + 1}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(b**2*atanh(c*x)**2/(c**2*x**2 + 2*c*x + 1), x) + Integral(2*a*b*atanh(c*x)/(c**2*x**2 + 2*c*x + 1), x))/d**2","F",0
108,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2}}{c^{2} x^{3} + 2 c x^{2} + x}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{3} + 2 c x^{2} + x}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{3} + 2 c x^{2} + x}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**2*x**3 + 2*c*x**2 + x), x) + Integral(b**2*atanh(c*x)**2/(c**2*x**3 + 2*c*x**2 + x), x) + Integral(2*a*b*atanh(c*x)/(c**2*x**3 + 2*c*x**2 + x), x))/d**2","F",0
109,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**2/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2}}{c^{2} x^{4} + 2 c x^{3} + x^{2}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{4} + 2 c x^{3} + x^{2}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{4} + 2 c x^{3} + x^{2}}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**2*x**4 + 2*c*x**3 + x**2), x) + Integral(b**2*atanh(c*x)**2/(c**2*x**4 + 2*c*x**3 + x**2), x) + Integral(2*a*b*atanh(c*x)/(c**2*x**4 + 2*c*x**3 + x**2), x))/d**2","F",0
110,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**3/(c*d*x+d)**2,x)","\frac{\int \frac{a^{2}}{c^{2} x^{5} + 2 c x^{4} + x^{3}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{5} + 2 c x^{4} + x^{3}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{5} + 2 c x^{4} + x^{3}}\, dx}{d^{2}}"," ",0,"(Integral(a**2/(c**2*x**5 + 2*c*x**4 + x**3), x) + Integral(b**2*atanh(c*x)**2/(c**2*x**5 + 2*c*x**4 + x**3), x) + Integral(2*a*b*atanh(c*x)/(c**2*x**5 + 2*c*x**4 + x**3), x))/d**2","F",0
111,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x))**2/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2} x^{4}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b^{2} x^{4} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{2 a b x^{4} \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x**4/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b**2*x**4*atanh(c*x)**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(2*a*b*x**4*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
112,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))**2/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2} x^{3}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b^{2} x^{3} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{2 a b x^{3} \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x**3/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b**2*x**3*atanh(c*x)**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(2*a*b*x**3*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
113,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))**2/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2} x^{2}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{2 a b x^{2} \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b**2*x**2*atanh(c*x)**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(2*a*b*x**2*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
114,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))**2/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2} x}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b^{2} x \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{2 a b x \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2*x/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b**2*x*atanh(c*x)**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(2*a*b*x*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
115,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{3} + 3 c^{2} x^{2} + 3 c x + 1}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(b**2*atanh(c*x)**2/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x) + Integral(2*a*b*atanh(c*x)/(c**3*x**3 + 3*c**2*x**2 + 3*c*x + 1), x))/d**3","F",0
116,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2}}{c^{3} x^{4} + 3 c^{2} x^{3} + 3 c x^{2} + x}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{4} + 3 c^{2} x^{3} + 3 c x^{2} + x}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{4} + 3 c^{2} x^{3} + 3 c x^{2} + x}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**3*x**4 + 3*c**2*x**3 + 3*c*x**2 + x), x) + Integral(b**2*atanh(c*x)**2/(c**3*x**4 + 3*c**2*x**3 + 3*c*x**2 + x), x) + Integral(2*a*b*atanh(c*x)/(c**3*x**4 + 3*c**2*x**3 + 3*c*x**2 + x), x))/d**3","F",0
117,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**2/(c*d*x+d)**3,x)","\frac{\int \frac{a^{2}}{c^{3} x^{5} + 3 c^{2} x^{4} + 3 c x^{3} + x^{2}}\, dx + \int \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{c^{3} x^{5} + 3 c^{2} x^{4} + 3 c x^{3} + x^{2}}\, dx + \int \frac{2 a b \operatorname{atanh}{\left(c x \right)}}{c^{3} x^{5} + 3 c^{2} x^{4} + 3 c x^{3} + x^{2}}\, dx}{d^{3}}"," ",0,"(Integral(a**2/(c**3*x**5 + 3*c**2*x**4 + 3*c*x**3 + x**2), x) + Integral(b**2*atanh(c*x)**2/(c**3*x**5 + 3*c**2*x**4 + 3*c*x**3 + x**2), x) + Integral(2*a*b*atanh(c*x)/(c**3*x**5 + 3*c**2*x**4 + 3*c*x**3 + x**2), x))/d**3","F",0
118,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(c*x+1)**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{\left(c x + 1\right)^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(c*x + 1)**4, x)","F",0
119,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a*c*x**2+c*x),x)","- \frac{\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a x^{2} - x}\, dx}{c}"," ",0,"-Integral(atanh(a*x)**2/(a*x**2 - x), x)/c","F",0
120,0,0,0,0.000000," ","integrate((c*x+1)**3*(a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3} \left(c x + 1\right)^{3}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3*(c*x + 1)**3, x)","F",0
121,0,0,0,0.000000," ","integrate((c*x+1)**2*(a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3} \left(c x + 1\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3*(c*x + 1)**2, x)","F",0
122,0,0,0,0.000000," ","integrate((c*x+1)*(a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3} \left(c x + 1\right)\, dx"," ",0,"Integral((a + b*atanh(c*x))**3*(c*x + 1), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(c*x+1),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{c x + 1}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(c*x + 1), x)","F",0
124,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(c*x+1)**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{\left(c x + 1\right)^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(c*x + 1)**2, x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(c*x+1)**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{\left(c x + 1\right)^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(c*x + 1)**3, x)","F",0
126,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/(c*x+1)**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{\left(c x + 1\right)^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/(c*x + 1)**4, x)","F",0
127,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**3/(a*c*x+c),x)","\frac{\int \frac{x^{2} \operatorname{atanh}^{3}{\left(a x \right)}}{a x + 1}\, dx}{c}"," ",0,"Integral(x**2*atanh(a*x)**3/(a*x + 1), x)/c","F",0
128,0,0,0,0.000000," ","integrate(x*atanh(a*x)**3/(a*c*x+c),x)","\frac{\int \frac{x \operatorname{atanh}^{3}{\left(a x \right)}}{a x + 1}\, dx}{c}"," ",0,"Integral(x*atanh(a*x)**3/(a*x + 1), x)/c","F",0
129,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(a*c*x+c),x)","\frac{\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a x + 1}\, dx}{c}"," ",0,"Integral(atanh(a*x)**3/(a*x + 1), x)/c","F",0
130,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x/(a*c*x+c),x)","\frac{\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a x^{2} + x}\, dx}{c}"," ",0,"Integral(atanh(a*x)**3/(a*x**2 + x), x)/c","F",0
131,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(a*c*x**2+c*x),x)","\frac{\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a x^{2} + x}\, dx}{c}"," ",0,"Integral(atanh(a*x)**3/(a*x**2 + x), x)/c","F",0
132,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**2/(a*c*x+c),x)","\frac{\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a x^{3} + x^{2}}\, dx}{c}"," ",0,"Integral(atanh(a*x)**3/(a*x**3 + x**2), x)/c","F",0
133,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**3/(a*c*x+c),x)","\frac{\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a x^{4} + x^{3}}\, dx}{c}"," ",0,"Integral(atanh(a*x)**3/(a*x**4 + x**3), x)/c","F",0
134,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**4/(-a*c*x+c),x)","- \frac{\int \frac{x^{2} \operatorname{atanh}^{4}{\left(a x \right)}}{a x - 1}\, dx}{c}"," ",0,"-Integral(x**2*atanh(a*x)**4/(a*x - 1), x)/c","F",0
135,0,0,0,0.000000," ","integrate(x*atanh(a*x)**4/(-a*c*x+c),x)","- \frac{\int \frac{x \operatorname{atanh}^{4}{\left(a x \right)}}{a x - 1}\, dx}{c}"," ",0,"-Integral(x*atanh(a*x)**4/(a*x - 1), x)/c","F",0
136,0,0,0,0.000000," ","integrate(atanh(a*x)**4/(-a*c*x+c),x)","- \frac{\int \frac{\operatorname{atanh}^{4}{\left(a x \right)}}{a x - 1}\, dx}{c}"," ",0,"-Integral(atanh(a*x)**4/(a*x - 1), x)/c","F",0
137,0,0,0,0.000000," ","integrate(atanh(a*x)**4/x/(-a*c*x+c),x)","- \frac{\int \frac{\operatorname{atanh}^{4}{\left(a x \right)}}{a x^{2} - x}\, dx}{c}"," ",0,"-Integral(atanh(a*x)**4/(a*x**2 - x), x)/c","F",0
138,0,0,0,0.000000," ","integrate(atanh(a*x)**4/(-a*c*x**2+c*x),x)","- \frac{\int \frac{\operatorname{atanh}^{4}{\left(a x \right)}}{a x^{2} - x}\, dx}{c}"," ",0,"-Integral(atanh(a*x)**4/(a*x**2 - x), x)/c","F",0
139,0,0,0,0.000000," ","integrate(atanh(a*x)**4/x**2/(-a*c*x+c),x)","- \frac{\int \frac{\operatorname{atanh}^{4}{\left(a x \right)}}{a x^{3} - x^{2}}\, dx}{c}"," ",0,"-Integral(atanh(a*x)**4/(a*x**3 - x**2), x)/c","F",0
140,0,0,0,0.000000," ","integrate(atanh(a*x)**4/x**3/(-a*c*x+c),x)","- \frac{\int \frac{\operatorname{atanh}^{4}{\left(a x \right)}}{a x^{4} - x^{3}}\, dx}{c}"," ",0,"-Integral(atanh(a*x)**4/(a*x**4 - x**3), x)/c","F",0
141,0,0,0,0.000000," ","integrate(x/(a*c*x+c)/atanh(a*x),x)","\frac{\int \frac{x}{a x \operatorname{atanh}{\left(a x \right)} + \operatorname{atanh}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a*x*atanh(a*x) + atanh(a*x)), x)/c","F",0
142,0,0,0,0.000000," ","integrate(1/(a*c*x+c)/atanh(a*x),x)","\frac{\int \frac{1}{a x \operatorname{atanh}{\left(a x \right)} + \operatorname{atanh}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a*x*atanh(a*x) + atanh(a*x)), x)/c","F",0
143,0,0,0,0.000000," ","integrate(1/x/(a*c*x+c)/atanh(a*x),x)","\frac{\int \frac{1}{a x^{2} \operatorname{atanh}{\left(a x \right)} + x \operatorname{atanh}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a*x**2*atanh(a*x) + x*atanh(a*x)), x)/c","F",0
144,0,0,0,0.000000," ","integrate(x/(a*c*x+c)/atanh(a*x)**2,x)","\frac{\int \frac{x}{a x \operatorname{atanh}^{2}{\left(a x \right)} + \operatorname{atanh}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(x/(a*x*atanh(a*x)**2 + atanh(a*x)**2), x)/c","F",0
145,0,0,0,0.000000," ","integrate(1/(a*c*x+c)/atanh(a*x)**2,x)","\frac{\int \frac{1}{a x \operatorname{atanh}^{2}{\left(a x \right)} + \operatorname{atanh}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a*x*atanh(a*x)**2 + atanh(a*x)**2), x)/c","F",0
146,0,0,0,0.000000," ","integrate(1/x/(a*c*x+c)/atanh(a*x)**2,x)","\frac{\int \frac{1}{a x^{2} \operatorname{atanh}^{2}{\left(a x \right)} + x \operatorname{atanh}^{2}{\left(a x \right)}}\, dx}{c}"," ",0,"Integral(1/(a*x**2*atanh(a*x)**2 + x*atanh(a*x)**2), x)/c","F",0
147,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))/(e*x+d),x)","\int \frac{x^{3} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x**3*(a + b*atanh(c*x))/(d + e*x), x)","F",0
148,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))/(e*x+d),x)","\int \frac{x^{2} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*x))/(d + e*x), x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))/(e*x+d),x)","\int \frac{x \left(a + b \operatorname{atanh}{\left(c x \right)}\right)}{d + e x}\, dx"," ",0,"Integral(x*(a + b*atanh(c*x))/(d + e*x), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(d + e*x), x)","F",0
151,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x/(e*x+d),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(x*(d + e*x)), x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**2/(e*x+d),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(x**2*(d + e*x)), x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x**3/(e*x+d),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(x**3*(d + e*x)), x)","F",0
154,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))**2/(e*x+d),x)","\int \frac{x^{2} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*x))**2/(d + e*x), x)","F",0
155,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))**2/(e*x+d),x)","\int \frac{x \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral(x*(a + b*atanh(c*x))**2/(d + e*x), x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(d + e*x), x)","F",0
157,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(x*(d + e*x)), x)","F",0
158,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/(x**2*(d + e*x)), x)","F",0
159,0,0,0,0.000000," ","integrate(atanh(c*x)**2/x/(e*x+d),x)","\int \frac{\operatorname{atanh}^{2}{\left(c x \right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(atanh(c*x)**2/(x*(d + e*x)), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*atan(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{atan}{\left(c x \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*atan(c*x))*(d + e*x)), x)","F",0
161,1,71,0,1.979816," ","integrate(x**4*(-a**2*x**2+1)*atanh(a*x),x)","\begin{cases} - \frac{a^{2} x^{7} \operatorname{atanh}{\left(a x \right)}}{7} - \frac{a x^{6}}{42} + \frac{x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{x^{4}}{70 a} + \frac{x^{2}}{35 a^{3}} + \frac{2 \log{\left(x - \frac{1}{a} \right)}}{35 a^{5}} + \frac{2 \operatorname{atanh}{\left(a x \right)}}{35 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**7*atanh(a*x)/7 - a*x**6/42 + x**5*atanh(a*x)/5 + x**4/(70*a) + x**2/(35*a**3) + 2*log(x - 1/a)/(35*a**5) + 2*atanh(a*x)/(35*a**5), Ne(a, 0)), (0, True))","A",0
162,1,54,0,1.551404," ","integrate(x**3*(-a**2*x**2+1)*atanh(a*x),x)","\begin{cases} - \frac{a^{2} x^{6} \operatorname{atanh}{\left(a x \right)}}{6} - \frac{a x^{5}}{30} + \frac{x^{4} \operatorname{atanh}{\left(a x \right)}}{4} + \frac{x^{3}}{36 a} + \frac{x}{12 a^{3}} - \frac{\operatorname{atanh}{\left(a x \right)}}{12 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**6*atanh(a*x)/6 - a*x**5/30 + x**4*atanh(a*x)/4 + x**3/(36*a) + x/(12*a**3) - atanh(a*x)/(12*a**4), Ne(a, 0)), (0, True))","A",0
163,1,63,0,1.222866," ","integrate(x**2*(-a**2*x**2+1)*atanh(a*x),x)","\begin{cases} - \frac{a^{2} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} - \frac{a x^{4}}{20} + \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{x^{2}}{15 a} + \frac{2 \log{\left(x - \frac{1}{a} \right)}}{15 a^{3}} + \frac{2 \operatorname{atanh}{\left(a x \right)}}{15 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**5*atanh(a*x)/5 - a*x**4/20 + x**3*atanh(a*x)/3 + x**2/(15*a) + 2*log(x - 1/a)/(15*a**3) + 2*atanh(a*x)/(15*a**3), Ne(a, 0)), (0, True))","A",0
164,1,46,0,0.845083," ","integrate(x*(-a**2*x**2+1)*atanh(a*x),x)","\begin{cases} - \frac{a^{2} x^{4} \operatorname{atanh}{\left(a x \right)}}{4} - \frac{a x^{3}}{12} + \frac{x^{2} \operatorname{atanh}{\left(a x \right)}}{2} + \frac{x}{4 a} - \frac{\operatorname{atanh}{\left(a x \right)}}{4 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**4*atanh(a*x)/4 - a*x**3/12 + x**2*atanh(a*x)/2 + x/(4*a) - atanh(a*x)/(4*a**2), Ne(a, 0)), (0, True))","A",0
165,1,49,0,0.678136," ","integrate((-a**2*x**2+1)*atanh(a*x),x)","\begin{cases} - \frac{a^{2} x^{3} \operatorname{atanh}{\left(a x \right)}}{3} - \frac{a x^{2}}{6} + x \operatorname{atanh}{\left(a x \right)} + \frac{2 \log{\left(x - \frac{1}{a} \right)}}{3 a} + \frac{2 \operatorname{atanh}{\left(a x \right)}}{3 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**3*atanh(a*x)/3 - a*x**2/6 + x*atanh(a*x) + 2*log(x - 1/a)/(3*a) + 2*atanh(a*x)/(3*a), Ne(a, 0)), (0, True))","A",0
166,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)/x,x)","- \int \left(- \frac{\operatorname{atanh}{\left(a x \right)}}{x}\right)\, dx - \int a^{2} x \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"-Integral(-atanh(a*x)/x, x) - Integral(a**2*x*atanh(a*x), x)","F",0
167,1,41,0,0.848531," ","integrate((-a**2*x**2+1)*atanh(a*x)/x**2,x)","\begin{cases} - a^{2} x \operatorname{atanh}{\left(a x \right)} + a \log{\left(x \right)} - 2 a \log{\left(x - \frac{1}{a} \right)} - 2 a \operatorname{atanh}{\left(a x \right)} - \frac{\operatorname{atanh}{\left(a x \right)}}{x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x*atanh(a*x) + a*log(x) - 2*a*log(x - 1/a) - 2*a*atanh(a*x) - atanh(a*x)/x, Ne(a, 0)), (0, True))","A",0
168,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)/x**3,x)","- \int \left(- \frac{\operatorname{atanh}{\left(a x \right)}}{x^{3}}\right)\, dx - \int \frac{a^{2} \operatorname{atanh}{\left(a x \right)}}{x}\, dx"," ",0,"-Integral(-atanh(a*x)/x**3, x) - Integral(a**2*atanh(a*x)/x, x)","F",0
169,1,63,0,1.189436," ","integrate((-a**2*x**2+1)*atanh(a*x)/x**4,x)","\begin{cases} - \frac{2 a^{3} \log{\left(x \right)}}{3} + \frac{2 a^{3} \log{\left(x - \frac{1}{a} \right)}}{3} + \frac{2 a^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{a^{2} \operatorname{atanh}{\left(a x \right)}}{x} - \frac{a}{6 x^{2}} - \frac{\operatorname{atanh}{\left(a x \right)}}{3 x^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**3*log(x)/3 + 2*a**3*log(x - 1/a)/3 + 2*a**3*atanh(a*x)/3 + a**2*atanh(a*x)/x - a/(6*x**2) - atanh(a*x)/(3*x**3), Ne(a, 0)), (0, True))","A",0
170,1,46,0,0.885115," ","integrate((-a**2*x**2+1)*atanh(a*x)/x**5,x)","- \frac{a^{4} \operatorname{atanh}{\left(a x \right)}}{4} + \frac{a^{3}}{4 x} + \frac{a^{2} \operatorname{atanh}{\left(a x \right)}}{2 x^{2}} - \frac{a}{12 x^{3}} - \frac{\operatorname{atanh}{\left(a x \right)}}{4 x^{4}}"," ",0,"-a**4*atanh(a*x)/4 + a**3/(4*x) + a**2*atanh(a*x)/(2*x**2) - a/(12*x**3) - atanh(a*x)/(4*x**4)","A",0
171,1,75,0,1.876546," ","integrate((-a**2*x**2+1)*atanh(a*x)/x**6,x)","\begin{cases} - \frac{2 a^{5} \log{\left(x \right)}}{15} + \frac{2 a^{5} \log{\left(x - \frac{1}{a} \right)}}{15} + \frac{2 a^{5} \operatorname{atanh}{\left(a x \right)}}{15} + \frac{a^{3}}{15 x^{2}} + \frac{a^{2} \operatorname{atanh}{\left(a x \right)}}{3 x^{3}} - \frac{a}{20 x^{4}} - \frac{\operatorname{atanh}{\left(a x \right)}}{5 x^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*a**5*log(x)/15 + 2*a**5*log(x - 1/a)/15 + 2*a**5*atanh(a*x)/15 + a**3/(15*x**2) + a**2*atanh(a*x)/(3*x**3) - a/(20*x**4) - atanh(a*x)/(5*x**5), Ne(a, 0)), (0, True))","A",0
172,0,0,0,0.000000," ","integrate(x**4*(-a**2*x**2+1)*atanh(a*x)**2,x)","- \int \left(- x^{4} \operatorname{atanh}^{2}{\left(a x \right)}\right)\, dx - \int a^{2} x^{6} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"-Integral(-x**4*atanh(a*x)**2, x) - Integral(a**2*x**6*atanh(a*x)**2, x)","F",0
173,1,114,0,2.143549," ","integrate(x**3*(-a**2*x**2+1)*atanh(a*x)**2,x)","\begin{cases} - \frac{a^{2} x^{6} \operatorname{atanh}^{2}{\left(a x \right)}}{6} - \frac{a x^{5} \operatorname{atanh}{\left(a x \right)}}{15} + \frac{x^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{4} - \frac{x^{4}}{60} + \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{18 a} - \frac{x^{2}}{180 a^{2}} + \frac{x \operatorname{atanh}{\left(a x \right)}}{6 a^{3}} + \frac{7 \log{\left(x - \frac{1}{a} \right)}}{45 a^{4}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{12 a^{4}} + \frac{7 \operatorname{atanh}{\left(a x \right)}}{45 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**6*atanh(a*x)**2/6 - a*x**5*atanh(a*x)/15 + x**4*atanh(a*x)**2/4 - x**4/60 + x**3*atanh(a*x)/(18*a) - x**2/(180*a**2) + x*atanh(a*x)/(6*a**3) + 7*log(x - 1/a)/(45*a**4) - atanh(a*x)**2/(12*a**4) + 7*atanh(a*x)/(45*a**4), Ne(a, 0)), (0, True))","A",0
174,0,0,0,0.000000," ","integrate(x**2*(-a**2*x**2+1)*atanh(a*x)**2,x)","- \int \left(- x^{2} \operatorname{atanh}^{2}{\left(a x \right)}\right)\, dx - \int a^{2} x^{4} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"-Integral(-x**2*atanh(a*x)**2, x) - Integral(a**2*x**4*atanh(a*x)**2, x)","F",0
175,1,88,0,1.278647," ","integrate(x*(-a**2*x**2+1)*atanh(a*x)**2,x)","\begin{cases} - \frac{a^{2} x^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{4} - \frac{a x^{3} \operatorname{atanh}{\left(a x \right)}}{6} + \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{2} - \frac{x^{2}}{12} + \frac{x \operatorname{atanh}{\left(a x \right)}}{2 a} + \frac{\log{\left(x - \frac{1}{a} \right)}}{3 a^{2}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{4 a^{2}} + \frac{\operatorname{atanh}{\left(a x \right)}}{3 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**4*atanh(a*x)**2/4 - a*x**3*atanh(a*x)/6 + x**2*atanh(a*x)**2/2 - x**2/12 + x*atanh(a*x)/(2*a) + log(x - 1/a)/(3*a**2) - atanh(a*x)**2/(4*a**2) + atanh(a*x)/(3*a**2), Ne(a, 0)), (0, True))","A",0
176,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**2,x)","- \int a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)}\, dx - \int \left(- \operatorname{atanh}^{2}{\left(a x \right)}\right)\, dx"," ",0,"-Integral(a**2*x**2*atanh(a*x)**2, x) - Integral(-atanh(a*x)**2, x)","F",0
177,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**2/x,x)","- \int \left(- \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x}\right)\, dx - \int a^{2} x \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"-Integral(-atanh(a*x)**2/x, x) - Integral(a**2*x*atanh(a*x)**2, x)","F",0
178,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**2/x**2,x)","- \int a^{2} \operatorname{atanh}^{2}{\left(a x \right)}\, dx - \int \left(- \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{2}}\right)\, dx"," ",0,"-Integral(a**2*atanh(a*x)**2, x) - Integral(-atanh(a*x)**2/x**2, x)","F",0
179,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**2/x**3,x)","- \int \left(- \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{3}}\right)\, dx - \int \frac{a^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"-Integral(-atanh(a*x)**2/x**3, x) - Integral(a**2*atanh(a*x)**2/x, x)","F",0
180,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**2/x**4,x)","- \int \left(- \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{4}}\right)\, dx - \int \frac{a^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"-Integral(-atanh(a*x)**2/x**4, x) - Integral(a**2*atanh(a*x)**2/x**2, x)","F",0
181,1,102,0,1.619396," ","integrate((-a**2*x**2+1)*atanh(a*x)**2/x**5,x)","\begin{cases} - \frac{a^{4} \log{\left(x \right)}}{3} + \frac{a^{4} \log{\left(x - \frac{1}{a} \right)}}{3} - \frac{a^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{4} + \frac{a^{4} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{a^{3} \operatorname{atanh}{\left(a x \right)}}{2 x} + \frac{a^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{2 x^{2}} - \frac{a^{2}}{12 x^{2}} - \frac{a \operatorname{atanh}{\left(a x \right)}}{6 x^{3}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{4 x^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*log(x)/3 + a**4*log(x - 1/a)/3 - a**4*atanh(a*x)**2/4 + a**4*atanh(a*x)/3 + a**3*atanh(a*x)/(2*x) + a**2*atanh(a*x)**2/(2*x**2) - a**2/(12*x**2) - a*atanh(a*x)/(6*x**3) - atanh(a*x)**2/(4*x**4), Ne(a, 0)), (0, True))","A",0
182,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**2/x**6,x)","- \int \left(- \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{6}}\right)\, dx - \int \frac{a^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"-Integral(-atanh(a*x)**2/x**6, x) - Integral(a**2*atanh(a*x)**2/x**4, x)","F",0
183,0,0,0,0.000000," ","integrate((-a**2*x**2+1)*atanh(a*x)**3,x)","- \int a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)}\, dx - \int \left(- \operatorname{atanh}^{3}{\left(a x \right)}\right)\, dx"," ",0,"-Integral(a**2*x**2*atanh(a*x)**3, x) - Integral(-atanh(a*x)**3, x)","F",0
184,0,0,0,0.000000," ","integrate(x*atanh(1/2*x*2**(1/2))/(-x**2+1),x)","- \int \frac{x \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{x^{2} - 1}\, dx"," ",0,"-Integral(x*atanh(sqrt(2)*x/2)/(x**2 - 1), x)","F",0
185,0,0,0,0.000000," ","integrate(x*(-a**2*x**2+1)/atanh(a*x),x)","- \int \left(- \frac{x}{\operatorname{atanh}{\left(a x \right)}}\right)\, dx - \int \frac{a^{2} x^{3}}{\operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(-x/atanh(a*x), x) - Integral(a**2*x**3/atanh(a*x), x)","F",0
186,0,0,0,0.000000," ","integrate((-a**2*x**2+1)/atanh(a*x),x)","- \int \frac{a^{2} x^{2}}{\operatorname{atanh}{\left(a x \right)}}\, dx - \int \left(- \frac{1}{\operatorname{atanh}{\left(a x \right)}}\right)\, dx"," ",0,"-Integral(a**2*x**2/atanh(a*x), x) - Integral(-1/atanh(a*x), x)","F",0
187,0,0,0,0.000000," ","integrate((-a**2*x**2+1)/x/atanh(a*x),x)","- \int \left(- \frac{1}{x \operatorname{atanh}{\left(a x \right)}}\right)\, dx - \int \frac{a^{2} x}{\operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(-1/(x*atanh(a*x)), x) - Integral(a**2*x/atanh(a*x), x)","F",0
188,0,0,0,0.000000," ","integrate(x*(-a**2*x**2+1)/atanh(a*x)**2,x)","- \int \left(- \frac{x}{\operatorname{atanh}^{2}{\left(a x \right)}}\right)\, dx - \int \frac{a^{2} x^{3}}{\operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(-x/atanh(a*x)**2, x) - Integral(a**2*x**3/atanh(a*x)**2, x)","F",0
189,0,0,0,0.000000," ","integrate((-a**2*x**2+1)/atanh(a*x)**2,x)","- \int \frac{a^{2} x^{2}}{\operatorname{atanh}^{2}{\left(a x \right)}}\, dx - \int \left(- \frac{1}{\operatorname{atanh}^{2}{\left(a x \right)}}\right)\, dx"," ",0,"-Integral(a**2*x**2/atanh(a*x)**2, x) - Integral(-1/atanh(a*x)**2, x)","F",0
190,0,0,0,0.000000," ","integrate((-a**2*x**2+1)/x/atanh(a*x)**2,x)","- \int \left(- \frac{1}{x \operatorname{atanh}^{2}{\left(a x \right)}}\right)\, dx - \int \frac{a^{2} x}{\operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(-1/(x*atanh(a*x)**2), x) - Integral(a**2*x/atanh(a*x)**2, x)","F",0
191,0,0,0,0.000000," ","integrate((-a**2*x**2+1)/atanh(a*x)**3,x)","- \int \frac{a^{2} x^{2}}{\operatorname{atanh}^{3}{\left(a x \right)}}\, dx - \int \left(- \frac{1}{\operatorname{atanh}^{3}{\left(a x \right)}}\right)\, dx"," ",0,"-Integral(a**2*x**2/atanh(a*x)**3, x) - Integral(-1/atanh(a*x)**3, x)","F",0
192,1,100,0,3.131851," ","integrate(x**4*(-a**2*x**2+1)**2*atanh(a*x),x)","\begin{cases} \frac{a^{4} x^{9} \operatorname{atanh}{\left(a x \right)}}{9} + \frac{a^{3} x^{8}}{72} - \frac{2 a^{2} x^{7} \operatorname{atanh}{\left(a x \right)}}{7} - \frac{11 a x^{6}}{378} + \frac{x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{2 x^{4}}{315 a} + \frac{4 x^{2}}{315 a^{3}} + \frac{8 \log{\left(x - \frac{1}{a} \right)}}{315 a^{5}} + \frac{8 \operatorname{atanh}{\left(a x \right)}}{315 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**9*atanh(a*x)/9 + a**3*x**8/72 - 2*a**2*x**7*atanh(a*x)/7 - 11*a*x**6/378 + x**5*atanh(a*x)/5 + 2*x**4/(315*a) + 4*x**2/(315*a**3) + 8*log(x - 1/a)/(315*a**5) + 8*atanh(a*x)/(315*a**5), Ne(a, 0)), (0, True))","A",0
193,1,76,0,2.533662," ","integrate(x**3*(-a**2*x**2+1)**2*atanh(a*x),x)","\begin{cases} \frac{a^{4} x^{8} \operatorname{atanh}{\left(a x \right)}}{8} + \frac{a^{3} x^{7}}{56} - \frac{a^{2} x^{6} \operatorname{atanh}{\left(a x \right)}}{3} - \frac{a x^{5}}{24} + \frac{x^{4} \operatorname{atanh}{\left(a x \right)}}{4} + \frac{x^{3}}{72 a} + \frac{x}{24 a^{3}} - \frac{\operatorname{atanh}{\left(a x \right)}}{24 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**8*atanh(a*x)/8 + a**3*x**7/56 - a**2*x**6*atanh(a*x)/3 - a*x**5/24 + x**4*atanh(a*x)/4 + x**3/(72*a) + x/(24*a**3) - atanh(a*x)/(24*a**4), Ne(a, 0)), (0, True))","A",0
194,1,90,0,2.005963," ","integrate(x**2*(-a**2*x**2+1)**2*atanh(a*x),x)","\begin{cases} \frac{a^{4} x^{7} \operatorname{atanh}{\left(a x \right)}}{7} + \frac{a^{3} x^{6}}{42} - \frac{2 a^{2} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} - \frac{9 a x^{4}}{140} + \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{4 x^{2}}{105 a} + \frac{8 \log{\left(x - \frac{1}{a} \right)}}{105 a^{3}} + \frac{8 \operatorname{atanh}{\left(a x \right)}}{105 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**7*atanh(a*x)/7 + a**3*x**6/42 - 2*a**2*x**5*atanh(a*x)/5 - 9*a*x**4/140 + x**3*atanh(a*x)/3 + 4*x**2/(105*a) + 8*log(x - 1/a)/(105*a**3) + 8*atanh(a*x)/(105*a**3), Ne(a, 0)), (0, True))","A",0
195,1,68,0,1.516783," ","integrate(x*(-a**2*x**2+1)**2*atanh(a*x),x)","\begin{cases} \frac{a^{4} x^{6} \operatorname{atanh}{\left(a x \right)}}{6} + \frac{a^{3} x^{5}}{30} - \frac{a^{2} x^{4} \operatorname{atanh}{\left(a x \right)}}{2} - \frac{a x^{3}}{9} + \frac{x^{2} \operatorname{atanh}{\left(a x \right)}}{2} + \frac{x}{6 a} - \frac{\operatorname{atanh}{\left(a x \right)}}{6 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**6*atanh(a*x)/6 + a**3*x**5/30 - a**2*x**4*atanh(a*x)/2 - a*x**3/9 + x**2*atanh(a*x)/2 + x/(6*a) - atanh(a*x)/(6*a**2), Ne(a, 0)), (0, True))","A",0
196,1,75,0,1.238496," ","integrate((-a**2*x**2+1)**2*atanh(a*x),x)","\begin{cases} \frac{a^{4} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{a^{3} x^{4}}{20} - \frac{2 a^{2} x^{3} \operatorname{atanh}{\left(a x \right)}}{3} - \frac{7 a x^{2}}{30} + x \operatorname{atanh}{\left(a x \right)} + \frac{8 \log{\left(x - \frac{1}{a} \right)}}{15 a} + \frac{8 \operatorname{atanh}{\left(a x \right)}}{15 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**5*atanh(a*x)/5 + a**3*x**4/20 - 2*a**2*x**3*atanh(a*x)/3 - 7*a*x**2/30 + x*atanh(a*x) + 8*log(x - 1/a)/(15*a) + 8*atanh(a*x)/(15*a), Ne(a, 0)), (0, True))","A",0
197,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)/x,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)/x, x)","F",0
198,1,68,0,1.500955," ","integrate((-a**2*x**2+1)**2*atanh(a*x)/x**2,x)","\begin{cases} \frac{a^{4} x^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{a^{3} x^{2}}{6} - 2 a^{2} x \operatorname{atanh}{\left(a x \right)} + a \log{\left(x \right)} - \frac{8 a \log{\left(x - \frac{1}{a} \right)}}{3} - \frac{8 a \operatorname{atanh}{\left(a x \right)}}{3} - \frac{\operatorname{atanh}{\left(a x \right)}}{x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**3*atanh(a*x)/3 + a**3*x**2/6 - 2*a**2*x*atanh(a*x) + a*log(x) - 8*a*log(x - 1/a)/3 - 8*a*atanh(a*x)/3 - atanh(a*x)/x, Ne(a, 0)), (0, True))","A",0
199,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)/x**3,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)/x**3, x)","F",0
200,1,75,0,1.527060," ","integrate((-a**2*x**2+1)**2*atanh(a*x)/x**4,x)","\begin{cases} a^{4} x \operatorname{atanh}{\left(a x \right)} - \frac{5 a^{3} \log{\left(x \right)}}{3} + \frac{8 a^{3} \log{\left(x - \frac{1}{a} \right)}}{3} + \frac{8 a^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{2 a^{2} \operatorname{atanh}{\left(a x \right)}}{x} - \frac{a}{6 x^{2}} - \frac{\operatorname{atanh}{\left(a x \right)}}{3 x^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x*atanh(a*x) - 5*a**3*log(x)/3 + 8*a**3*log(x - 1/a)/3 + 8*a**3*atanh(a*x)/3 + 2*a**2*atanh(a*x)/x - a/(6*x**2) - atanh(a*x)/(3*x**3), Ne(a, 0)), (0, True))","A",0
201,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)/x**5,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)/x**5, x)","F",0
202,1,88,0,1.934762," ","integrate((-a**2*x**2+1)**2*atanh(a*x)/x**6,x)","\begin{cases} \frac{8 a^{5} \log{\left(x \right)}}{15} - \frac{8 a^{5} \log{\left(x - \frac{1}{a} \right)}}{15} - \frac{8 a^{5} \operatorname{atanh}{\left(a x \right)}}{15} - \frac{a^{4} \operatorname{atanh}{\left(a x \right)}}{x} + \frac{7 a^{3}}{30 x^{2}} + \frac{2 a^{2} \operatorname{atanh}{\left(a x \right)}}{3 x^{3}} - \frac{a}{20 x^{4}} - \frac{\operatorname{atanh}{\left(a x \right)}}{5 x^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**5*log(x)/15 - 8*a**5*log(x - 1/a)/15 - 8*a**5*atanh(a*x)/15 - a**4*atanh(a*x)/x + 7*a**3/(30*x**2) + 2*a**2*atanh(a*x)/(3*x**3) - a/(20*x**4) - atanh(a*x)/(5*x**5), Ne(a, 0)), (0, True))","A",0
203,0,0,0,0.000000," ","integrate(x**4*(-a**2*x**2+1)**2*atanh(a*x)**2,x)","\int x^{4} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**4*(a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2, x)","F",0
204,1,153,0,3.419144," ","integrate(x**3*(-a**2*x**2+1)**2*atanh(a*x)**2,x)","\begin{cases} \frac{a^{4} x^{8} \operatorname{atanh}^{2}{\left(a x \right)}}{8} + \frac{a^{3} x^{7} \operatorname{atanh}{\left(a x \right)}}{28} - \frac{a^{2} x^{6} \operatorname{atanh}^{2}{\left(a x \right)}}{3} + \frac{a^{2} x^{6}}{168} - \frac{a x^{5} \operatorname{atanh}{\left(a x \right)}}{12} + \frac{x^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{4} - \frac{x^{4}}{84} + \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{36 a} - \frac{5 x^{2}}{504 a^{2}} + \frac{x \operatorname{atanh}{\left(a x \right)}}{12 a^{3}} + \frac{4 \log{\left(x - \frac{1}{a} \right)}}{63 a^{4}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{24 a^{4}} + \frac{4 \operatorname{atanh}{\left(a x \right)}}{63 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**8*atanh(a*x)**2/8 + a**3*x**7*atanh(a*x)/28 - a**2*x**6*atanh(a*x)**2/3 + a**2*x**6/168 - a*x**5*atanh(a*x)/12 + x**4*atanh(a*x)**2/4 - x**4/84 + x**3*atanh(a*x)/(36*a) - 5*x**2/(504*a**2) + x*atanh(a*x)/(12*a**3) + 4*log(x - 1/a)/(63*a**4) - atanh(a*x)**2/(24*a**4) + 4*atanh(a*x)/(63*a**4), Ne(a, 0)), (0, True))","A",0
205,0,0,0,0.000000," ","integrate(x**2*(-a**2*x**2+1)**2*atanh(a*x)**2,x)","\int x^{2} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2, x)","F",0
206,1,133,0,2.110891," ","integrate(x*(-a**2*x**2+1)**2*atanh(a*x)**2,x)","\begin{cases} \frac{a^{4} x^{6} \operatorname{atanh}^{2}{\left(a x \right)}}{6} + \frac{a^{3} x^{5} \operatorname{atanh}{\left(a x \right)}}{15} - \frac{a^{2} x^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{2} + \frac{a^{2} x^{4}}{60} - \frac{2 a x^{3} \operatorname{atanh}{\left(a x \right)}}{9} + \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{2} - \frac{7 x^{2}}{90} + \frac{x \operatorname{atanh}{\left(a x \right)}}{3 a} + \frac{8 \log{\left(x - \frac{1}{a} \right)}}{45 a^{2}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{6 a^{2}} + \frac{8 \operatorname{atanh}{\left(a x \right)}}{45 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x**6*atanh(a*x)**2/6 + a**3*x**5*atanh(a*x)/15 - a**2*x**4*atanh(a*x)**2/2 + a**2*x**4/60 - 2*a*x**3*atanh(a*x)/9 + x**2*atanh(a*x)**2/2 - 7*x**2/90 + x*atanh(a*x)/(3*a) + 8*log(x - 1/a)/(45*a**2) - atanh(a*x)**2/(6*a**2) + 8*atanh(a*x)/(45*a**2), Ne(a, 0)), (0, True))","A",0
207,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2,x)","\int \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2, x)","F",0
208,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x, x)","F",0
209,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**2,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x**2, x)","F",0
210,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**3,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x**3, x)","F",0
211,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**4,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x**4, x)","F",0
212,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**5,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x**5, x)","F",0
213,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**6,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{6}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x**6, x)","F",0
214,1,148,0,2.596745," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**7,x)","\begin{cases} \frac{8 a^{6} \log{\left(x \right)}}{45} - \frac{8 a^{6} \log{\left(x - \frac{1}{a} \right)}}{45} + \frac{a^{6} \operatorname{atanh}^{2}{\left(a x \right)}}{6} - \frac{8 a^{6} \operatorname{atanh}{\left(a x \right)}}{45} - \frac{a^{5} \operatorname{atanh}{\left(a x \right)}}{3 x} - \frac{a^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{2 x^{2}} + \frac{7 a^{4}}{90 x^{2}} + \frac{2 a^{3} \operatorname{atanh}{\left(a x \right)}}{9 x^{3}} + \frac{a^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{2 x^{4}} - \frac{a^{2}}{60 x^{4}} - \frac{a \operatorname{atanh}{\left(a x \right)}}{15 x^{5}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{6 x^{6}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**6*log(x)/45 - 8*a**6*log(x - 1/a)/45 + a**6*atanh(a*x)**2/6 - 8*a**6*atanh(a*x)/45 - a**5*atanh(a*x)/(3*x) - a**4*atanh(a*x)**2/(2*x**2) + 7*a**4/(90*x**2) + 2*a**3*atanh(a*x)/(9*x**3) + a**2*atanh(a*x)**2/(2*x**4) - a**2/(60*x**4) - a*atanh(a*x)/(15*x**5) - atanh(a*x)**2/(6*x**6), Ne(a, 0)), (0, True))","A",0
215,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**8,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{8}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2/x**8, x)","F",0
216,1,168,0,3.988302," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**2/x**9,x)","\begin{cases} \frac{4 a^{8} \log{\left(x \right)}}{63} - \frac{4 a^{8} \log{\left(x - \frac{1}{a} \right)}}{63} + \frac{a^{8} \operatorname{atanh}^{2}{\left(a x \right)}}{24} - \frac{4 a^{8} \operatorname{atanh}{\left(a x \right)}}{63} - \frac{a^{7} \operatorname{atanh}{\left(a x \right)}}{12 x} + \frac{5 a^{6}}{504 x^{2}} - \frac{a^{5} \operatorname{atanh}{\left(a x \right)}}{36 x^{3}} - \frac{a^{4} \operatorname{atanh}^{2}{\left(a x \right)}}{4 x^{4}} + \frac{a^{4}}{84 x^{4}} + \frac{a^{3} \operatorname{atanh}{\left(a x \right)}}{12 x^{5}} + \frac{a^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{3 x^{6}} - \frac{a^{2}}{168 x^{6}} - \frac{a \operatorname{atanh}{\left(a x \right)}}{28 x^{7}} - \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{8 x^{8}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a**8*log(x)/63 - 4*a**8*log(x - 1/a)/63 + a**8*atanh(a*x)**2/24 - 4*a**8*atanh(a*x)/63 - a**7*atanh(a*x)/(12*x) + 5*a**6/(504*x**2) - a**5*atanh(a*x)/(36*x**3) - a**4*atanh(a*x)**2/(4*x**4) + a**4/(84*x**4) + a**3*atanh(a*x)/(12*x**5) + a**2*atanh(a*x)**2/(3*x**6) - a**2/(168*x**6) - a*atanh(a*x)/(28*x**7) - atanh(a*x)**2/(8*x**8), Ne(a, 0)), (0, True))","A",0
217,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2*atanh(a*x)**3,x)","\int \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{3}{\left(a x \right)}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**3, x)","F",0
218,0,0,0,0.000000," ","integrate(x*(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}{\operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(a*x - 1)**2*(a*x + 1)**2/atanh(a*x), x)","F",0
219,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}{\operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2/atanh(a*x), x)","F",0
220,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2/x/atanh(a*x),x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}{x \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2/(x*atanh(a*x)), x)","F",0
221,0,0,0,0.000000," ","integrate(x*(-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}{\operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x*(a*x - 1)**2*(a*x + 1)**2/atanh(a*x)**2, x)","F",0
222,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}{\operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2/atanh(a*x)**2, x)","F",0
223,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**2/x/atanh(a*x)**2,x)","\int \frac{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}{x \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral((a*x - 1)**2*(a*x + 1)**2/(x*atanh(a*x)**2), x)","F",0
224,1,97,0,2.039866," ","integrate((-a**2*x**2+1)**3*atanh(a*x),x)","\begin{cases} - \frac{a^{6} x^{7} \operatorname{atanh}{\left(a x \right)}}{7} - \frac{a^{5} x^{6}}{42} + \frac{3 a^{4} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{4 a^{3} x^{4}}{35} - a^{2} x^{3} \operatorname{atanh}{\left(a x \right)} - \frac{19 a x^{2}}{70} + x \operatorname{atanh}{\left(a x \right)} + \frac{16 \log{\left(x - \frac{1}{a} \right)}}{35 a} + \frac{16 \operatorname{atanh}{\left(a x \right)}}{35 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**6*x**7*atanh(a*x)/7 - a**5*x**6/42 + 3*a**4*x**5*atanh(a*x)/5 + 4*a**3*x**4/35 - a**2*x**3*atanh(a*x) - 19*a*x**2/70 + x*atanh(a*x) + 16*log(x - 1/a)/(35*a) + 16*atanh(a*x)/(35*a), Ne(a, 0)), (0, True))","A",0
225,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**3*atanh(a*x)**2,x)","- \int 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)}\, dx - \int \left(- 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)}\right)\, dx - \int a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)}\, dx - \int \left(- \operatorname{atanh}^{2}{\left(a x \right)}\right)\, dx"," ",0,"-Integral(3*a**2*x**2*atanh(a*x)**2, x) - Integral(-3*a**4*x**4*atanh(a*x)**2, x) - Integral(a**6*x**6*atanh(a*x)**2, x) - Integral(-atanh(a*x)**2, x)","F",0
226,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**3*atanh(a*x)**3,x)","- \int 3 a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)}\, dx - \int \left(- 3 a^{4} x^{4} \operatorname{atanh}^{3}{\left(a x \right)}\right)\, dx - \int a^{6} x^{6} \operatorname{atanh}^{3}{\left(a x \right)}\, dx - \int \left(- \operatorname{atanh}^{3}{\left(a x \right)}\right)\, dx"," ",0,"-Integral(3*a**2*x**2*atanh(a*x)**3, x) - Integral(-3*a**4*x**4*atanh(a*x)**3, x) - Integral(a**6*x**6*atanh(a*x)**3, x) - Integral(-atanh(a*x)**3, x)","F",0
227,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)/(-a**2*x**2+1),x)","- \int \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**3*atanh(a*x)/(a**2*x**2 - 1), x)","F",0
228,1,41,0,0.985580," ","integrate(x**2*atanh(a*x)/(-a**2*x**2+1),x)","\begin{cases} - \frac{x \operatorname{atanh}{\left(a x \right)}}{a^{2}} - \frac{\log{\left(x - \frac{1}{a} \right)}}{a^{3}} + \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{2 a^{3}} - \frac{\operatorname{atanh}{\left(a x \right)}}{a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x*atanh(a*x)/a**2 - log(x - 1/a)/a**3 + atanh(a*x)**2/(2*a**3) - atanh(a*x)/a**3, Ne(a, 0)), (0, True))","A",0
229,0,0,0,0.000000," ","integrate(x*atanh(a*x)/(-a**2*x**2+1),x)","- \int \frac{x \operatorname{atanh}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x*atanh(a*x)/(a**2*x**2 - 1), x)","F",0
230,1,10,0,0.900523," ","integrate(atanh(a*x)/(-a**2*x**2+1),x)","\begin{cases} \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{2 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((atanh(a*x)**2/(2*a), Ne(a, 0)), (0, True))","A",0
231,0,0,0,0.000000," ","integrate(atanh(a*x)/x/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}{\left(a x \right)}}{a^{2} x^{3} - x}\, dx"," ",0,"-Integral(atanh(a*x)/(a**2*x**3 - x), x)","F",0
232,1,37,0,1.416393," ","integrate(atanh(a*x)/x**2/(-a**2*x**2+1),x)","\begin{cases} a \log{\left(x \right)} - a \log{\left(x - \frac{1}{a} \right)} + \frac{a \operatorname{atanh}^{2}{\left(a x \right)}}{2} - a \operatorname{atanh}{\left(a x \right)} - \frac{\operatorname{atanh}{\left(a x \right)}}{x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(x) - a*log(x - 1/a) + a*atanh(a*x)**2/2 - a*atanh(a*x) - atanh(a*x)/x, Ne(a, 0)), (0, True))","A",0
233,0,0,0,0.000000," ","integrate(atanh(a*x)/x**3/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}{\left(a x \right)}}{a^{2} x^{5} - x^{3}}\, dx"," ",0,"-Integral(atanh(a*x)/(a**2*x**5 - x**3), x)","F",0
234,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**2/(-a**2*x**2+1),x)","- \int \frac{x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**3*atanh(a*x)**2/(a**2*x**2 - 1), x)","F",0
235,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**2/(-a**2*x**2+1),x)","- \int \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**2*atanh(a*x)**2/(a**2*x**2 - 1), x)","F",0
236,0,0,0,0.000000," ","integrate(x*atanh(a*x)**2/(-a**2*x**2+1),x)","- \int \frac{x \operatorname{atanh}^{2}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x*atanh(a*x)**2/(a**2*x**2 - 1), x)","F",0
237,1,10,0,0.931107," ","integrate(atanh(a*x)**2/(-a**2*x**2+1),x)","\begin{cases} \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{3 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((atanh(a*x)**3/(3*a), Ne(a, 0)), (0, True))","A",0
238,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a^{2} x^{3} - x}\, dx"," ",0,"-Integral(atanh(a*x)**2/(a**2*x**3 - x), x)","F",0
239,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**2/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a^{2} x^{4} - x^{2}}\, dx"," ",0,"-Integral(atanh(a*x)**2/(a**2*x**4 - x**2), x)","F",0
240,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**3/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a^{2} x^{5} - x^{3}}\, dx"," ",0,"-Integral(atanh(a*x)**2/(a**2*x**5 - x**3), x)","F",0
241,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**3/(-a**2*x**2+1),x)","- \int \frac{x^{3} \operatorname{atanh}^{3}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**3*atanh(a*x)**3/(a**2*x**2 - 1), x)","F",0
242,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**3/(-a**2*x**2+1),x)","- \int \frac{x^{2} \operatorname{atanh}^{3}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**2*atanh(a*x)**3/(a**2*x**2 - 1), x)","F",0
243,0,0,0,0.000000," ","integrate(x*atanh(a*x)**3/(-a**2*x**2+1),x)","- \int \frac{x \operatorname{atanh}^{3}{\left(a x \right)}}{a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x*atanh(a*x)**3/(a**2*x**2 - 1), x)","F",0
244,1,10,0,0.959192," ","integrate(atanh(a*x)**3/(-a**2*x**2+1),x)","\begin{cases} \frac{\operatorname{atanh}^{4}{\left(a x \right)}}{4 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((atanh(a*x)**4/(4*a), Ne(a, 0)), (0, True))","A",0
245,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a^{2} x^{3} - x}\, dx"," ",0,"-Integral(atanh(a*x)**3/(a**2*x**3 - x), x)","F",0
246,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**2/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a^{2} x^{4} - x^{2}}\, dx"," ",0,"-Integral(atanh(a*x)**3/(a**2*x**4 - x**2), x)","F",0
247,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**3/(-a**2*x**2+1),x)","- \int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a^{2} x^{5} - x^{3}}\, dx"," ",0,"-Integral(atanh(a*x)**3/(a**2*x**5 - x**3), x)","F",0
248,1,14,0,1.215512," ","integrate(atanh(a*x)**(1/2)/(-a**2*x**2+1),x)","\begin{cases} \frac{2 \operatorname{atanh}^{\frac{3}{2}}{\left(a x \right)}}{3 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*atanh(a*x)**(3/2)/(3*a), Ne(a, 0)), (0, True))","A",0
249,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)/atanh(a*x),x)","- \int \frac{x}{a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x/(a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
250,1,7,0,0.643809," ","integrate(1/(-a**2*x**2+1)/atanh(a*x),x)","\frac{\log{\left(\operatorname{atanh}{\left(a x \right)} \right)}}{a}"," ",0,"log(atanh(a*x))/a","A",0
251,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)/atanh(a*x),x)","- \int \frac{1}{a^{2} x^{3} \operatorname{atanh}{\left(a x \right)} - x \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**3*atanh(a*x) - x*atanh(a*x)), x)","F",0
252,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)/atanh(a*x)**2,x)","- \int \frac{x}{a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(x/(a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
253,1,8,0,0.932034," ","integrate(1/(-a**2*x**2+1)/atanh(a*x)**2,x)","- \frac{1}{a \operatorname{atanh}{\left(a x \right)}}"," ",0,"-1/(a*atanh(a*x))","A",0
254,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)/atanh(a*x)**2,x)","- \int \frac{1}{a^{2} x^{3} \operatorname{atanh}^{2}{\left(a x \right)} - x \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**3*atanh(a*x)**2 - x*atanh(a*x)**2), x)","F",0
255,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)/atanh(a*x)**3,x)","- \int \frac{x}{a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)} - \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(x/(a**2*x**2*atanh(a*x)**3 - atanh(a*x)**3), x)","F",0
256,1,12,0,1.115981," ","integrate(1/(-a**2*x**2+1)/atanh(a*x)**3,x)","- \frac{1}{2 a \operatorname{atanh}^{2}{\left(a x \right)}}"," ",0,"-1/(2*a*atanh(a*x)**2)","A",0
257,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)/atanh(a*x)**3,x)","- \int \frac{1}{a^{2} x^{3} \operatorname{atanh}^{3}{\left(a x \right)} - x \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**2*x**3*atanh(a*x)**3 - x*atanh(a*x)**3), x)","F",0
258,1,26,0,1.525432," ","integrate(atanh(a*x)**p/(-a**2*x**2+1),x)","\begin{cases} \frac{\begin{cases} \frac{\operatorname{atanh}^{p + 1}{\left(a x \right)}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(\operatorname{atanh}{\left(a x \right)} \right)} & \text{otherwise} \end{cases}}{a} & \text{for}\: a \neq 0 \\0^{p} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((Piecewise((atanh(a*x)**(p + 1)/(p + 1), Ne(p, -1)), (log(atanh(a*x)), True))/a, Ne(a, 0)), (0**p*x, True))","A",0
259,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)/(-a**2*x**2+1)**2,x)","\int \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x**3*atanh(a*x)/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
260,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)/(-a**2*x**2+1)**2,x)","\int \frac{x^{2} \operatorname{atanh}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x**2*atanh(a*x)/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
261,1,61,0,1.311993," ","integrate(x*atanh(a*x)/(-a**2*x**2+1)**2,x)","\begin{cases} - \frac{a^{2} x^{2} \operatorname{atanh}{\left(a x \right)}}{4 a^{4} x^{2} - 4 a^{2}} + \frac{a x}{4 a^{4} x^{2} - 4 a^{2}} - \frac{\operatorname{atanh}{\left(a x \right)}}{4 a^{4} x^{2} - 4 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x**2*atanh(a*x)/(4*a**4*x**2 - 4*a**2) + a*x/(4*a**4*x**2 - 4*a**2) - atanh(a*x)/(4*a**4*x**2 - 4*a**2), Ne(a, 0)), (0, True))","A",0
262,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
263,0,0,0,0.000000," ","integrate(atanh(a*x)/x/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)/(x*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
264,1,253,0,2.720948," ","integrate(atanh(a*x)/x**2/(-a**2*x**2+1)**2,x)","\begin{cases} \frac{4 a^{3} x^{3} \log{\left(x \right)}}{4 a^{2} x^{3} - 4 x} - \frac{4 a^{3} x^{3} \log{\left(x - \frac{1}{a} \right)}}{4 a^{2} x^{3} - 4 x} + \frac{3 a^{3} x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{4 a^{2} x^{3} - 4 x} - \frac{4 a^{3} x^{3} \operatorname{atanh}{\left(a x \right)}}{4 a^{2} x^{3} - 4 x} - \frac{6 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)}}{4 a^{2} x^{3} - 4 x} - \frac{4 a x \log{\left(x \right)}}{4 a^{2} x^{3} - 4 x} + \frac{4 a x \log{\left(x - \frac{1}{a} \right)}}{4 a^{2} x^{3} - 4 x} - \frac{3 a x \operatorname{atanh}^{2}{\left(a x \right)}}{4 a^{2} x^{3} - 4 x} + \frac{4 a x \operatorname{atanh}{\left(a x \right)}}{4 a^{2} x^{3} - 4 x} + \frac{a x}{4 a^{2} x^{3} - 4 x} + \frac{4 \operatorname{atanh}{\left(a x \right)}}{4 a^{2} x^{3} - 4 x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a**3*x**3*log(x)/(4*a**2*x**3 - 4*x) - 4*a**3*x**3*log(x - 1/a)/(4*a**2*x**3 - 4*x) + 3*a**3*x**3*atanh(a*x)**2/(4*a**2*x**3 - 4*x) - 4*a**3*x**3*atanh(a*x)/(4*a**2*x**3 - 4*x) - 6*a**2*x**2*atanh(a*x)/(4*a**2*x**3 - 4*x) - 4*a*x*log(x)/(4*a**2*x**3 - 4*x) + 4*a*x*log(x - 1/a)/(4*a**2*x**3 - 4*x) - 3*a*x*atanh(a*x)**2/(4*a**2*x**3 - 4*x) + 4*a*x*atanh(a*x)/(4*a**2*x**3 - 4*x) + a*x/(4*a**2*x**3 - 4*x) + 4*atanh(a*x)/(4*a**2*x**3 - 4*x), Ne(a, 0)), (0, True))","A",0
265,0,0,0,0.000000," ","integrate(atanh(a*x)/x**3/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x^{3} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)/(x**3*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
266,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**2/(-a**2*x**2+1)**2,x)","\int \frac{x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x**3*atanh(a*x)**2/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
267,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**2/(-a**2*x**2+1)**2,x)","\int \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x**2*atanh(a*x)**2/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
268,0,0,0,0.000000," ","integrate(x*atanh(a*x)**2/(-a**2*x**2+1)**2,x)","\int \frac{x \operatorname{atanh}^{2}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x*atanh(a*x)**2/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
269,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**2/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
270,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
271,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**2/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{2} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x**2*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
272,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**3/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{3} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x**3*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
273,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**3/(-a**2*x**2+1)**2,x)","\int \frac{x^{3} \operatorname{atanh}^{3}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x**3*atanh(a*x)**3/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
274,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**3/(-a**2*x**2+1)**2,x)","\int \frac{x^{2} \operatorname{atanh}^{3}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x**2*atanh(a*x)**3/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
275,0,0,0,0.000000," ","integrate(x*atanh(a*x)**3/(-a**2*x**2+1)**2,x)","\int \frac{x \operatorname{atanh}^{3}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(x*atanh(a*x)**3/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
276,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**3/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
277,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
278,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**2/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x^{2} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x**2*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
279,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**3/(-a**2*x**2+1)**2,x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x^{3} \left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x**3*(a*x - 1)**2*(a*x + 1)**2), x)","F",0
280,0,0,0,0.000000," ","integrate(atanh(a*x)**(1/2)/(-a**2*x**2+1)**2,x)","\int \frac{\sqrt{\operatorname{atanh}{\left(a x \right)}}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2}}\, dx"," ",0,"Integral(sqrt(atanh(a*x))/((a*x - 1)**2*(a*x + 1)**2), x)","F",0
281,0,0,0,0.000000," ","integrate(x**4/(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{x^{4}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)), x)","F",0
282,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{x^{3}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)), x)","F",0
283,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{x^{2}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)), x)","F",0
284,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{x}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)), x)","F",0
285,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)), x)","F",0
286,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**2/atanh(a*x),x)","\int \frac{1}{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(a*x - 1)**2*(a*x + 1)**2*atanh(a*x)), x)","F",0
287,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{x^{3}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2), x)","F",0
288,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{x^{2}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2), x)","F",0
289,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{x}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2), x)","F",0
291,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**2/atanh(a*x)**2,x)","\int \frac{1}{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**2), x)","F",0
292,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**2/atanh(a*x)**3,x)","\int \frac{x^{3}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**3), x)","F",0
293,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**2/atanh(a*x)**3,x)","\int \frac{x^{2}}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**3), x)","F",0
294,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**2/atanh(a*x)**3,x)","\int \frac{x}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**3), x)","F",0
295,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**3,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**3), x)","F",0
296,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**2/atanh(a*x)**3,x)","\int \frac{1}{x \left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**3), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**4,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{4}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**4), x)","F",0
298,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**5,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{5}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**5), x)","F",0
299,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**6,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{6}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**6), x)","F",0
300,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**7,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{7}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**7), x)","F",0
301,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**2/atanh(a*x)**8,x)","\int \frac{1}{\left(a x - 1\right)^{2} \left(a x + 1\right)^{2} \operatorname{atanh}^{8}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**2*(a*x + 1)**2*atanh(a*x)**8), x)","F",0
302,1,158,0,2.411917," ","integrate(x**3*atanh(a*x)/(-a**2*x**2+1)**3,x)","\begin{cases} \frac{5 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)}}{32 a^{8} x^{4} - 64 a^{6} x^{2} + 32 a^{4}} - \frac{5 a^{3} x^{3}}{32 a^{8} x^{4} - 64 a^{6} x^{2} + 32 a^{4}} + \frac{6 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)}}{32 a^{8} x^{4} - 64 a^{6} x^{2} + 32 a^{4}} + \frac{3 a x}{32 a^{8} x^{4} - 64 a^{6} x^{2} + 32 a^{4}} - \frac{3 \operatorname{atanh}{\left(a x \right)}}{32 a^{8} x^{4} - 64 a^{6} x^{2} + 32 a^{4}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**4*x**4*atanh(a*x)/(32*a**8*x**4 - 64*a**6*x**2 + 32*a**4) - 5*a**3*x**3/(32*a**8*x**4 - 64*a**6*x**2 + 32*a**4) + 6*a**2*x**2*atanh(a*x)/(32*a**8*x**4 - 64*a**6*x**2 + 32*a**4) + 3*a*x/(32*a**8*x**4 - 64*a**6*x**2 + 32*a**4) - 3*atanh(a*x)/(32*a**8*x**4 - 64*a**6*x**2 + 32*a**4), Ne(a, 0)), (0, True))","A",0
303,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)/(-a**2*x**2+1)**3,x)","- \int \frac{x^{2} \operatorname{atanh}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**2*atanh(a*x)/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
304,1,158,0,2.410283," ","integrate(x*atanh(a*x)/(-a**2*x**2+1)**3,x)","\begin{cases} - \frac{3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)}}{32 a^{6} x^{4} - 64 a^{4} x^{2} + 32 a^{2}} + \frac{3 a^{3} x^{3}}{32 a^{6} x^{4} - 64 a^{4} x^{2} + 32 a^{2}} + \frac{6 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)}}{32 a^{6} x^{4} - 64 a^{4} x^{2} + 32 a^{2}} - \frac{5 a x}{32 a^{6} x^{4} - 64 a^{4} x^{2} + 32 a^{2}} + \frac{5 \operatorname{atanh}{\left(a x \right)}}{32 a^{6} x^{4} - 64 a^{4} x^{2} + 32 a^{2}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**4*x**4*atanh(a*x)/(32*a**6*x**4 - 64*a**4*x**2 + 32*a**2) + 3*a**3*x**3/(32*a**6*x**4 - 64*a**4*x**2 + 32*a**2) + 6*a**2*x**2*atanh(a*x)/(32*a**6*x**4 - 64*a**4*x**2 + 32*a**2) - 5*a*x/(32*a**6*x**4 - 64*a**4*x**2 + 32*a**2) + 5*atanh(a*x)/(32*a**6*x**4 - 64*a**4*x**2 + 32*a**2), Ne(a, 0)), (0, True))","A",0
305,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(atanh(a*x)/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
306,0,0,0,0.000000," ","integrate(atanh(a*x)/x/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}{\left(a x \right)}}{a^{6} x^{7} - 3 a^{4} x^{5} + 3 a^{2} x^{3} - x}\, dx"," ",0,"-Integral(atanh(a*x)/(a**6*x**7 - 3*a**4*x**5 + 3*a**2*x**3 - x), x)","F",0
307,1,549,0,4.903452," ","integrate(atanh(a*x)/x**2/(-a**2*x**2+1)**3,x)","\begin{cases} \frac{16 a^{5} x^{5} \log{\left(x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{16 a^{5} x^{5} \log{\left(x - \frac{1}{a} \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{15 a^{5} x^{5} \operatorname{atanh}^{2}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{16 a^{5} x^{5} \operatorname{atanh}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{30 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{32 a^{3} x^{3} \log{\left(x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{32 a^{3} x^{3} \log{\left(x - \frac{1}{a} \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{30 a^{3} x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{32 a^{3} x^{3} \operatorname{atanh}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{7 a^{3} x^{3}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{50 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{16 a x \log{\left(x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{16 a x \log{\left(x - \frac{1}{a} \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} + \frac{15 a x \operatorname{atanh}^{2}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{16 a x \operatorname{atanh}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{8 a x}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} - \frac{16 \operatorname{atanh}{\left(a x \right)}}{16 a^{4} x^{5} - 32 a^{2} x^{3} + 16 x} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**5*x**5*log(x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 16*a**5*x**5*log(x - 1/a)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 15*a**5*x**5*atanh(a*x)**2/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 16*a**5*x**5*atanh(a*x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 30*a**4*x**4*atanh(a*x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 32*a**3*x**3*log(x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 32*a**3*x**3*log(x - 1/a)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 30*a**3*x**3*atanh(a*x)**2/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 32*a**3*x**3*atanh(a*x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 7*a**3*x**3/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 50*a**2*x**2*atanh(a*x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 16*a*x*log(x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 16*a*x*log(x - 1/a)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) + 15*a*x*atanh(a*x)**2/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 16*a*x*atanh(a*x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 8*a*x/(16*a**4*x**5 - 32*a**2*x**3 + 16*x) - 16*atanh(a*x)/(16*a**4*x**5 - 32*a**2*x**3 + 16*x), Ne(a, 0)), (0, True))","A",0
308,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**2/(-a**2*x**2+1)**3,x)","- \int \frac{x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**3*atanh(a*x)**2/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
309,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**2/(-a**2*x**2+1)**3,x)","- \int \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**2*atanh(a*x)**2/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
310,0,0,0,0.000000," ","integrate(x*atanh(a*x)**2/(-a**2*x**2+1)**3,x)","- \int \frac{x \operatorname{atanh}^{2}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x*atanh(a*x)**2/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
311,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(atanh(a*x)**2/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
312,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a^{6} x^{7} - 3 a^{4} x^{5} + 3 a^{2} x^{3} - x}\, dx"," ",0,"-Integral(atanh(a*x)**2/(a**6*x**7 - 3*a**4*x**5 + 3*a**2*x**3 - x), x)","F",0
313,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**2/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{a^{6} x^{8} - 3 a^{4} x^{6} + 3 a^{2} x^{4} - x^{2}}\, dx"," ",0,"-Integral(atanh(a*x)**2/(a**6*x**8 - 3*a**4*x**6 + 3*a**2*x**4 - x**2), x)","F",0
314,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**3/(-a**2*x**2+1)**3,x)","- \int \frac{x^{3} \operatorname{atanh}^{3}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**3*atanh(a*x)**3/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
315,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**3/(-a**2*x**2+1)**3,x)","- \int \frac{x^{2} \operatorname{atanh}^{3}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x**2*atanh(a*x)**3/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
316,0,0,0,0.000000," ","integrate(x*atanh(a*x)**3/(-a**2*x**2+1)**3,x)","- \int \frac{x \operatorname{atanh}^{3}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(x*atanh(a*x)**3/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
317,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(atanh(a*x)**3/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
318,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a^{6} x^{7} - 3 a^{4} x^{5} + 3 a^{2} x^{3} - x}\, dx"," ",0,"-Integral(atanh(a*x)**3/(a**6*x**7 - 3*a**4*x**5 + 3*a**2*x**3 - x), x)","F",0
319,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**2/(-a**2*x**2+1)**3,x)","- \int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{a^{6} x^{8} - 3 a^{4} x^{6} + 3 a^{2} x^{4} - x^{2}}\, dx"," ",0,"-Integral(atanh(a*x)**3/(a**6*x**8 - 3*a**4*x**6 + 3*a**2*x**4 - x**2), x)","F",0
320,0,0,0,0.000000," ","integrate(atanh(a*x)**(1/2)/(-a**2*x**2+1)**3,x)","- \int \frac{\sqrt{\operatorname{atanh}{\left(a x \right)}}}{a^{6} x^{6} - 3 a^{4} x^{4} + 3 a^{2} x^{2} - 1}\, dx"," ",0,"-Integral(sqrt(atanh(a*x))/(a**6*x**6 - 3*a**4*x**4 + 3*a**2*x**2 - 1), x)","F",0
321,0,0,0,0.000000," ","integrate(x**6/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{x^{6}}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**6/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
322,0,0,0,0.000000," ","integrate(x**5/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{x^{5}}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**5/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
323,0,0,0,0.000000," ","integrate(x**4/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{x^{4}}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**4/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
324,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{x^{3}}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**3/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
325,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{x^{2}}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**2/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
326,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{x}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(x/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{1}{a^{6} x^{6} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}{\left(a x \right)} - \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - atanh(a*x)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**3/atanh(a*x),x)","- \int \frac{1}{a^{6} x^{7} \operatorname{atanh}{\left(a x \right)} - 3 a^{4} x^{5} \operatorname{atanh}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atanh}{\left(a x \right)} - x \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**7*atanh(a*x) - 3*a**4*x**5*atanh(a*x) + 3*a**2*x**3*atanh(a*x) - x*atanh(a*x)), x)","F",0
329,0,0,0,0.000000," ","integrate(x**5/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{x^{5}}{a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**5/(a**6*x**6*atanh(a*x)**2 - 3*a**4*x**4*atanh(a*x)**2 + 3*a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
330,0,0,0,0.000000," ","integrate(x**4/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{x^{4}}{a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**4/(a**6*x**6*atanh(a*x)**2 - 3*a**4*x**4*atanh(a*x)**2 + 3*a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
331,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{x^{3}}{a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**3/(a**6*x**6*atanh(a*x)**2 - 3*a**4*x**4*atanh(a*x)**2 + 3*a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
332,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{x^{2}}{a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**2/(a**6*x**6*atanh(a*x)**2 - 3*a**4*x**4*atanh(a*x)**2 + 3*a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
333,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{x}{a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(x/(a**6*x**6*atanh(a*x)**2 - 3*a**4*x**4*atanh(a*x)**2 + 3*a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
334,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{1}{a^{6} x^{6} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{2}{\left(a x \right)} - \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**6*atanh(a*x)**2 - 3*a**4*x**4*atanh(a*x)**2 + 3*a**2*x**2*atanh(a*x)**2 - atanh(a*x)**2), x)","F",0
335,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**3/atanh(a*x)**2,x)","- \int \frac{1}{a^{6} x^{7} \operatorname{atanh}^{2}{\left(a x \right)} - 3 a^{4} x^{5} \operatorname{atanh}^{2}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atanh}^{2}{\left(a x \right)} - x \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**7*atanh(a*x)**2 - 3*a**4*x**5*atanh(a*x)**2 + 3*a**2*x**3*atanh(a*x)**2 - x*atanh(a*x)**2), x)","F",0
336,0,0,0,0.000000," ","integrate(x**4/(-a**2*x**2+1)**3/atanh(a*x)**3,x)","- \int \frac{x^{4}}{a^{6} x^{6} \operatorname{atanh}^{3}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)} - \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**4/(a**6*x**6*atanh(a*x)**3 - 3*a**4*x**4*atanh(a*x)**3 + 3*a**2*x**2*atanh(a*x)**3 - atanh(a*x)**3), x)","F",0
337,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**3/atanh(a*x)**3,x)","- \int \frac{x^{3}}{a^{6} x^{6} \operatorname{atanh}^{3}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)} - \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**3/(a**6*x**6*atanh(a*x)**3 - 3*a**4*x**4*atanh(a*x)**3 + 3*a**2*x**2*atanh(a*x)**3 - atanh(a*x)**3), x)","F",0
338,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**3/atanh(a*x)**3,x)","- \int \frac{x^{2}}{a^{6} x^{6} \operatorname{atanh}^{3}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)} - \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(x**2/(a**6*x**6*atanh(a*x)**3 - 3*a**4*x**4*atanh(a*x)**3 + 3*a**2*x**2*atanh(a*x)**3 - atanh(a*x)**3), x)","F",0
339,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**3/atanh(a*x)**3,x)","- \int \frac{x}{a^{6} x^{6} \operatorname{atanh}^{3}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)} - \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(x/(a**6*x**6*atanh(a*x)**3 - 3*a**4*x**4*atanh(a*x)**3 + 3*a**2*x**2*atanh(a*x)**3 - atanh(a*x)**3), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**3/atanh(a*x)**3,x)","- \int \frac{1}{a^{6} x^{6} \operatorname{atanh}^{3}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{3}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{3}{\left(a x \right)} - \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**6*atanh(a*x)**3 - 3*a**4*x**4*atanh(a*x)**3 + 3*a**2*x**2*atanh(a*x)**3 - atanh(a*x)**3), x)","F",0
341,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**3/atanh(a*x)**3,x)","- \int \frac{1}{a^{6} x^{7} \operatorname{atanh}^{3}{\left(a x \right)} - 3 a^{4} x^{5} \operatorname{atanh}^{3}{\left(a x \right)} + 3 a^{2} x^{3} \operatorname{atanh}^{3}{\left(a x \right)} - x \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**7*atanh(a*x)**3 - 3*a**4*x**5*atanh(a*x)**3 + 3*a**2*x**3*atanh(a*x)**3 - x*atanh(a*x)**3), x)","F",0
342,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**3/atanh(a*x)**4,x)","- \int \frac{1}{a^{6} x^{6} \operatorname{atanh}^{4}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{4}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{4}{\left(a x \right)} - \operatorname{atanh}^{4}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**6*atanh(a*x)**4 - 3*a**4*x**4*atanh(a*x)**4 + 3*a**2*x**2*atanh(a*x)**4 - atanh(a*x)**4), x)","F",0
343,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**3/atanh(a*x)**5,x)","- \int \frac{1}{a^{6} x^{6} \operatorname{atanh}^{5}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{5}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{5}{\left(a x \right)} - \operatorname{atanh}^{5}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**6*atanh(a*x)**5 - 3*a**4*x**4*atanh(a*x)**5 + 3*a**2*x**2*atanh(a*x)**5 - atanh(a*x)**5), x)","F",0
344,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**3/atanh(a*x)**6,x)","- \int \frac{1}{a^{6} x^{6} \operatorname{atanh}^{6}{\left(a x \right)} - 3 a^{4} x^{4} \operatorname{atanh}^{6}{\left(a x \right)} + 3 a^{2} x^{2} \operatorname{atanh}^{6}{\left(a x \right)} - \operatorname{atanh}^{6}{\left(a x \right)}}\, dx"," ",0,"-Integral(1/(a**6*x**6*atanh(a*x)**6 - 3*a**4*x**4*atanh(a*x)**6 + 3*a**2*x**2*atanh(a*x)**6 - atanh(a*x)**6), x)","F",0
345,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**4,x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4}}\, dx"," ",0,"Integral(atanh(a*x)/((a*x - 1)**4*(a*x + 1)**4), x)","F",0
346,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**4,x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4}}\, dx"," ",0,"Integral(atanh(a*x)**2/((a*x - 1)**4*(a*x + 1)**4), x)","F",0
347,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**4,x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4}}\, dx"," ",0,"Integral(atanh(a*x)**3/((a*x - 1)**4*(a*x + 1)**4), x)","F",0
348,0,0,0,0.000000," ","integrate(atanh(a*x)**(1/2)/(-a**2*x**2+1)**4,x)","\int \frac{\sqrt{\operatorname{atanh}{\left(a x \right)}}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4}}\, dx"," ",0,"Integral(sqrt(atanh(a*x))/((a*x - 1)**4*(a*x + 1)**4), x)","F",0
349,0,0,0,0.000000," ","integrate(x**8/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{8}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**8/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
350,0,0,0,0.000000," ","integrate(x**7/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{7}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**7/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
351,0,0,0,0.000000," ","integrate(x**6/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{6}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**6/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
352,0,0,0,0.000000," ","integrate(x**5/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{5}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**5/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
353,0,0,0,0.000000," ","integrate(x**4/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{4}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**4/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
354,0,0,0,0.000000," ","integrate(x**3/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{3}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
355,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x^{2}}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
356,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{x}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
357,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{1}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
358,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{1}{x \left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
359,0,0,0,0.000000," ","integrate(1/x**2/(-a**2*x**2+1)**4/atanh(a*x),x)","\int \frac{1}{x^{2} \left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x**2*(a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)","F",0
360,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**4/atanh(a*x)**2,x)","\int \frac{x}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)**2), x)","F",0
361,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**4/atanh(a*x)**2,x)","\int \frac{1}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)**2), x)","F",0
362,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**4/atanh(a*x)**3,x)","\int \frac{x}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)**3), x)","F",0
363,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**4/atanh(a*x)**3,x)","\int \frac{1}{\left(a x - 1\right)^{4} \left(a x + 1\right)^{4} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((a*x - 1)**4*(a*x + 1)**4*atanh(a*x)**3), x)","F",0
364,0,0,0,0.000000," ","integrate(x**5*atanh(a*x)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{5} \operatorname{atanh}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**5*atanh(a*x)/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
365,0,0,0,0.000000," ","integrate(x**4*atanh(a*x)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{4} \operatorname{atanh}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**4*atanh(a*x)/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
366,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**3*atanh(a*x)/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
367,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{2} \operatorname{atanh}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**2*atanh(a*x)/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
368,0,0,0,0.000000," ","integrate(x*atanh(a*x)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x \operatorname{atanh}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x*atanh(a*x)/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
369,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
370,0,0,0,0.000000," ","integrate(atanh(a*x)/x/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)/(x*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
371,0,0,0,0.000000," ","integrate(atanh(a*x)/x**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x^{2} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)/(x**2*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
372,0,0,0,0.000000," ","integrate(atanh(a*x)/x**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x^{3} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)/(x**3*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
373,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**3*atanh(a*x)**2/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
374,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**2*atanh(a*x)**2/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
375,0,0,0,0.000000," ","integrate(x*atanh(a*x)**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{x \operatorname{atanh}^{2}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x*atanh(a*x)**2/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
376,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**2/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
377,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
378,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{2} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x**2*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
379,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{3} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x**3*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
380,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{3} \operatorname{atanh}^{3}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**3*atanh(a*x)**3/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
381,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{2} \operatorname{atanh}^{3}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x**2*atanh(a*x)**3/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
382,0,0,0,0.000000," ","integrate(x*atanh(a*x)**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{x \operatorname{atanh}^{3}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(x*atanh(a*x)**3/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
383,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**3/sqrt(-(a*x - 1)*(a*x + 1)), x)","F",0
384,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
385,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**2/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x^{2} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x**2*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
386,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**3/(-a**2*x**2+1)**(1/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x^{3} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x**3*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
387,0,0,0,0.000000," ","integrate(x**m*atanh(a*x)/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{m} \operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
388,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{3} \operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
389,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{2} \operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
390,0,0,0,0.000000," ","integrate(x*atanh(a*x)/(-a**2*x**2+1)**(3/2),x)","\int \frac{x \operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
391,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
392,0,0,0,0.000000," ","integrate(atanh(a*x)/x/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(x*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
393,0,0,0,0.000000," ","integrate(atanh(a*x)/x**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x^{2} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(x**2*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
394,0,0,0,0.000000," ","integrate(atanh(a*x)/x**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{x^{3} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(x**3*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
395,0,0,0,0.000000," ","integrate(x**m*atanh(a*x)**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{m} \operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{3} \operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
397,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{2} \operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate(x*atanh(a*x)**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{x \operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
400,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
401,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{2} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x**2*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
402,0,0,0,0.000000," ","integrate(atanh(a*x)**2/x**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{x^{3} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(x**3*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
403,0,0,0,0.000000," ","integrate(x**m*atanh(a*x)**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{m} \operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**m*atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
404,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{3} \operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3*atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
405,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{x^{2} \operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2*atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
406,0,0,0,0.000000," ","integrate(x*atanh(a*x)**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{x \operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x*atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
407,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
408,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
409,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**2/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x^{2} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x**2*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
410,0,0,0,0.000000," ","integrate(atanh(a*x)**3/x**3/(-a**2*x**2+1)**(3/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{x^{3} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(x**3*(-(a*x - 1)*(a*x + 1))**(3/2)), x)","F",0
411,0,0,0,0.000000," ","integrate(x**m/(-a**2*x**2+1)**(3/2)/atanh(a*x),x)","\int \frac{x^{m}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)), x)","F",0
412,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**(3/2)/atanh(a*x),x)","\int \frac{x^{2}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)), x)","F",0
413,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**(3/2)/atanh(a*x),x)","\int \frac{x}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(3/2)/atanh(a*x),x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)), x)","F",0
415,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**(3/2)/atanh(a*x),x)","\int \frac{1}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)), x)","F",0
416,0,0,0,0.000000," ","integrate(x**m/(-a**2*x**2+1)**(3/2)/atanh(a*x)**2,x)","\int \frac{x^{m}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**m/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**2), x)","F",0
417,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**(3/2)/atanh(a*x)**2,x)","\int \frac{x^{2}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**2), x)","F",0
418,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**(3/2)/atanh(a*x)**2,x)","\int \frac{x}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**2), x)","F",0
419,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(3/2)/atanh(a*x)**2,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**2), x)","F",0
420,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**(3/2)/atanh(a*x)**2,x)","\int \frac{1}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**2), x)","F",0
421,-1,0,0,0.000000," ","integrate(x**m/(-a**2*x**2+1)**(3/2)/atanh(a*x)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,0,0,0,0.000000," ","integrate(x**2/(-a**2*x**2+1)**(3/2)/atanh(a*x)**3,x)","\int \frac{x^{2}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**3), x)","F",0
423,0,0,0,0.000000," ","integrate(x/(-a**2*x**2+1)**(3/2)/atanh(a*x)**3,x)","\int \frac{x}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(x/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**3), x)","F",0
424,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(3/2)/atanh(a*x)**3,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**3), x)","F",0
425,0,0,0,0.000000," ","integrate(1/x/(-a**2*x**2+1)**(3/2)/atanh(a*x)**3,x)","\int \frac{1}{x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(x*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**3), x)","F",0
426,0,0,0,0.000000," ","integrate(x**4*atanh(a*x)*(-a**2*x**2+1)**(1/2),x)","\int x^{4} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x**4*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
427,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)*(-a**2*x**2+1)**(1/2),x)","\int x^{3} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
428,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)*(-a**2*x**2+1)**(1/2),x)","\int x^{2} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
429,0,0,0,0.000000," ","integrate(x*atanh(a*x)*(-a**2*x**2+1)**(1/2),x)","\int x \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
430,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)*atanh(a*x),x)","\int \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
431,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x, x)","F",0
432,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x**2,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x**2, x)","F",0
433,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x**3,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x**3, x)","F",0
434,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x**4,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x**4, x)","F",0
435,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x**5,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x**5, x)","F",0
436,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x**6,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x^{6}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x**6, x)","F",0
437,0,0,0,0.000000," ","integrate(atanh(a*x)*(-a**2*x**2+1)**(1/2)/x**7,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}{x^{7}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)/x**7, x)","F",0
438,0,0,0,0.000000," ","integrate(x**4*atanh(a*x)**2*(-a**2*x**2+1)**(1/2),x)","\int x^{4} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**4*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2, x)","F",0
439,0,0,0,0.000000," ","integrate(x**3*atanh(a*x)**2*(-a**2*x**2+1)**(1/2),x)","\int x^{3} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2, x)","F",0
440,0,0,0,0.000000," ","integrate(x**2*atanh(a*x)**2*(-a**2*x**2+1)**(1/2),x)","\int x^{2} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2, x)","F",0
441,0,0,0,0.000000," ","integrate(x*atanh(a*x)**2*(-a**2*x**2+1)**(1/2),x)","\int x \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x*sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2, x)","F",0
442,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)*atanh(a*x)**2,x)","\int \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2, x)","F",0
443,0,0,0,0.000000," ","integrate(atanh(a*x)**2*(-a**2*x**2+1)**(1/2)/x,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2/x, x)","F",0
444,0,0,0,0.000000," ","integrate(atanh(a*x)**2*(-a**2*x**2+1)**(1/2)/x**2,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2/x**2, x)","F",0
445,0,0,0,0.000000," ","integrate(atanh(a*x)**2*(-a**2*x**2+1)**(1/2)/x**3,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2/x**3, x)","F",0
446,0,0,0,0.000000," ","integrate(atanh(a*x)**2*(-a**2*x**2+1)**(1/2)/x**4,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2/x**4, x)","F",0
447,0,0,0,0.000000," ","integrate(x**4*(-a**2*x**2+1)**(3/2)*atanh(a*x),x)","\int x^{4} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x**4*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
448,0,0,0,0.000000," ","integrate(x**3*(-a**2*x**2+1)**(3/2)*atanh(a*x),x)","\int x^{3} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
449,0,0,0,0.000000," ","integrate(x**2*(-a**2*x**2+1)**(3/2)*atanh(a*x),x)","\int x^{2} \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
450,0,0,0,0.000000," ","integrate(x*(-a**2*x**2+1)**(3/2)*atanh(a*x),x)","\int x \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(x*(-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
451,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x),x)","\int \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
452,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x, x)","F",0
453,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x**2,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x**2, x)","F",0
454,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x**3,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x**3, x)","F",0
455,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x**4,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x**4, x)","F",0
456,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x**5,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x**5, x)","F",0
457,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x**6,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x^{6}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x**6, x)","F",0
458,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x)/x**7,x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}{x^{7}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)/x**7, x)","F",0
459,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(5/2)*atanh(a*x),x)","\int \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(5/2)*atanh(a*x), x)","F",0
460,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)*atanh(a*x),x)","\int \left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
461,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)*atanh(a*x),x)","\int \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
462,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**(5/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
463,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**(7/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(7/2), x)","F",0
464,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*x**2+1)**(9/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-(a*x - 1)*(a*x + 1))**(9/2), x)","F",0
465,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(3/2)*atanh(a*x),x)","\int \left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral((-c*(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x), x)","F",0
466,0,0,0,0.000000," ","integrate((-a**2*c*x**2+c)**(1/2)*atanh(a*x),x)","\int \sqrt{- c \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1)*(a*x + 1))*atanh(a*x), x)","F",0
467,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*c*x**2+c)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\sqrt{- c \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(atanh(a*x)/sqrt(-c*(a*x - 1)*(a*x + 1)), x)","F",0
468,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*c*x**2+c)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-c*(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
469,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*c*x**2+c)**(5/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-c*(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
470,0,0,0,0.000000," ","integrate(atanh(a*x)/(-a**2*c*x**2+c)**(7/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(- c \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(-c*(a*x - 1)*(a*x + 1))**(7/2), x)","F",0
471,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)*atanh(a*x)**2,x)","\int \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2, x)","F",0
472,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**(5/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
473,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**(7/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(7/2), x)","F",0
474,0,0,0,0.000000," ","integrate(atanh(a*x)**2/(-a**2*x**2+1)**(9/2),x)","\int \frac{\operatorname{atanh}^{2}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**2/(-(a*x - 1)*(a*x + 1))**(9/2), x)","F",0
475,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)*atanh(a*x)**3,x)","\int \sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**3, x)","F",0
476,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**(5/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
477,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**(7/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(7/2), x)","F",0
478,0,0,0,0.000000," ","integrate(atanh(a*x)**3/(-a**2*x**2+1)**(9/2),x)","\int \frac{\operatorname{atanh}^{3}{\left(a x \right)}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(atanh(a*x)**3/(-(a*x - 1)*(a*x + 1))**(9/2), x)","F",0
479,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)/atanh(a*x),x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))/atanh(a*x), x)","F",0
480,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(1/2)/atanh(a*x),x)","\int \frac{1}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)), x)","F",0
481,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(3/2)/atanh(a*x),x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)), x)","F",0
482,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(5/2)/atanh(a*x),x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(5/2)*atanh(a*x)), x)","F",0
483,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(7/2)/atanh(a*x),x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(7/2)*atanh(a*x)), x)","F",0
484,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(9/2)/atanh(a*x),x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}} \operatorname{atanh}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(9/2)*atanh(a*x)), x)","F",0
485,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)/atanh(a*x)**2,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))/atanh(a*x)**2, x)","F",0
486,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(1/2)/atanh(a*x)**2,x)","\int \frac{1}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**2), x)","F",0
487,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(3/2)/atanh(a*x)**2,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**2), x)","F",0
488,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(5/2)/atanh(a*x)**2,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(5/2)*atanh(a*x)**2), x)","F",0
489,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(7/2)/atanh(a*x)**2,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(7/2)*atanh(a*x)**2), x)","F",0
490,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(9/2)/atanh(a*x)**2,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}} \operatorname{atanh}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(9/2)*atanh(a*x)**2), x)","F",0
491,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)/atanh(a*x)**3,x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))/atanh(a*x)**3, x)","F",0
492,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(1/2)/atanh(a*x)**3,x)","\int \frac{1}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/(sqrt(-(a*x - 1)*(a*x + 1))*atanh(a*x)**3), x)","F",0
493,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(3/2)/atanh(a*x)**3,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(3/2)*atanh(a*x)**3), x)","F",0
494,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(5/2)/atanh(a*x)**3,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(5/2)*atanh(a*x)**3), x)","F",0
495,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(7/2)/atanh(a*x)**3,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{7}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(7/2)*atanh(a*x)**3), x)","F",0
496,0,0,0,0.000000," ","integrate(1/(-a**2*x**2+1)**(9/2)/atanh(a*x)**3,x)","\int \frac{1}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{9}{2}} \operatorname{atanh}^{3}{\left(a x \right)}}\, dx"," ",0,"Integral(1/((-(a*x - 1)*(a*x + 1))**(9/2)*atanh(a*x)**3), x)","F",0
497,0,0,0,0.000000," ","integrate((e*x+d)*(a+b*atanh(c*x))**2/(-c**2*x**2+1),x)","- \int \frac{a^{2} d}{c^{2} x^{2} - 1}\, dx - \int \frac{a^{2} e x}{c^{2} x^{2} - 1}\, dx - \int \frac{b^{2} d \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{2 a b d \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{b^{2} e x \operatorname{atanh}^{2}{\left(c x \right)}}{c^{2} x^{2} - 1}\, dx - \int \frac{2 a b e x \operatorname{atanh}{\left(c x \right)}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral(a**2*d/(c**2*x**2 - 1), x) - Integral(a**2*e*x/(c**2*x**2 - 1), x) - Integral(b**2*d*atanh(c*x)**2/(c**2*x**2 - 1), x) - Integral(2*a*b*d*atanh(c*x)/(c**2*x**2 - 1), x) - Integral(b**2*e*x*atanh(c*x)**2/(c**2*x**2 - 1), x) - Integral(2*a*b*e*x*atanh(c*x)/(c**2*x**2 - 1), x)","F",0
498,1,372,0,5.554695," ","integrate((d*x**2+c)**4*atanh(a*x),x)","\begin{cases} c^{4} x \operatorname{atanh}{\left(a x \right)} + \frac{4 c^{3} d x^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{6 c^{2} d^{2} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{4 c d^{3} x^{7} \operatorname{atanh}{\left(a x \right)}}{7} + \frac{d^{4} x^{9} \operatorname{atanh}{\left(a x \right)}}{9} + \frac{c^{4} \log{\left(x - \frac{1}{a} \right)}}{a} + \frac{c^{4} \operatorname{atanh}{\left(a x \right)}}{a} + \frac{2 c^{3} d x^{2}}{3 a} + \frac{3 c^{2} d^{2} x^{4}}{10 a} + \frac{2 c d^{3} x^{6}}{21 a} + \frac{d^{4} x^{8}}{72 a} + \frac{4 c^{3} d \log{\left(x - \frac{1}{a} \right)}}{3 a^{3}} + \frac{4 c^{3} d \operatorname{atanh}{\left(a x \right)}}{3 a^{3}} + \frac{3 c^{2} d^{2} x^{2}}{5 a^{3}} + \frac{c d^{3} x^{4}}{7 a^{3}} + \frac{d^{4} x^{6}}{54 a^{3}} + \frac{6 c^{2} d^{2} \log{\left(x - \frac{1}{a} \right)}}{5 a^{5}} + \frac{6 c^{2} d^{2} \operatorname{atanh}{\left(a x \right)}}{5 a^{5}} + \frac{2 c d^{3} x^{2}}{7 a^{5}} + \frac{d^{4} x^{4}}{36 a^{5}} + \frac{4 c d^{3} \log{\left(x - \frac{1}{a} \right)}}{7 a^{7}} + \frac{4 c d^{3} \operatorname{atanh}{\left(a x \right)}}{7 a^{7}} + \frac{d^{4} x^{2}}{18 a^{7}} + \frac{d^{4} \log{\left(x - \frac{1}{a} \right)}}{9 a^{9}} + \frac{d^{4} \operatorname{atanh}{\left(a x \right)}}{9 a^{9}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x*atanh(a*x) + 4*c**3*d*x**3*atanh(a*x)/3 + 6*c**2*d**2*x**5*atanh(a*x)/5 + 4*c*d**3*x**7*atanh(a*x)/7 + d**4*x**9*atanh(a*x)/9 + c**4*log(x - 1/a)/a + c**4*atanh(a*x)/a + 2*c**3*d*x**2/(3*a) + 3*c**2*d**2*x**4/(10*a) + 2*c*d**3*x**6/(21*a) + d**4*x**8/(72*a) + 4*c**3*d*log(x - 1/a)/(3*a**3) + 4*c**3*d*atanh(a*x)/(3*a**3) + 3*c**2*d**2*x**2/(5*a**3) + c*d**3*x**4/(7*a**3) + d**4*x**6/(54*a**3) + 6*c**2*d**2*log(x - 1/a)/(5*a**5) + 6*c**2*d**2*atanh(a*x)/(5*a**5) + 2*c*d**3*x**2/(7*a**5) + d**4*x**4/(36*a**5) + 4*c*d**3*log(x - 1/a)/(7*a**7) + 4*c*d**3*atanh(a*x)/(7*a**7) + d**4*x**2/(18*a**7) + d**4*log(x - 1/a)/(9*a**9) + d**4*atanh(a*x)/(9*a**9), Ne(a, 0)), (0, True))","A",0
499,1,245,0,3.191832," ","integrate((d*x**2+c)**3*atanh(a*x),x)","\begin{cases} c^{3} x \operatorname{atanh}{\left(a x \right)} + c^{2} d x^{3} \operatorname{atanh}{\left(a x \right)} + \frac{3 c d^{2} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{d^{3} x^{7} \operatorname{atanh}{\left(a x \right)}}{7} + \frac{c^{3} \log{\left(x - \frac{1}{a} \right)}}{a} + \frac{c^{3} \operatorname{atanh}{\left(a x \right)}}{a} + \frac{c^{2} d x^{2}}{2 a} + \frac{3 c d^{2} x^{4}}{20 a} + \frac{d^{3} x^{6}}{42 a} + \frac{c^{2} d \log{\left(x - \frac{1}{a} \right)}}{a^{3}} + \frac{c^{2} d \operatorname{atanh}{\left(a x \right)}}{a^{3}} + \frac{3 c d^{2} x^{2}}{10 a^{3}} + \frac{d^{3} x^{4}}{28 a^{3}} + \frac{3 c d^{2} \log{\left(x - \frac{1}{a} \right)}}{5 a^{5}} + \frac{3 c d^{2} \operatorname{atanh}{\left(a x \right)}}{5 a^{5}} + \frac{d^{3} x^{2}}{14 a^{5}} + \frac{d^{3} \log{\left(x - \frac{1}{a} \right)}}{7 a^{7}} + \frac{d^{3} \operatorname{atanh}{\left(a x \right)}}{7 a^{7}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*x*atanh(a*x) + c**2*d*x**3*atanh(a*x) + 3*c*d**2*x**5*atanh(a*x)/5 + d**3*x**7*atanh(a*x)/7 + c**3*log(x - 1/a)/a + c**3*atanh(a*x)/a + c**2*d*x**2/(2*a) + 3*c*d**2*x**4/(20*a) + d**3*x**6/(42*a) + c**2*d*log(x - 1/a)/a**3 + c**2*d*atanh(a*x)/a**3 + 3*c*d**2*x**2/(10*a**3) + d**3*x**4/(28*a**3) + 3*c*d**2*log(x - 1/a)/(5*a**5) + 3*c*d**2*atanh(a*x)/(5*a**5) + d**3*x**2/(14*a**5) + d**3*log(x - 1/a)/(7*a**7) + d**3*atanh(a*x)/(7*a**7), Ne(a, 0)), (0, True))","A",0
500,1,155,0,1.735473," ","integrate((d*x**2+c)**2*atanh(a*x),x)","\begin{cases} c^{2} x \operatorname{atanh}{\left(a x \right)} + \frac{2 c d x^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{d^{2} x^{5} \operatorname{atanh}{\left(a x \right)}}{5} + \frac{c^{2} \log{\left(x - \frac{1}{a} \right)}}{a} + \frac{c^{2} \operatorname{atanh}{\left(a x \right)}}{a} + \frac{c d x^{2}}{3 a} + \frac{d^{2} x^{4}}{20 a} + \frac{2 c d \log{\left(x - \frac{1}{a} \right)}}{3 a^{3}} + \frac{2 c d \operatorname{atanh}{\left(a x \right)}}{3 a^{3}} + \frac{d^{2} x^{2}}{10 a^{3}} + \frac{d^{2} \log{\left(x - \frac{1}{a} \right)}}{5 a^{5}} + \frac{d^{2} \operatorname{atanh}{\left(a x \right)}}{5 a^{5}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*x*atanh(a*x) + 2*c*d*x**3*atanh(a*x)/3 + d**2*x**5*atanh(a*x)/5 + c**2*log(x - 1/a)/a + c**2*atanh(a*x)/a + c*d*x**2/(3*a) + d**2*x**4/(20*a) + 2*c*d*log(x - 1/a)/(3*a**3) + 2*c*d*atanh(a*x)/(3*a**3) + d**2*x**2/(10*a**3) + d**2*log(x - 1/a)/(5*a**5) + d**2*atanh(a*x)/(5*a**5), Ne(a, 0)), (0, True))","A",0
501,1,73,0,0.791855," ","integrate((d*x**2+c)*atanh(a*x),x)","\begin{cases} c x \operatorname{atanh}{\left(a x \right)} + \frac{d x^{3} \operatorname{atanh}{\left(a x \right)}}{3} + \frac{c \log{\left(x - \frac{1}{a} \right)}}{a} + \frac{c \operatorname{atanh}{\left(a x \right)}}{a} + \frac{d x^{2}}{6 a} + \frac{d \log{\left(x - \frac{1}{a} \right)}}{3 a^{3}} + \frac{d \operatorname{atanh}{\left(a x \right)}}{3 a^{3}} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x*atanh(a*x) + d*x**3*atanh(a*x)/3 + c*log(x - 1/a)/a + c*atanh(a*x)/a + d*x**2/(6*a) + d*log(x - 1/a)/(3*a**3) + d*atanh(a*x)/(3*a**3), Ne(a, 0)), (0, True))","A",0
502,0,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{c + d x^{2}}\, dx"," ",0,"Integral(atanh(a*x)/(c + d*x**2), x)","F",0
503,-1,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,1,14,0,0.556247," ","integrate(1/(-a*x**2+a)/(b-2*b*atanh(x)),x)","- \frac{\log{\left(\operatorname{atanh}{\left(x \right)} - \frac{1}{2} \right)}}{2 a b}"," ",0,"-log(atanh(x) - 1/2)/(2*a*b)","A",0
506,0,0,0,0.000000," ","integrate(atanh(b*x)/(-x**2+1),x)","- \int \frac{\operatorname{atanh}{\left(b x \right)}}{x^{2} - 1}\, dx"," ",0,"-Integral(atanh(b*x)/(x**2 - 1), x)","F",0
507,0,0,0,0.000000," ","integrate(atanh(b*x+a)/(-x**2+1),x)","- \int \frac{\operatorname{atanh}{\left(a + b x \right)}}{x^{2} - 1}\, dx"," ",0,"-Integral(atanh(a + b*x)/(x**2 - 1), x)","F",0
508,0,0,0,0.000000," ","integrate(atanh(x)/(b*x+a),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{a + b x}\, dx"," ",0,"Integral(atanh(x)/(a + b*x), x)","F",0
509,0,0,0,0.000000," ","integrate(atanh(x)/(b*x**2+a),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{a + b x^{2}}\, dx"," ",0,"Integral(atanh(x)/(a + b*x**2), x)","F",0
510,0,0,0,0.000000," ","integrate(atanh(x)/(c*x**2+b*x+a),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{a + b x + c x^{2}}\, dx"," ",0,"Integral(atanh(x)/(a + b*x + c*x**2), x)","F",0
511,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)*atanh(a*x),x)","\int \sqrt{c + d x^{2}} \operatorname{atanh}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x**2)*atanh(a*x), x)","F",0
512,0,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(atanh(a*x)/sqrt(c + d*x**2), x)","F",0
513,0,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(c + d*x**2)**(3/2), x)","F",0
514,0,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**(5/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(c + d*x**2)**(5/2), x)","F",0
515,0,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**(7/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(c + d*x**2)**(7/2), x)","F",0
516,0,0,0,0.000000," ","integrate(atanh(a*x)/(d*x**2+c)**(9/2),x)","\int \frac{\operatorname{atanh}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(atanh(a*x)/(c + d*x**2)**(9/2), x)","F",0
517,0,0,0,0.000000," ","integrate((-a*x**2+a)**(1/2)*atanh(x),x)","\int \sqrt{- a \left(x - 1\right) \left(x + 1\right)} \operatorname{atanh}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(-a*(x - 1)*(x + 1))*atanh(x), x)","F",0
518,0,0,0,0.000000," ","integrate(atanh(x)/(-a*x**2+a)**(1/2),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{\sqrt{- a \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral(atanh(x)/sqrt(-a*(x - 1)*(x + 1)), x)","F",0
519,0,0,0,0.000000," ","integrate(atanh(x)/(-a*x**2+a)**(3/2),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{\left(- a \left(x - 1\right) \left(x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(atanh(x)/(-a*(x - 1)*(x + 1))**(3/2), x)","F",0
520,0,0,0,0.000000," ","integrate(atanh(x)/(-a*x**2+a)**(5/2),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{\left(- a \left(x - 1\right) \left(x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(atanh(x)/(-a*(x - 1)*(x + 1))**(5/2), x)","F",0
521,0,0,0,0.000000," ","integrate(atanh(x)/(-a*x**2+a)**(7/2),x)","\int \frac{\operatorname{atanh}{\left(x \right)}}{\left(- a \left(x - 1\right) \left(x + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(atanh(x)/(-a*(x - 1)*(x + 1))**(7/2), x)","F",0
522,1,338,0,15.180806," ","integrate(x**4*(a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{5}}{5} + \frac{a e x^{5} \log{\left(- c^{2} x^{2} + 1 \right)}}{5} - \frac{2 a e x^{5}}{25} - \frac{2 a e x^{3}}{15 c^{2}} - \frac{2 a e x}{5 c^{4}} + \frac{2 a e \operatorname{atanh}{\left(c x \right)}}{5 c^{5}} + \frac{b d x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b e x^{5} \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)}}{5} - \frac{2 b e x^{5} \operatorname{atanh}{\left(c x \right)}}{25} + \frac{b d x^{4}}{20 c} + \frac{b e x^{4} \log{\left(- c^{2} x^{2} + 1 \right)}}{20 c} - \frac{9 b e x^{4}}{200 c} - \frac{2 b e x^{3} \operatorname{atanh}{\left(c x \right)}}{15 c^{2}} + \frac{b d x^{2}}{10 c^{3}} + \frac{b e x^{2} \log{\left(- c^{2} x^{2} + 1 \right)}}{10 c^{3}} - \frac{77 b e x^{2}}{300 c^{3}} - \frac{2 b e x \operatorname{atanh}{\left(c x \right)}}{5 c^{4}} + \frac{b d \log{\left(- c^{2} x^{2} + 1 \right)}}{10 c^{5}} + \frac{b e \log{\left(- c^{2} x^{2} + 1 \right)}^{2}}{20 c^{5}} - \frac{137 b e \log{\left(- c^{2} x^{2} + 1 \right)}}{300 c^{5}} + \frac{b e \operatorname{atanh}^{2}{\left(c x \right)}}{5 c^{5}} & \text{for}\: c \neq 0 \\\frac{a d x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**5/5 + a*e*x**5*log(-c**2*x**2 + 1)/5 - 2*a*e*x**5/25 - 2*a*e*x**3/(15*c**2) - 2*a*e*x/(5*c**4) + 2*a*e*atanh(c*x)/(5*c**5) + b*d*x**5*atanh(c*x)/5 + b*e*x**5*log(-c**2*x**2 + 1)*atanh(c*x)/5 - 2*b*e*x**5*atanh(c*x)/25 + b*d*x**4/(20*c) + b*e*x**4*log(-c**2*x**2 + 1)/(20*c) - 9*b*e*x**4/(200*c) - 2*b*e*x**3*atanh(c*x)/(15*c**2) + b*d*x**2/(10*c**3) + b*e*x**2*log(-c**2*x**2 + 1)/(10*c**3) - 77*b*e*x**2/(300*c**3) - 2*b*e*x*atanh(c*x)/(5*c**4) + b*d*log(-c**2*x**2 + 1)/(10*c**5) + b*e*log(-c**2*x**2 + 1)**2/(20*c**5) - 137*b*e*log(-c**2*x**2 + 1)/(300*c**5) + b*e*atanh(c*x)**2/(5*c**5), Ne(c, 0)), (a*d*x**5/5, True))","A",0
523,1,279,0,9.741716," ","integrate(x**3*(a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{4}}{4} + \frac{a e x^{4} \log{\left(- c^{2} x^{2} + 1 \right)}}{4} - \frac{a e x^{4}}{8} - \frac{a e x^{2}}{4 c^{2}} - \frac{a e \log{\left(- c^{2} x^{2} + 1 \right)}}{4 c^{4}} + \frac{b d x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b e x^{4} \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)}}{4} - \frac{b e x^{4} \operatorname{atanh}{\left(c x \right)}}{8} + \frac{b d x^{3}}{12 c} + \frac{b e x^{3} \log{\left(- c^{2} x^{2} + 1 \right)}}{12 c} - \frac{7 b e x^{3}}{72 c} - \frac{b e x^{2} \operatorname{atanh}{\left(c x \right)}}{4 c^{2}} + \frac{b d x}{4 c^{3}} + \frac{b e x \log{\left(- c^{2} x^{2} + 1 \right)}}{4 c^{3}} - \frac{25 b e x}{24 c^{3}} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{4 c^{4}} - \frac{b e \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)}}{4 c^{4}} + \frac{25 b e \operatorname{atanh}{\left(c x \right)}}{24 c^{4}} & \text{for}\: c \neq 0 \\\frac{a d x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**4/4 + a*e*x**4*log(-c**2*x**2 + 1)/4 - a*e*x**4/8 - a*e*x**2/(4*c**2) - a*e*log(-c**2*x**2 + 1)/(4*c**4) + b*d*x**4*atanh(c*x)/4 + b*e*x**4*log(-c**2*x**2 + 1)*atanh(c*x)/4 - b*e*x**4*atanh(c*x)/8 + b*d*x**3/(12*c) + b*e*x**3*log(-c**2*x**2 + 1)/(12*c) - 7*b*e*x**3/(72*c) - b*e*x**2*atanh(c*x)/(4*c**2) + b*d*x/(4*c**3) + b*e*x*log(-c**2*x**2 + 1)/(4*c**3) - 25*b*e*x/(24*c**3) - b*d*atanh(c*x)/(4*c**4) - b*e*log(-c**2*x**2 + 1)*atanh(c*x)/(4*c**4) + 25*b*e*atanh(c*x)/(24*c**4), Ne(c, 0)), (a*d*x**4/4, True))","A",0
524,1,258,0,6.539983," ","integrate(x**2*(a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{3}}{3} + \frac{a e x^{3} \log{\left(- c^{2} x^{2} + 1 \right)}}{3} - \frac{2 a e x^{3}}{9} - \frac{2 a e x}{3 c^{2}} + \frac{2 a e \operatorname{atanh}{\left(c x \right)}}{3 c^{3}} + \frac{b d x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b e x^{3} \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)}}{3} - \frac{2 b e x^{3} \operatorname{atanh}{\left(c x \right)}}{9} + \frac{b d x^{2}}{6 c} + \frac{b e x^{2} \log{\left(- c^{2} x^{2} + 1 \right)}}{6 c} - \frac{5 b e x^{2}}{18 c} - \frac{2 b e x \operatorname{atanh}{\left(c x \right)}}{3 c^{2}} + \frac{b d \log{\left(- c^{2} x^{2} + 1 \right)}}{6 c^{3}} + \frac{b e \log{\left(- c^{2} x^{2} + 1 \right)}^{2}}{12 c^{3}} - \frac{11 b e \log{\left(- c^{2} x^{2} + 1 \right)}}{18 c^{3}} + \frac{b e \operatorname{atanh}^{2}{\left(c x \right)}}{3 c^{3}} & \text{for}\: c \neq 0 \\\frac{a d x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**3/3 + a*e*x**3*log(-c**2*x**2 + 1)/3 - 2*a*e*x**3/9 - 2*a*e*x/(3*c**2) + 2*a*e*atanh(c*x)/(3*c**3) + b*d*x**3*atanh(c*x)/3 + b*e*x**3*log(-c**2*x**2 + 1)*atanh(c*x)/3 - 2*b*e*x**3*atanh(c*x)/9 + b*d*x**2/(6*c) + b*e*x**2*log(-c**2*x**2 + 1)/(6*c) - 5*b*e*x**2/(18*c) - 2*b*e*x*atanh(c*x)/(3*c**2) + b*d*log(-c**2*x**2 + 1)/(6*c**3) + b*e*log(-c**2*x**2 + 1)**2/(12*c**3) - 11*b*e*log(-c**2*x**2 + 1)/(18*c**3) + b*e*atanh(c*x)**2/(3*c**3), Ne(c, 0)), (a*d*x**3/3, True))","A",0
525,1,202,0,3.780851," ","integrate(x*(a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1)),x)","\begin{cases} \frac{a d x^{2}}{2} + \frac{a e x^{2} \log{\left(- c^{2} x^{2} + 1 \right)}}{2} - \frac{a e x^{2}}{2} - \frac{a e \log{\left(- c^{2} x^{2} + 1 \right)}}{2 c^{2}} + \frac{b d x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b e x^{2} \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)}}{2} - \frac{b e x^{2} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{b d x}{2 c} + \frac{b e x \log{\left(- c^{2} x^{2} + 1 \right)}}{2 c} - \frac{3 b e x}{2 c} - \frac{b d \operatorname{atanh}{\left(c x \right)}}{2 c^{2}} - \frac{b e \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)}}{2 c^{2}} + \frac{3 b e \operatorname{atanh}{\left(c x \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\\frac{a d x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x**2/2 + a*e*x**2*log(-c**2*x**2 + 1)/2 - a*e*x**2/2 - a*e*log(-c**2*x**2 + 1)/(2*c**2) + b*d*x**2*atanh(c*x)/2 + b*e*x**2*log(-c**2*x**2 + 1)*atanh(c*x)/2 - b*e*x**2*atanh(c*x)/2 + b*d*x/(2*c) + b*e*x*log(-c**2*x**2 + 1)/(2*c) - 3*b*e*x/(2*c) - b*d*atanh(c*x)/(2*c**2) - b*e*log(-c**2*x**2 + 1)*atanh(c*x)/(2*c**2) + 3*b*e*atanh(c*x)/(2*c**2), Ne(c, 0)), (a*d*x**2/2, True))","A",0
526,1,148,0,2.264715," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1)),x)","\begin{cases} a d x + a e x \log{\left(- c^{2} x^{2} + 1 \right)} - 2 a e x + \frac{2 a e \operatorname{atanh}{\left(c x \right)}}{c} + b d x \operatorname{atanh}{\left(c x \right)} + b e x \log{\left(- c^{2} x^{2} + 1 \right)} \operatorname{atanh}{\left(c x \right)} - 2 b e x \operatorname{atanh}{\left(c x \right)} + \frac{b d \log{\left(- c^{2} x^{2} + 1 \right)}}{2 c} + \frac{b e \log{\left(- c^{2} x^{2} + 1 \right)}^{2}}{4 c} - \frac{b e \log{\left(- c^{2} x^{2} + 1 \right)}}{c} + \frac{b e \operatorname{atanh}^{2}{\left(c x \right)}}{c} & \text{for}\: c \neq 0 \\a d x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x*log(-c**2*x**2 + 1) - 2*a*e*x + 2*a*e*atanh(c*x)/c + b*d*x*atanh(c*x) + b*e*x*log(-c**2*x**2 + 1)*atanh(c*x) - 2*b*e*x*atanh(c*x) + b*d*log(-c**2*x**2 + 1)/(2*c) + b*e*log(-c**2*x**2 + 1)**2/(4*c) - b*e*log(-c**2*x**2 + 1)/c + b*e*atanh(c*x)**2/c, Ne(c, 0)), (a*d*x, True))","A",0
527,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1))/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \left(d + e \log{\left(- c^{2} x^{2} + 1 \right)}\right)}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x))*(d + e*log(-c**2*x**2 + 1))/x, x)","F",0
528,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1))/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \left(d + e \log{\left(- c^{2} x^{2} + 1 \right)}\right)}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))*(d + e*log(-c**2*x**2 + 1))/x**2, x)","F",0
529,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1))/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \left(d + e \log{\left(- c^{2} x^{2} + 1 \right)}\right)}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x))*(d + e*log(-c**2*x**2 + 1))/x**3, x)","F",0
530,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1))/x**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \left(d + e \log{\left(- c^{2} x^{2} + 1 \right)}\right)}{x^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x))*(d + e*log(-c**2*x**2 + 1))/x**4, x)","F",0
531,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1))/x**5,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \left(d + e \log{\left(- c^{2} x^{2} + 1 \right)}\right)}{x^{5}}\, dx"," ",0,"Integral((a + b*atanh(c*x))*(d + e*log(-c**2*x**2 + 1))/x**5, x)","F",0
532,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(-c**2*x**2+1))/x**6,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \left(d + e \log{\left(- c^{2} x^{2} + 1 \right)}\right)}{x^{6}}\, dx"," ",0,"Integral((a + b*atanh(c*x))*(d + e*log(-c**2*x**2 + 1))/x**6, x)","F",0
533,-1,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))*(d+e*ln(g*x**2+f)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(g*x**2+f)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(g*x**2+f))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(g*x**2+f))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x))*(d+e*ln(g*x**2+f))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,0,0,0,0.000000," ","integrate(atanh(c*x)*(a+b*atanh(c*x))/(c*x+1)**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right) \operatorname{atanh}{\left(c x \right)}}{\left(c x + 1\right)^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))*atanh(c*x)/(c*x + 1)**2, x)","F",0
