1,1,63,0,1.620873," ","integrate(x**5*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{atanh}{\left(c x \right)}}{6} + \frac{b x^{5}}{30 c} + \frac{b x^{3}}{18 c^{3}} + \frac{b x}{6 c^{5}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{6 c^{6}} & \text{for}\: c \neq 0 \\\frac{a x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*x**6*atanh(c*x)/6 + b*x**5/(30*c) + b*x**3/(18*c**3) + b*x/(6*c**5) - b*atanh(c*x)/(6*c**6), Ne(c, 0)), (a*x**6/6, True))","A",0
2,1,68,0,1.267341," ","integrate(x**4*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a x^{5}}{5} + \frac{b x^{5} \operatorname{atanh}{\left(c x \right)}}{5} + \frac{b x^{4}}{20 c} + \frac{b x^{2}}{10 c^{3}} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{5 c^{5}} + \frac{b \operatorname{atanh}{\left(c x \right)}}{5 c^{5}} & \text{for}\: c \neq 0 \\\frac{a x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**5/5 + b*x**5*atanh(c*x)/5 + b*x**4/(20*c) + b*x**2/(10*c**3) + b*log(x - 1/c)/(5*c**5) + b*atanh(c*x)/(5*c**5), Ne(c, 0)), (a*x**5/5, True))","A",0
3,1,53,0,0.914131," ","integrate(x**3*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{atanh}{\left(c x \right)}}{4} + \frac{b x^{3}}{12 c} + \frac{b x}{4 c^{3}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{4 c^{4}} & \text{for}\: c \neq 0 \\\frac{a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 + b*x**4*atanh(c*x)/4 + b*x**3/(12*c) + b*x/(4*c**3) - b*atanh(c*x)/(4*c**4), Ne(c, 0)), (a*x**4/4, True))","A",0
4,1,58,0,0.725702," ","integrate(x**2*(a+b*atanh(c*x)),x)","\begin{cases} \frac{a x^{3}}{3} + \frac{b x^{3} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{b x^{2}}{6 c} + \frac{b \log{\left(x - \frac{1}{c} \right)}}{3 c^{3}} + \frac{b \operatorname{atanh}{\left(c x \right)}}{3 c^{3}} & \text{for}\: c \neq 0 \\\frac{a x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**3/3 + b*x**3*atanh(c*x)/3 + b*x**2/(6*c) + b*log(x - 1/c)/(3*c**3) + b*atanh(c*x)/(3*c**3), Ne(c, 0)), (a*x**3/3, True))","A",0
5,1,42,0,0.492025," ","integrate(x*(a+b*atanh(c*x)),x)","\begin{cases} \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}} & \text{for}\: c \neq 0 \\\frac{a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*x**2*atanh(c*x)/2 + b*x/(2*c) - b*atanh(c*x)/(2*c**2), Ne(c, 0)), (a*x**2/2, True))","A",0
6,1,27,0,0.330511," ","integrate(a+b*atanh(c*x),x)","a x + b \left(\begin{cases} x \operatorname{atanh}{\left(c x \right)} + \frac{\log{\left(c x + 1 \right)}}{c} - \frac{\operatorname{atanh}{\left(c x \right)}}{c} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x*atanh(c*x) + log(c*x + 1)/c - atanh(c*x)/c, Ne(c, 0)), (0, True))","A",0
7,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/x,x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x))/x, x)","F",0
8,1,41,0,0.726495," ","integrate((a+b*atanh(c*x))/x**2,x)","\begin{cases} - \frac{a}{x} + b c \log{\left(x \right)} - b c \log{\left(x - \frac{1}{c} \right)} - b c \operatorname{atanh}{\left(c x \right)} - \frac{b \operatorname{atanh}{\left(c x \right)}}{x} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + b*c*log(x) - b*c*log(x - 1/c) - b*c*atanh(c*x) - b*atanh(c*x)/x, Ne(c, 0)), (-a/x, True))","A",0
9,1,36,0,0.578466," ","integrate((a+b*atanh(c*x))/x**3,x)","- \frac{a}{2 x^{2}} + \frac{b c^{2} \operatorname{atanh}{\left(c x \right)}}{2} - \frac{b c}{2 x} - \frac{b \operatorname{atanh}{\left(c x \right)}}{2 x^{2}}"," ",0,"-a/(2*x**2) + b*c**2*atanh(c*x)/2 - b*c/(2*x) - b*atanh(c*x)/(2*x**2)","A",0
10,1,70,0,1.219208," ","integrate((a+b*atanh(c*x))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} + \frac{b c^{3} \log{\left(x \right)}}{3} - \frac{b c^{3} \log{\left(x - \frac{1}{c} \right)}}{3} - \frac{b c^{3} \operatorname{atanh}{\left(c x \right)}}{3} - \frac{b c}{6 x^{2}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{3 x^{3}} & \text{for}\: c \neq 0 \\- \frac{a}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3) + b*c**3*log(x)/3 - b*c**3*log(x - 1/c)/3 - b*c**3*atanh(c*x)/3 - b*c/(6*x**2) - b*atanh(c*x)/(3*x**3), Ne(c, 0)), (-a/(3*x**3), True))","A",0
11,1,46,0,0.895756," ","integrate((a+b*atanh(c*x))/x**5,x)","- \frac{a}{4 x^{4}} + \frac{b c^{4} \operatorname{atanh}{\left(c x \right)}}{4} - \frac{b c^{3}}{4 x} - \frac{b c}{12 x^{3}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{4 x^{4}}"," ",0,"-a/(4*x**4) + b*c**4*atanh(c*x)/4 - b*c**3/(4*x) - b*c/(12*x**3) - b*atanh(c*x)/(4*x**4)","A",0
12,1,80,0,1.911031," ","integrate((a+b*atanh(c*x))/x**6,x)","\begin{cases} - \frac{a}{5 x^{5}} + \frac{b c^{5} \log{\left(x \right)}}{5} - \frac{b c^{5} \log{\left(x - \frac{1}{c} \right)}}{5} - \frac{b c^{5} \operatorname{atanh}{\left(c x \right)}}{5} - \frac{b c^{3}}{10 x^{2}} - \frac{b c}{20 x^{4}} - \frac{b \operatorname{atanh}{\left(c x \right)}}{5 x^{5}} & \text{for}\: c \neq 0 \\- \frac{a}{5 x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(5*x**5) + b*c**5*log(x)/5 - b*c**5*log(x - 1/c)/5 - b*c**5*atanh(c*x)/5 - b*c**3/(10*x**2) - b*c/(20*x**4) - b*atanh(c*x)/(5*x**5), Ne(c, 0)), (-a/(5*x**5), True))","A",0
13,1,211,0,2.737049," ","integrate(x**5*(a+b*atanh(c*x))**2,x)","\begin{cases} \frac{a^{2} x^{6}}{6} + \frac{a b x^{6} \operatorname{atanh}{\left(c x \right)}}{3} + \frac{a b x^{5}}{15 c} + \frac{a b x^{3}}{9 c^{3}} + \frac{a b x}{3 c^{5}} - \frac{a b \operatorname{atanh}{\left(c x \right)}}{3 c^{6}} + \frac{b^{2} x^{6} \operatorname{atanh}^{2}{\left(c x \right)}}{6} + \frac{b^{2} x^{5} \operatorname{atanh}{\left(c x \right)}}{15 c} + \frac{b^{2} x^{4}}{60 c^{2}} + \frac{b^{2} x^{3} \operatorname{atanh}{\left(c x \right)}}{9 c^{3}} + \frac{4 b^{2} x^{2}}{45 c^{4}} + \frac{b^{2} x \operatorname{atanh}{\left(c x \right)}}{3 c^{5}} + \frac{23 b^{2} \log{\left(x - \frac{1}{c} \right)}}{45 c^{6}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{6 c^{6}} + \frac{23 b^{2} \operatorname{atanh}{\left(c x \right)}}{45 c^{6}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**6/6 + a*b*x**6*atanh(c*x)/3 + a*b*x**5/(15*c) + a*b*x**3/(9*c**3) + a*b*x/(3*c**5) - a*b*atanh(c*x)/(3*c**6) + b**2*x**6*atanh(c*x)**2/6 + b**2*x**5*atanh(c*x)/(15*c) + b**2*x**4/(60*c**2) + b**2*x**3*atanh(c*x)/(9*c**3) + 4*b**2*x**2/(45*c**4) + b**2*x*atanh(c*x)/(3*c**5) + 23*b**2*log(x - 1/c)/(45*c**6) - b**2*atanh(c*x)**2/(6*c**6) + 23*b**2*atanh(c*x)/(45*c**6), Ne(c, 0)), (a**2*x**6/6, True))","A",0
14,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x))**2,x)","\int x^{4} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**4*(a + b*atanh(c*x))**2, x)","F",0
15,1,168,0,1.679078," ","integrate(x**3*(a+b*atanh(c*x))**2,x)","\begin{cases} \frac{a^{2} x^{4}}{4} + \frac{a b x^{4} \operatorname{atanh}{\left(c x \right)}}{2} + \frac{a b x^{3}}{6 c} + \frac{a b x}{2 c^{3}} - \frac{a b \operatorname{atanh}{\left(c x \right)}}{2 c^{4}} + \frac{b^{2} x^{4} \operatorname{atanh}^{2}{\left(c x \right)}}{4} + \frac{b^{2} x^{3} \operatorname{atanh}{\left(c x \right)}}{6 c} + \frac{b^{2} x^{2}}{12 c^{2}} + \frac{b^{2} x \operatorname{atanh}{\left(c x \right)}}{2 c^{3}} + \frac{2 b^{2} \log{\left(x - \frac{1}{c} \right)}}{3 c^{4}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{4 c^{4}} + \frac{2 b^{2} \operatorname{atanh}{\left(c x \right)}}{3 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**4/4 + a*b*x**4*atanh(c*x)/2 + a*b*x**3/(6*c) + a*b*x/(2*c**3) - a*b*atanh(c*x)/(2*c**4) + b**2*x**4*atanh(c*x)**2/4 + b**2*x**3*atanh(c*x)/(6*c) + b**2*x**2/(12*c**2) + b**2*x*atanh(c*x)/(2*c**3) + 2*b**2*log(x - 1/c)/(3*c**4) - b**2*atanh(c*x)**2/(4*c**4) + 2*b**2*atanh(c*x)/(3*c**4), Ne(c, 0)), (a**2*x**4/4, True))","A",0
16,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))**2,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*x))**2, x)","F",0
17,1,114,0,0.839715," ","integrate(x*(a+b*atanh(c*x))**2,x)","\begin{cases} \frac{a^{2} x^{2}}{2} + a b x^{2} \operatorname{atanh}{\left(c x \right)} + \frac{a b x}{c} - \frac{a b \operatorname{atanh}{\left(c x \right)}}{c^{2}} + \frac{b^{2} x^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{2} + \frac{b^{2} x \operatorname{atanh}{\left(c x \right)}}{c} + \frac{b^{2} \log{\left(x - \frac{1}{c} \right)}}{c^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{2 c^{2}} + \frac{b^{2} \operatorname{atanh}{\left(c x \right)}}{c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**2/2 + a*b*x**2*atanh(c*x) + a*b*x/c - a*b*atanh(c*x)/c**2 + b**2*x**2*atanh(c*x)**2/2 + b**2*x*atanh(c*x)/c + b**2*log(x - 1/c)/c**2 - b**2*atanh(c*x)**2/(2*c**2) + b**2*atanh(c*x)/c**2, Ne(c, 0)), (a**2*x**2/2, True))","A",0
18,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2, x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/x, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/x**2, x)","F",0
21,1,126,0,1.144026," ","integrate((a+b*atanh(c*x))**2/x**3,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} + a b c^{2} \operatorname{atanh}{\left(c x \right)} - \frac{a b c}{x} - \frac{a b \operatorname{atanh}{\left(c x \right)}}{x^{2}} + b^{2} c^{2} \log{\left(x \right)} - b^{2} c^{2} \log{\left(x - \frac{1}{c} \right)} + \frac{b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{2} - b^{2} c^{2} \operatorname{atanh}{\left(c x \right)} - \frac{b^{2} c \operatorname{atanh}{\left(c x \right)}}{x} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{2 x^{2}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) + a*b*c**2*atanh(c*x) - a*b*c/x - a*b*atanh(c*x)/x**2 + b**2*c**2*log(x) - b**2*c**2*log(x - 1/c) + b**2*c**2*atanh(c*x)**2/2 - b**2*c**2*atanh(c*x) - b**2*c*atanh(c*x)/x - b**2*atanh(c*x)**2/(2*x**2), Ne(c, 0)), (-a**2/(2*x**2), True))","A",0
22,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**2/x**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**2/x**4, x)","F",0
23,1,184,0,1.996467," ","integrate((a+b*atanh(c*x))**2/x**5,x)","\begin{cases} - \frac{a^{2}}{4 x^{4}} + \frac{a b c^{4} \operatorname{atanh}{\left(c x \right)}}{2} - \frac{a b c^{3}}{2 x} - \frac{a b c}{6 x^{3}} - \frac{a b \operatorname{atanh}{\left(c x \right)}}{2 x^{4}} + \frac{2 b^{2} c^{4} \log{\left(x \right)}}{3} - \frac{2 b^{2} c^{4} \log{\left(x - \frac{1}{c} \right)}}{3} + \frac{b^{2} c^{4} \operatorname{atanh}^{2}{\left(c x \right)}}{4} - \frac{2 b^{2} c^{4} \operatorname{atanh}{\left(c x \right)}}{3} - \frac{b^{2} c^{3} \operatorname{atanh}{\left(c x \right)}}{2 x} - \frac{b^{2} c^{2}}{12 x^{2}} - \frac{b^{2} c \operatorname{atanh}{\left(c x \right)}}{6 x^{3}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(4*x**4) + a*b*c**4*atanh(c*x)/2 - a*b*c**3/(2*x) - a*b*c/(6*x**3) - a*b*atanh(c*x)/(2*x**4) + 2*b**2*c**4*log(x)/3 - 2*b**2*c**4*log(x - 1/c)/3 + b**2*c**4*atanh(c*x)**2/4 - 2*b**2*c**4*atanh(c*x)/3 - b**2*c**3*atanh(c*x)/(2*x) - b**2*c**2/(12*x**2) - b**2*c*atanh(c*x)/(6*x**3) - b**2*atanh(c*x)**2/(4*x**4), Ne(c, 0)), (-a**2/(4*x**4), True))","A",0
24,0,0,0,0.000000," ","integrate(x**5*(a+b*atanh(c*x))**3,x)","\int x^{5} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**5*(a + b*atanh(c*x))**3, x)","F",0
25,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x))**3,x)","\int x^{4} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**4*(a + b*atanh(c*x))**3, x)","F",0
26,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x))**3,x)","\int x^{3} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atanh(c*x))**3, x)","F",0
27,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x))**3,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*x))**3, x)","F",0
28,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x))**3,x)","\int x \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atanh(c*x))**3, x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3, x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/x, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/x**2, x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/x**3, x)","F",0
33,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/x**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{x^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/x**4, x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**3/x**5,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}}{x^{5}}\, dx"," ",0,"Integral((a + b*atanh(c*x))**3/x**5, x)","F",0
35,0,0,0,0.000000," ","integrate((d*x)**(5/2)*(a+b*atanh(c*x)),x)","\int \left(d x\right)^{\frac{5}{2}} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)\, dx"," ",0,"Integral((d*x)**(5/2)*(a + b*atanh(c*x)), x)","F",0
36,0,0,0,0.000000," ","integrate((d*x)**(3/2)*(a+b*atanh(c*x)),x)","\int \left(d x\right)^{\frac{3}{2}} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)\, dx"," ",0,"Integral((d*x)**(3/2)*(a + b*atanh(c*x)), x)","F",0
37,1,685,0,11.725094," ","integrate((d*x)**(1/2)*(a+b*atanh(c*x)),x)","\frac{2 a \left(d x\right)^{\frac{3}{2}}}{3 d} + \frac{2 b \left(\begin{cases} \frac{4 c^{2} \sqrt{d} \left(d x\right)^{\frac{3}{2}} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x \right)}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{4 i c^{2} \sqrt{d} \left(d x\right)^{\frac{3}{2}} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x \right)}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{2 i c^{2} d^{2} \log{\left(i \sqrt{d} \sqrt{\frac{1}{c}} + \sqrt{d x} \right)}}{12 c^{4} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{4} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{8 c d^{\frac{3}{2}} \sqrt{d x} \sqrt{\frac{1}{c}}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{8 i c d^{\frac{3}{2}} \sqrt{d x} \sqrt{\frac{1}{c}}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{4 i c d^{2} \log{\left(- \sqrt{d} \sqrt{\frac{1}{c}} + \sqrt{d x} \right)}}{12 c^{3} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{3} \sqrt{d} \sqrt{\frac{1}{c}}} - \frac{6 i c d^{2} \log{\left(i \sqrt{d} \sqrt{\frac{1}{c}} + \sqrt{d x} \right)}}{12 c^{3} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{3} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{4 i c d^{2} \operatorname{atanh}{\left(c x \right)}}{12 c^{3} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{3} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{4 d^{2} \log{\left(- \sqrt{d} \sqrt{\frac{1}{c}} + \sqrt{d x} \right)}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} - \frac{4 d^{2} \log{\left(- i \sqrt{d} \sqrt{\frac{1}{c}} + \sqrt{d x} \right)}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} + \frac{4 d^{2} \operatorname{atanh}{\left(c x \right)}}{12 c^{2} \sqrt{d} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{d} \sqrt{\frac{1}{c}}} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{d}"," ",0,"2*a*(d*x)**(3/2)/(3*d) + 2*b*Piecewise((4*c**2*sqrt(d)*(d*x)**(3/2)*sqrt(1/c)*atanh(c*x)/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)) + 4*I*c**2*sqrt(d)*(d*x)**(3/2)*sqrt(1/c)*atanh(c*x)/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)) + 2*I*c**2*d**2*log(I*sqrt(d)*sqrt(1/c) + sqrt(d*x))/(12*c**4*sqrt(d)*sqrt(1/c) + 12*I*c**4*sqrt(d)*sqrt(1/c)) + 8*c*d**(3/2)*sqrt(d*x)*sqrt(1/c)/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)) + 8*I*c*d**(3/2)*sqrt(d*x)*sqrt(1/c)/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)) + 4*I*c*d**2*log(-sqrt(d)*sqrt(1/c) + sqrt(d*x))/(12*c**3*sqrt(d)*sqrt(1/c) + 12*I*c**3*sqrt(d)*sqrt(1/c)) - 6*I*c*d**2*log(I*sqrt(d)*sqrt(1/c) + sqrt(d*x))/(12*c**3*sqrt(d)*sqrt(1/c) + 12*I*c**3*sqrt(d)*sqrt(1/c)) + 4*I*c*d**2*atanh(c*x)/(12*c**3*sqrt(d)*sqrt(1/c) + 12*I*c**3*sqrt(d)*sqrt(1/c)) + 4*d**2*log(-sqrt(d)*sqrt(1/c) + sqrt(d*x))/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)) - 4*d**2*log(-I*sqrt(d)*sqrt(1/c) + sqrt(d*x))/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)) + 4*d**2*atanh(c*x)/(12*c**2*sqrt(d)*sqrt(1/c) + 12*I*c**2*sqrt(d)*sqrt(1/c)), Ne(c, 0)), (0, True))/d","C",0
38,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(d*x)**(1/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{\sqrt{d x}}\, dx"," ",0,"Integral((a + b*atanh(c*x))/sqrt(d*x), x)","F",0
39,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(d*x)**(3/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(d*x)**(3/2), x)","F",0
40,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(d*x)**(5/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(d*x)**(5/2), x)","F",0
41,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(d*x)**(7/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x \right)}}{\left(d x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x))/(d*x)**(7/2), x)","F",0
42,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x))/(d*x)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x))**3,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{3}\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x))**3, x)","F",0
44,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x))**2,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x))**2, x)","F",0
45,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x)),x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x \right)}\right)\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x)), x)","F",0
46,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x)),x)","\int \frac{\left(d x\right)^{m}}{a + b \operatorname{atanh}{\left(c x \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*atanh(c*x)), x)","F",0
47,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x))**2,x)","\int \frac{\left(d x\right)^{m}}{\left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d*x)**m/(a + b*atanh(c*x))**2, x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*atanh(c*x))**p,x)","\int \left(a + b \operatorname{atanh}{\left(c x \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*atanh(c*x))**p, x)","F",0
49,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,1,58,0,17.367313," ","integrate(x**7*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{a x^{8}}{8} + \frac{b x^{8} \operatorname{atanh}{\left(c x^{2} \right)}}{8} + \frac{b x^{6}}{24 c} + \frac{b x^{2}}{8 c^{3}} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{8 c^{4}} & \text{for}\: c \neq 0 \\\frac{a x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**8/8 + b*x**8*atanh(c*x**2)/8 + b*x**6/(24*c) + b*x**2/(8*c**3) - b*atanh(c*x**2)/(8*c**4), Ne(c, 0)), (a*x**8/8, True))","A",0
51,1,85,0,12.460748," ","integrate(x**5*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{atanh}{\left(c x^{2} \right)}}{6} + \frac{b x^{4}}{12 c} + \frac{b \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{6 c^{3}} + \frac{b \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{6 c^{3}} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\\frac{a x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*x**6*atanh(c*x**2)/6 + b*x**4/(12*c) + b*log(x - I*sqrt(1/c))/(6*c**3) + b*log(x + I*sqrt(1/c))/(6*c**3) - b*atanh(c*x**2)/(6*c**3), Ne(c, 0)), (a*x**6/6, True))","A",0
52,1,48,0,8.412053," ","integrate(x**3*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{atanh}{\left(c x^{2} \right)}}{4} + \frac{b x^{2}}{4 c} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\\frac{a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 + b*x**4*atanh(c*x**2)/4 + b*x**2/(4*c) - b*atanh(c*x**2)/(4*c**2), Ne(c, 0)), (a*x**4/4, True))","A",0
53,1,71,0,6.943445," ","integrate(x*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2} + \frac{b \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2 c} + \frac{b \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2 c} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{2 c} & \text{for}\: c \neq 0 \\\frac{a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*x**2*atanh(c*x**2)/2 + b*log(x - I*sqrt(1/c))/(2*c) + b*log(x + I*sqrt(1/c))/(2*c) - b*atanh(c*x**2)/(2*c), Ne(c, 0)), (a*x**2/2, True))","A",0
54,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/x,x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{2} \right)}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))/x, x)","F",0
55,1,80,0,11.509260," ","integrate((a+b*atanh(c*x**2))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} + b c \log{\left(x \right)} - \frac{b c \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{b c \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2} + \frac{b c \operatorname{atanh}{\left(c x^{2} \right)}}{2} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{2 x^{2}} & \text{for}\: c \neq 0 \\- \frac{a}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) + b*c*log(x) - b*c*log(x - I*sqrt(1/c))/2 - b*c*log(x + I*sqrt(1/c))/2 + b*c*atanh(c*x**2)/2 - b*atanh(c*x**2)/(2*x**2), Ne(c, 0)), (-a/(2*x**2), True))","A",0
56,1,41,0,8.072909," ","integrate((a+b*atanh(c*x**2))/x**5,x)","- \frac{a}{4 x^{4}} + \frac{b c^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{4} - \frac{b c}{4 x^{2}} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{4 x^{4}}"," ",0,"-a/(4*x**4) + b*c**2*atanh(c*x**2)/4 - b*c/(4*x**2) - b*atanh(c*x**2)/(4*x**4)","A",0
57,1,97,0,22.254731," ","integrate((a+b*atanh(c*x**2))/x**7,x)","\begin{cases} - \frac{a}{6 x^{6}} + \frac{b c^{3} \log{\left(x \right)}}{3} - \frac{b c^{3} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{6} - \frac{b c^{3} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{6} + \frac{b c^{3} \operatorname{atanh}{\left(c x^{2} \right)}}{6} - \frac{b c}{12 x^{4}} - \frac{b \operatorname{atanh}{\left(c x^{2} \right)}}{6 x^{6}} & \text{for}\: c \neq 0 \\- \frac{a}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(6*x**6) + b*c**3*log(x)/3 - b*c**3*log(x - I*sqrt(1/c))/6 - b*c**3*log(x + I*sqrt(1/c))/6 + b*c**3*atanh(c*x**2)/6 - b*c/(12*x**4) - b*atanh(c*x**2)/(6*x**6), Ne(c, 0)), (-a/(6*x**6), True))","A",0
58,1,238,0,11.707747," ","integrate(x**4*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{a x^{5}}{5} + \frac{b x^{5} \operatorname{atanh}{\left(c x^{2} \right)}}{5} + \frac{2 b x^{3}}{15 c} + \frac{b \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{20 c} - \frac{i b \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{20 c} - \frac{b \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{10 c^{2}} - \frac{i b \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{10 c^{2}} - \frac{3 b \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{20 c^{2}} + \frac{3 i b \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{20 c^{2}} + \frac{b \sqrt{\frac{1}{c}} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{5 c^{2}} + \frac{b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{5 c^{2}} & \text{for}\: c \neq 0 \\\frac{a x^{5}}{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**5/5 + b*x**5*atanh(c*x**2)/5 + 2*b*x**3/(15*c) + b*(1/c)**(3/2)*log(x + I*sqrt(1/c))/(20*c) - I*b*(1/c)**(3/2)*log(x + I*sqrt(1/c))/(20*c) - b*sqrt(1/c)*log(x - I*sqrt(1/c))/(10*c**2) - I*b*sqrt(1/c)*log(x - I*sqrt(1/c))/(10*c**2) - 3*b*sqrt(1/c)*log(x + I*sqrt(1/c))/(20*c**2) + 3*I*b*sqrt(1/c)*log(x + I*sqrt(1/c))/(20*c**2) + b*sqrt(1/c)*log(x - sqrt(1/c))/(5*c**2) + b*sqrt(1/c)*atanh(c*x**2)/(5*c**2), Ne(c, 0)), (a*x**5/5, True))","A",0
59,1,559,0,8.537571," ","integrate(x**2*(a+b*atanh(c*x**2)),x)","\begin{cases} \frac{4 a c^{2} x^{3} \sqrt{\frac{1}{c}}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 i a c^{2} x^{3} \sqrt{\frac{1}{c}}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 b c^{2} x^{3} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 i b c^{2} x^{3} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{2 i b c^{2} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{12 c^{4} \sqrt{\frac{1}{c}} + 12 i c^{4} \sqrt{\frac{1}{c}}} + \frac{8 b c x \sqrt{\frac{1}{c}}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{8 i b c x \sqrt{\frac{1}{c}}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} - \frac{6 i b c \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{12 c^{3} \sqrt{\frac{1}{c}} + 12 i c^{3} \sqrt{\frac{1}{c}}} + \frac{4 i b c \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{12 c^{3} \sqrt{\frac{1}{c}} + 12 i c^{3} \sqrt{\frac{1}{c}}} + \frac{4 i b c \operatorname{atanh}{\left(c x^{2} \right)}}{12 c^{3} \sqrt{\frac{1}{c}} + 12 i c^{3} \sqrt{\frac{1}{c}}} - \frac{4 b \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 b \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} + \frac{4 b \operatorname{atanh}{\left(c x^{2} \right)}}{12 c^{2} \sqrt{\frac{1}{c}} + 12 i c^{2} \sqrt{\frac{1}{c}}} & \text{for}\: c \neq 0 \\\frac{a x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*a*c**2*x**3*sqrt(1/c)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 4*I*a*c**2*x**3*sqrt(1/c)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 4*b*c**2*x**3*sqrt(1/c)*atanh(c*x**2)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 4*I*b*c**2*x**3*sqrt(1/c)*atanh(c*x**2)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 2*I*b*c**2*log(x + I*sqrt(1/c))/(12*c**4*sqrt(1/c) + 12*I*c**4*sqrt(1/c)) + 8*b*c*x*sqrt(1/c)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 8*I*b*c*x*sqrt(1/c)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) - 6*I*b*c*log(x + I*sqrt(1/c))/(12*c**3*sqrt(1/c) + 12*I*c**3*sqrt(1/c)) + 4*I*b*c*log(x - sqrt(1/c))/(12*c**3*sqrt(1/c) + 12*I*c**3*sqrt(1/c)) + 4*I*b*c*atanh(c*x**2)/(12*c**3*sqrt(1/c) + 12*I*c**3*sqrt(1/c)) - 4*b*log(x - I*sqrt(1/c))/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 4*b*log(x - sqrt(1/c))/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)) + 4*b*atanh(c*x**2)/(12*c**2*sqrt(1/c) + 12*I*c**2*sqrt(1/c)), Ne(c, 0)), (a*x**3/3, True))","A",0
60,1,178,0,5.613899," ","integrate(a+b*atanh(c*x**2),x)","a x + b \left(\begin{cases} \frac{c \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} - \frac{i c \left(\frac{1}{c}\right)^{\frac{3}{2}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + x \operatorname{atanh}{\left(c x^{2} \right)} - \frac{\sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{i \sqrt{\frac{1}{c}} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{3 \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + \frac{3 i \sqrt{\frac{1}{c}} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{4} + \sqrt{\frac{1}{c}} \log{\left(x - \sqrt{\frac{1}{c}} \right)} + \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((c*(1/c)**(3/2)*log(x + I*sqrt(1/c))/4 - I*c*(1/c)**(3/2)*log(x + I*sqrt(1/c))/4 + x*atanh(c*x**2) - sqrt(1/c)*log(x - I*sqrt(1/c))/2 - I*sqrt(1/c)*log(x - I*sqrt(1/c))/2 - 3*sqrt(1/c)*log(x + I*sqrt(1/c))/4 + 3*I*sqrt(1/c)*log(x + I*sqrt(1/c))/4 + sqrt(1/c)*log(x - sqrt(1/c)) + sqrt(1/c)*atanh(c*x**2), Ne(c, 0)), (0, True))","A",0
61,1,1292,0,10.148337," ","integrate((a+b*atanh(c*x**2))/x**2,x)","\begin{cases} - \frac{a}{x} & \text{for}\: c = 0 \\- \frac{a - \infty b}{x} & \text{for}\: c = - \frac{1}{x^{2}} \\- \frac{a + \infty b}{x} & \text{for}\: c = \frac{1}{x^{2}} \\- \frac{a c x^{4} \sqrt{\frac{1}{c}}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} - \frac{i a c x^{4} \sqrt{\frac{1}{c}}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} + \frac{a \sqrt{\frac{1}{c}}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{i a \sqrt{\frac{1}{c}}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{i b c^{2} x^{5} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} - \frac{i b c^{2} x^{5} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} - \frac{i b c^{2} x^{5} \operatorname{atanh}{\left(c x^{2} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{b c x^{5} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} - \frac{b c x^{5} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} - \frac{b c x^{5} \operatorname{atanh}{\left(c x^{2} \right)}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} - \frac{b c x^{4} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} - \frac{i b c x^{4} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{c x^{5} \sqrt{\frac{1}{c}} + i c x^{5} \sqrt{\frac{1}{c}} - \frac{x \sqrt{\frac{1}{c}}}{c} - \frac{i x \sqrt{\frac{1}{c}}}{c}} - \frac{b x \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} - \frac{i b x \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{b x \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{i b x \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{b x \operatorname{atanh}{\left(c x^{2} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{i b x \operatorname{atanh}{\left(c x^{2} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} + \frac{i b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{c^{2} x^{5} \sqrt{\frac{1}{c}} + i c^{2} x^{5} \sqrt{\frac{1}{c}} - x \sqrt{\frac{1}{c}} - i x \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x, Eq(c, 0)), (-(a - oo*b)/x, Eq(c, -1/x**2)), (-(a + oo*b)/x, Eq(c, x**(-2))), (-a*c*x**4*sqrt(1/c)/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) - I*a*c*x**4*sqrt(1/c)/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) + a*sqrt(1/c)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + I*a*sqrt(1/c)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + I*b*c**2*x**5*log(x + I*sqrt(1/c))/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) - I*b*c**2*x**5*log(x - sqrt(1/c))/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) - I*b*c**2*x**5*atanh(c*x**2)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + b*c*x**5*log(x - I*sqrt(1/c))/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) - b*c*x**5*log(x - sqrt(1/c))/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) - b*c*x**5*atanh(c*x**2)/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) - b*c*x**4*sqrt(1/c)*atanh(c*x**2)/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) - I*b*c*x**4*sqrt(1/c)*atanh(c*x**2)/(c*x**5*sqrt(1/c) + I*c*x**5*sqrt(1/c) - x*sqrt(1/c)/c - I*x*sqrt(1/c)/c) - b*x*log(x - I*sqrt(1/c))/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) - I*b*x*log(x + I*sqrt(1/c))/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + b*x*log(x - sqrt(1/c))/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + I*b*x*log(x - sqrt(1/c))/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + b*x*atanh(c*x**2)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + I*b*x*atanh(c*x**2)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + b*sqrt(1/c)*atanh(c*x**2)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)) + I*b*sqrt(1/c)*atanh(c*x**2)/(c**2*x**5*sqrt(1/c) + I*c**2*x**5*sqrt(1/c) - x*sqrt(1/c) - I*x*sqrt(1/c)), True))","A",0
62,1,1822,0,14.517790," ","integrate((a+b*atanh(c*x**2))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} & \text{for}\: c = 0 \\- \frac{a - \infty b}{3 x^{3}} & \text{for}\: c = - \frac{1}{x^{2}} \\- \frac{a + \infty b}{3 x^{3}} & \text{for}\: c = \frac{1}{x^{2}} \\\frac{a c x^{4} \sqrt{\frac{1}{c}}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{i a c x^{4} \sqrt{\frac{1}{c}}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{a \sqrt{\frac{1}{c}}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} + \frac{i a \sqrt{\frac{1}{c}}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} + \frac{i b c^{3} x^{7} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} - \frac{i b c^{3} x^{7} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} - \frac{i b c^{3} x^{7} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} - \frac{b c^{2} x^{7} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} + \frac{b c^{2} x^{7} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} + \frac{b c^{2} x^{7} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} + \frac{2 b c^{2} x^{6} \sqrt{\frac{1}{c}}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{2 i b c^{2} x^{6} \sqrt{\frac{1}{c}}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} + \frac{b c x^{4} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{i b c x^{4} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{i b c x^{3} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} + \frac{i b c x^{3} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} + \frac{i b c x^{3} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} + \frac{b x^{3} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{b x^{3} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{b x^{3} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{2 b x^{2} \sqrt{\frac{1}{c}}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} + \frac{2 i b x^{2} \sqrt{\frac{1}{c}}}{- 3 c x^{7} \sqrt{\frac{1}{c}} + 3 i c x^{7} \sqrt{\frac{1}{c}} + \frac{3 x^{3} \sqrt{\frac{1}{c}}}{c} - \frac{3 i x^{3} \sqrt{\frac{1}{c}}}{c}} - \frac{b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} + \frac{i b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{- 3 c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 i c^{2} x^{7} \sqrt{\frac{1}{c}} + 3 x^{3} \sqrt{\frac{1}{c}} - 3 i x^{3} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3), Eq(c, 0)), (-(a - oo*b)/(3*x**3), Eq(c, -1/x**2)), (-(a + oo*b)/(3*x**3), Eq(c, x**(-2))), (a*c*x**4*sqrt(1/c)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - I*a*c*x**4*sqrt(1/c)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - a*sqrt(1/c)/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) + I*a*sqrt(1/c)/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) + I*b*c**3*x**7*log(x + I*sqrt(1/c))/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) - I*b*c**3*x**7*log(x - sqrt(1/c))/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) - I*b*c**3*x**7*atanh(c*x**2)/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) - b*c**2*x**7*log(x - I*sqrt(1/c))/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) + b*c**2*x**7*log(x - sqrt(1/c))/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) + b*c**2*x**7*atanh(c*x**2)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) + 2*b*c**2*x**6*sqrt(1/c)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - 2*I*b*c**2*x**6*sqrt(1/c)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) + b*c*x**4*sqrt(1/c)*atanh(c*x**2)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - I*b*c*x**4*sqrt(1/c)*atanh(c*x**2)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - I*b*c*x**3*log(x + I*sqrt(1/c))/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) + I*b*c*x**3*log(x - sqrt(1/c))/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) + I*b*c*x**3*atanh(c*x**2)/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) + b*x**3*log(x - I*sqrt(1/c))/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - b*x**3*log(x - sqrt(1/c))/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - b*x**3*atanh(c*x**2)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - 2*b*x**2*sqrt(1/c)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) + 2*I*b*x**2*sqrt(1/c)/(-3*c*x**7*sqrt(1/c) + 3*I*c*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c)/c - 3*I*x**3*sqrt(1/c)/c) - b*sqrt(1/c)*atanh(c*x**2)/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)) + I*b*sqrt(1/c)*atanh(c*x**2)/(-3*c**2*x**7*sqrt(1/c) + 3*I*c**2*x**7*sqrt(1/c) + 3*x**3*sqrt(1/c) - 3*I*x**3*sqrt(1/c)), True))","A",0
63,1,1867,0,20.466151," ","integrate((a+b*atanh(c*x**2))/x**6,x)","\begin{cases} - \frac{a - \infty b}{5 x^{5}} & \text{for}\: c = - \frac{1}{x^{2}} \\- \frac{a + \infty b}{5 x^{5}} & \text{for}\: c = \frac{1}{x^{2}} \\- \frac{a}{5 x^{5}} & \text{for}\: c = 0 \\- \frac{3 a c x^{4} \sqrt{\frac{1}{c}}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{3 i a c x^{4} \sqrt{\frac{1}{c}}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} + \frac{3 a \sqrt{\frac{1}{c}}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} + \frac{3 i a \sqrt{\frac{1}{c}}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} + \frac{3 i b c^{4} x^{9} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} - \frac{3 i b c^{4} x^{9} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} - \frac{3 i b c^{4} x^{9} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} + \frac{3 b c^{3} x^{9} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{3 b c^{3} x^{9} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{3 b c^{3} x^{9} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{2 b c^{2} x^{6} \sqrt{\frac{1}{c}}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{2 i b c^{2} x^{6} \sqrt{\frac{1}{c}}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{3 i b c^{2} x^{5} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} + \frac{3 i b c^{2} x^{5} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} + \frac{3 i b c^{2} x^{5} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} - \frac{3 b c x^{5} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} + \frac{3 b c x^{5} \log{\left(x - \sqrt{\frac{1}{c}} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} + \frac{3 b c x^{5} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{3 b c x^{4} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} - \frac{3 i b c x^{4} \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} + \frac{2 b x^{2} \sqrt{\frac{1}{c}}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} + \frac{2 i b x^{2} \sqrt{\frac{1}{c}}}{15 c x^{9} \sqrt{\frac{1}{c}} + 15 i c x^{9} \sqrt{\frac{1}{c}} - \frac{15 x^{5} \sqrt{\frac{1}{c}}}{c} - \frac{15 i x^{5} \sqrt{\frac{1}{c}}}{c}} + \frac{3 b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} + \frac{3 i b \sqrt{\frac{1}{c}} \operatorname{atanh}{\left(c x^{2} \right)}}{15 c^{2} x^{9} \sqrt{\frac{1}{c}} + 15 i c^{2} x^{9} \sqrt{\frac{1}{c}} - 15 x^{5} \sqrt{\frac{1}{c}} - 15 i x^{5} \sqrt{\frac{1}{c}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(a - oo*b)/(5*x**5), Eq(c, -1/x**2)), (-(a + oo*b)/(5*x**5), Eq(c, x**(-2))), (-a/(5*x**5), Eq(c, 0)), (-3*a*c*x**4*sqrt(1/c)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 3*I*a*c*x**4*sqrt(1/c)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) + 3*a*sqrt(1/c)/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) + 3*I*a*sqrt(1/c)/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) + 3*I*b*c**4*x**9*log(x + I*sqrt(1/c))/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) - 3*I*b*c**4*x**9*log(x - sqrt(1/c))/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) - 3*I*b*c**4*x**9*atanh(c*x**2)/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) + 3*b*c**3*x**9*log(x - I*sqrt(1/c))/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 3*b*c**3*x**9*log(x - sqrt(1/c))/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 3*b*c**3*x**9*atanh(c*x**2)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 2*b*c**2*x**6*sqrt(1/c)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 2*I*b*c**2*x**6*sqrt(1/c)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 3*I*b*c**2*x**5*log(x + I*sqrt(1/c))/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) + 3*I*b*c**2*x**5*log(x - sqrt(1/c))/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) + 3*I*b*c**2*x**5*atanh(c*x**2)/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) - 3*b*c*x**5*log(x - I*sqrt(1/c))/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) + 3*b*c*x**5*log(x - sqrt(1/c))/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) + 3*b*c*x**5*atanh(c*x**2)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 3*b*c*x**4*sqrt(1/c)*atanh(c*x**2)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) - 3*I*b*c*x**4*sqrt(1/c)*atanh(c*x**2)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) + 2*b*x**2*sqrt(1/c)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) + 2*I*b*x**2*sqrt(1/c)/(15*c*x**9*sqrt(1/c) + 15*I*c*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c)/c - 15*I*x**5*sqrt(1/c)/c) + 3*b*sqrt(1/c)*atanh(c*x**2)/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)) + 3*I*b*sqrt(1/c)*atanh(c*x**2)/(15*c**2*x**9*sqrt(1/c) + 15*I*c**2*x**9*sqrt(1/c) - 15*x**5*sqrt(1/c) - 15*I*x**5*sqrt(1/c)), True))","A",0
64,1,206,0,23.145377," ","integrate(x**7*(a+b*atanh(c*x**2))**2,x)","\begin{cases} \frac{a^{2} x^{8}}{8} + \frac{a b x^{8} \operatorname{atanh}{\left(c x^{2} \right)}}{4} + \frac{a b x^{6}}{12 c} + \frac{a b x^{2}}{4 c^{3}} - \frac{a b \operatorname{atanh}{\left(c x^{2} \right)}}{4 c^{4}} + \frac{b^{2} x^{8} \operatorname{atanh}^{2}{\left(c x^{2} \right)}}{8} + \frac{b^{2} x^{6} \operatorname{atanh}{\left(c x^{2} \right)}}{12 c} + \frac{b^{2} x^{4}}{24 c^{2}} + \frac{b^{2} x^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{4 c^{3}} + \frac{b^{2} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{3 c^{4}} + \frac{b^{2} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{3 c^{4}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x^{2} \right)}}{8 c^{4}} - \frac{b^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{3 c^{4}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**8/8 + a*b*x**8*atanh(c*x**2)/4 + a*b*x**6/(12*c) + a*b*x**2/(4*c**3) - a*b*atanh(c*x**2)/(4*c**4) + b**2*x**8*atanh(c*x**2)**2/8 + b**2*x**6*atanh(c*x**2)/(12*c) + b**2*x**4/(24*c**2) + b**2*x**2*atanh(c*x**2)/(4*c**3) + b**2*log(x - I*sqrt(1/c))/(3*c**4) + b**2*log(x + I*sqrt(1/c))/(3*c**4) - b**2*atanh(c*x**2)**2/(8*c**4) - b**2*atanh(c*x**2)/(3*c**4), Ne(c, 0)), (a**2*x**8/8, True))","A",0
65,0,0,0,0.000000," ","integrate(x**5*(a+b*atanh(c*x**2))**2,x)","\int x^{5} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x**5*(a + b*atanh(c*x**2))**2, x)","F",0
66,1,163,0,11.526218," ","integrate(x**3*(a+b*atanh(c*x**2))**2,x)","\begin{cases} \frac{a^{2} x^{4}}{4} + \frac{a b x^{4} \operatorname{atanh}{\left(c x^{2} \right)}}{2} + \frac{a b x^{2}}{2 c} - \frac{a b \operatorname{atanh}{\left(c x^{2} \right)}}{2 c^{2}} + \frac{b^{2} x^{4} \operatorname{atanh}^{2}{\left(c x^{2} \right)}}{4} + \frac{b^{2} x^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2 c} + \frac{b^{2} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2 c^{2}} + \frac{b^{2} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2 c^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x^{2} \right)}}{4 c^{2}} - \frac{b^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\\frac{a^{2} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x**4/4 + a*b*x**4*atanh(c*x**2)/2 + a*b*x**2/(2*c) - a*b*atanh(c*x**2)/(2*c**2) + b**2*x**4*atanh(c*x**2)**2/4 + b**2*x**2*atanh(c*x**2)/(2*c) + b**2*log(x - I*sqrt(1/c))/(2*c**2) + b**2*log(x + I*sqrt(1/c))/(2*c**2) - b**2*atanh(c*x**2)**2/(4*c**2) - b**2*atanh(c*x**2)/(2*c**2), Ne(c, 0)), (a**2*x**4/4, True))","A",0
67,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**2))**2,x)","\int x \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*atanh(c*x**2))**2, x)","F",0
68,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/x, x)","F",0
69,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/x**3, x)","F",0
70,1,175,0,17.023479," ","integrate((a+b*atanh(c*x**2))**2/x**5,x)","\begin{cases} - \frac{a^{2}}{4 x^{4}} + \frac{a b c^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2} - \frac{a b c}{2 x^{2}} - \frac{a b \operatorname{atanh}{\left(c x^{2} \right)}}{2 x^{4}} + b^{2} c^{2} \log{\left(x \right)} - \frac{b^{2} c^{2} \log{\left(x - i \sqrt{\frac{1}{c}} \right)}}{2} - \frac{b^{2} c^{2} \log{\left(x + i \sqrt{\frac{1}{c}} \right)}}{2} + \frac{b^{2} c^{2} \operatorname{atanh}^{2}{\left(c x^{2} \right)}}{4} + \frac{b^{2} c^{2} \operatorname{atanh}{\left(c x^{2} \right)}}{2} - \frac{b^{2} c \operatorname{atanh}{\left(c x^{2} \right)}}{2 x^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(c x^{2} \right)}}{4 x^{4}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(4*x**4) + a*b*c**2*atanh(c*x**2)/2 - a*b*c/(2*x**2) - a*b*atanh(c*x**2)/(2*x**4) + b**2*c**2*log(x) - b**2*c**2*log(x - I*sqrt(1/c))/2 - b**2*c**2*log(x + I*sqrt(1/c))/2 + b**2*c**2*atanh(c*x**2)**2/4 + b**2*c**2*atanh(c*x**2)/2 - b**2*c*atanh(c*x**2)/(2*x**2) - b**2*atanh(c*x**2)**2/(4*x**4), Ne(c, 0)), (-a**2/(4*x**4), True))","A",0
71,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x**2))**2,x)","\int x^{4} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x**4*(a + b*atanh(c*x**2))**2, x)","F",0
72,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**2))**2,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*x**2))**2, x)","F",0
73,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2, x)","F",0
74,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/x**2, x)","F",0
75,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/x**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/x**4, x)","F",0
76,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/x**6,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{x^{6}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/x**6, x)","F",0
77,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**2))**3,x)","\int x^{3} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atanh(c*x**2))**3, x)","F",0
78,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**2))**3,x)","\int x \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atanh(c*x**2))**3, x)","F",0
79,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**3/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**3/x, x)","F",0
80,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**3/x**3, x)","F",0
81,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**3/x**5,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{3}}{x^{5}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**3/x**5, x)","F",0
82,-1,0,0,0.000000," ","integrate((d*x)**(5/2)*(a+b*atanh(c*x**2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate((d*x)**(3/2)*(a+b*atanh(c*x**2)),x)","\int \left(d x\right)^{\frac{3}{2}} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)\, dx"," ",0,"Integral((d*x)**(3/2)*(a + b*atanh(c*x**2)), x)","F",0
84,-1,0,0,0.000000," ","integrate((d*x)**(1/2)*(a+b*atanh(c*x**2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(d*x)**(1/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{2} \right)}}{\sqrt{d x}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))/sqrt(d*x), x)","F",0
86,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(d*x)**(3/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{2} \right)}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))/(d*x)**(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(d*x)**(5/2),x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{2} \right)}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))/(d*x)**(5/2), x)","F",0
88,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(d*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))/(d*x)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((d*x)**(1/2)*(a+b*atanh(c*x**2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/(d*x)**(1/2),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{\sqrt{d x}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/sqrt(d*x), x)","F",0
92,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/(d*x)**(3/2),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{\left(d x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/(d*x)**(3/2), x)","F",0
93,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**2))**2/(d*x)**(5/2),x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}}{\left(d x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*atanh(c*x**2))**2/(d*x)**(5/2), x)","F",0
94,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**2))**3,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{3}\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x**2))**3, x)","F",0
95,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**2))**2,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)^{2}\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x**2))**2, x)","F",0
96,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**2)),x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x^{2} \right)}\right)\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x**2)), x)","F",0
97,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x**2)),x)","\int \frac{\left(d x\right)^{m}}{a + b \operatorname{atanh}{\left(c x^{2} \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*atanh(c*x**2)), x)","F",0
98,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x**2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(x**11*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(x**8*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(x**5*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(a+b*atanh(c*x**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(x**7*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))/x**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(x**11*(a+b*atanh(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(x**8*(a+b*atanh(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate(x**5*(a+b*atanh(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**2/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**2/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**2/x**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(x**8*(a+b*atanh(c*x**3))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate(x**5*(a+b*atanh(c*x**3))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**3))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**3/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**3/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**3))**3/x**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**3))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x**3)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x**3))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,1,46,0,0.560921," ","integrate(x**3*(a+b*atanh(c/x)),x)","\frac{a x^{4}}{4} - \frac{b c^{4} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{4} + \frac{b c^{3} x}{4} + \frac{b c x^{3}}{12} + \frac{b x^{4} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{4}"," ",0,"a*x**4/4 - b*c**4*atanh(c/x)/4 + b*c**3*x/4 + b*c*x**3/12 + b*x**4*atanh(c/x)/4","A",0
136,1,49,0,0.447512," ","integrate(x**2*(a+b*atanh(c/x)),x)","\frac{a x^{3}}{3} + \frac{b c^{3} \log{\left(- c + x \right)}}{3} + \frac{b c^{3} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{3} + \frac{b c x^{2}}{6} + \frac{b x^{3} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{3}"," ",0,"a*x**3/3 + b*c**3*log(-c + x)/3 + b*c**3*atanh(c/x)/3 + b*c*x**2/6 + b*x**3*atanh(c/x)/3","A",0
137,1,36,0,0.336180," ","integrate(x*(a+b*atanh(c/x)),x)","\frac{a x^{2}}{2} - \frac{b c^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2} + \frac{b c x}{2} + \frac{b x^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2}"," ",0,"a*x**2/2 - b*c**2*atanh(c/x)/2 + b*c*x/2 + b*x**2*atanh(c/x)/2","A",0
138,1,24,0,0.247032," ","integrate(a+b*atanh(c/x),x)","a x + b \left(c \log{\left(c - x \right)} + c \operatorname{atanh}{\left(\frac{c}{x} \right)} + x \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)"," ",0,"a*x + b*(c*log(c - x) + c*atanh(c/x) + x*atanh(c/x))","A",0
139,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))/x,x)","\int \frac{a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{x}\, dx"," ",0,"Integral((a + b*atanh(c/x))/x, x)","F",0
140,1,39,0,0.791670," ","integrate((a+b*atanh(c/x))/x**2,x)","\begin{cases} - \frac{a}{x} - \frac{b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{x} + \frac{b \log{\left(x \right)}}{c} - \frac{b \log{\left(- c + x \right)}}{c} - \frac{b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{c} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x - b*atanh(c/x)/x + b*log(x)/c - b*log(-c + x)/c - b*atanh(c/x)/c, Ne(c, 0)), (-a/x, True))","A",0
141,1,44,0,0.953315," ","integrate((a+b*atanh(c/x))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} - \frac{b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2 x^{2}} - \frac{b}{2 c x} + \frac{b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\- \frac{a}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) - b*atanh(c/x)/(2*x**2) - b/(2*c*x) + b*atanh(c/x)/(2*c**2), Ne(c, 0)), (-a/(2*x**2), True))","A",0
142,1,68,0,1.287883," ","integrate((a+b*atanh(c/x))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} - \frac{b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{3 x^{3}} - \frac{b}{6 c x^{2}} + \frac{b \log{\left(x \right)}}{3 c^{3}} - \frac{b \log{\left(- c + x \right)}}{3 c^{3}} - \frac{b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{3 c^{3}} & \text{for}\: c \neq 0 \\- \frac{a}{3 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3) - b*atanh(c/x)/(3*x**3) - b/(6*c*x**2) + b*log(x)/(3*c**3) - b*log(-c + x)/(3*c**3) - b*atanh(c/x)/(3*c**3), Ne(c, 0)), (-a/(3*x**3), True))","A",0
143,1,158,0,0.957119," ","integrate(x**3*(a+b*atanh(c/x))**2,x)","\frac{a^{2} x^{4}}{4} - \frac{a b c^{4} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2} + \frac{a b c^{3} x}{2} + \frac{a b c x^{3}}{6} + \frac{a b x^{4} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2} + \frac{2 b^{2} c^{4} \log{\left(- c + x \right)}}{3} - \frac{b^{2} c^{4} \operatorname{atanh}^{2}{\left(\frac{c}{x} \right)}}{4} + \frac{2 b^{2} c^{4} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{3} + \frac{b^{2} c^{3} x \operatorname{atanh}{\left(\frac{c}{x} \right)}}{2} + \frac{b^{2} c^{2} x^{2}}{12} + \frac{b^{2} c x^{3} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{6} + \frac{b^{2} x^{4} \operatorname{atanh}^{2}{\left(\frac{c}{x} \right)}}{4}"," ",0,"a**2*x**4/4 - a*b*c**4*atanh(c/x)/2 + a*b*c**3*x/2 + a*b*c*x**3/6 + a*b*x**4*atanh(c/x)/2 + 2*b**2*c**4*log(-c + x)/3 - b**2*c**4*atanh(c/x)**2/4 + 2*b**2*c**4*atanh(c/x)/3 + b**2*c**3*x*atanh(c/x)/2 + b**2*c**2*x**2/12 + b**2*c*x**3*atanh(c/x)/6 + b**2*x**4*atanh(c/x)**2/4","A",0
144,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c/x))**2,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c/x))**2, x)","F",0
145,1,104,0,0.517707," ","integrate(x*(a+b*atanh(c/x))**2,x)","\frac{a^{2} x^{2}}{2} - a b c^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)} + a b c x + a b x^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)} + b^{2} c^{2} \log{\left(- c + x \right)} - \frac{b^{2} c^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x} \right)}}{2} + b^{2} c^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)} + b^{2} c x \operatorname{atanh}{\left(\frac{c}{x} \right)} + \frac{b^{2} x^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x} \right)}}{2}"," ",0,"a**2*x**2/2 - a*b*c**2*atanh(c/x) + a*b*c*x + a*b*x**2*atanh(c/x) + b**2*c**2*log(-c + x) - b**2*c**2*atanh(c/x)**2/2 + b**2*c**2*atanh(c/x) + b**2*c*x*atanh(c/x) + b**2*x**2*atanh(c/x)**2/2","A",0
146,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**2,x)","\int \left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c/x))**2, x)","F",0
147,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**2/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atanh(c/x))**2/x, x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c/x))**2/x**2, x)","F",0
149,1,124,0,1.173481," ","integrate((a+b*atanh(c/x))**2/x**3,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} - \frac{a b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{x^{2}} - \frac{a b}{c x} + \frac{a b \operatorname{atanh}{\left(\frac{c}{x} \right)}}{c^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x} \right)}}{2 x^{2}} - \frac{b^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{c x} + \frac{b^{2} \log{\left(x \right)}}{c^{2}} - \frac{b^{2} \log{\left(- c + x \right)}}{c^{2}} + \frac{b^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x} \right)}}{2 c^{2}} - \frac{b^{2} \operatorname{atanh}{\left(\frac{c}{x} \right)}}{c^{2}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2) - a*b*atanh(c/x)/x**2 - a*b/(c*x) + a*b*atanh(c/x)/c**2 - b**2*atanh(c/x)**2/(2*x**2) - b**2*atanh(c/x)/(c*x) + b**2*log(x)/c**2 - b**2*log(-c + x)/c**2 + b**2*atanh(c/x)**2/(2*c**2) - b**2*atanh(c/x)/c**2, Ne(c, 0)), (-a**2/(2*x**2), True))","A",0
150,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c/x))**3,x)","\int x^{3} \left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atanh(c/x))**3, x)","F",0
151,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c/x))**3,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c/x))**3, x)","F",0
152,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c/x))**3,x)","\int x \left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atanh(c/x))**3, x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**3,x)","\int \left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*atanh(c/x))**3, x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**3/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atanh(c/x))**3/x, x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**3/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c/x))**3/x**2, x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*atanh(c/x))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x} \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c/x))**3/x**3, x)","F",0
157,1,51,0,9.894925," ","integrate(x**7*(a+b*atanh(c/x**2)),x)","\frac{a x^{8}}{8} - \frac{b c^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{8} + \frac{b c^{3} x^{2}}{8} + \frac{b c x^{6}}{24} + \frac{b x^{8} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{8}"," ",0,"a*x**8/8 - b*c**4*atanh(c/x**2)/8 + b*c**3*x**2/8 + b*c*x**6/24 + b*x**8*atanh(c/x**2)/8","A",0
158,1,75,0,6.844508," ","integrate(x**5*(a+b*atanh(c/x**2)),x)","\frac{a x^{6}}{6} + \frac{b c^{3} \log{\left(- i \sqrt{c} + x \right)}}{6} + \frac{b c^{3} \log{\left(i \sqrt{c} + x \right)}}{6} - \frac{b c^{3} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{6} + \frac{b c x^{4}}{12} + \frac{b x^{6} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{6}"," ",0,"a*x**6/6 + b*c**3*log(-I*sqrt(c) + x)/6 + b*c**3*log(I*sqrt(c) + x)/6 - b*c**3*atanh(c/x**2)/6 + b*c*x**4/12 + b*x**6*atanh(c/x**2)/6","C",0
159,1,41,0,4.598515," ","integrate(x**3*(a+b*atanh(c/x**2)),x)","\frac{a x^{4}}{4} - \frac{b c^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{4} + \frac{b c x^{2}}{4} + \frac{b x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{4}"," ",0,"a*x**4/4 - b*c**2*atanh(c/x**2)/4 + b*c*x**2/4 + b*x**4*atanh(c/x**2)/4","A",0
160,1,61,0,3.200065," ","integrate(x*(a+b*atanh(c/x**2)),x)","\frac{a x^{2}}{2} + \frac{b c \log{\left(- i \sqrt{c} + x \right)}}{2} + \frac{b c \log{\left(i \sqrt{c} + x \right)}}{2} - \frac{b c \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2} + \frac{b x^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2}"," ",0,"a*x**2/2 + b*c*log(-I*sqrt(c) + x)/2 + b*c*log(I*sqrt(c) + x)/2 - b*c*atanh(c/x**2)/2 + b*x**2*atanh(c/x**2)/2","C",0
161,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))/x,x)","\int \frac{a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{x}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))/x, x)","F",0
162,1,76,0,11.523338," ","integrate((a+b*atanh(c/x**2))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} - \frac{b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2 x^{2}} + \frac{b \log{\left(x \right)}}{c} - \frac{b \log{\left(- i \sqrt{c} + x \right)}}{2 c} - \frac{b \log{\left(i \sqrt{c} + x \right)}}{2 c} + \frac{b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2 c} & \text{for}\: c \neq 0 \\- \frac{a}{2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) - b*atanh(c/x**2)/(2*x**2) + b*log(x)/c - b*log(-I*sqrt(c) + x)/(2*c) - b*log(I*sqrt(c) + x)/(2*c) + b*atanh(c/x**2)/(2*c), Ne(c, 0)), (-a/(2*x**2), True))","A",0
163,1,49,0,15.088466," ","integrate((a+b*atanh(c/x**2))/x**5,x)","\begin{cases} - \frac{a}{4 x^{4}} - \frac{b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{4 x^{4}} - \frac{b}{4 c x^{2}} + \frac{b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\- \frac{a}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(4*x**4) - b*atanh(c/x**2)/(4*x**4) - b/(4*c*x**2) + b*atanh(c/x**2)/(4*c**2), Ne(c, 0)), (-a/(4*x**4), True))","A",0
164,1,94,0,23.617837," ","integrate((a+b*atanh(c/x**2))/x**7,x)","\begin{cases} - \frac{a}{6 x^{6}} - \frac{b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{6 x^{6}} - \frac{b}{12 c x^{4}} + \frac{b \log{\left(x \right)}}{3 c^{3}} - \frac{b \log{\left(- i \sqrt{c} + x \right)}}{6 c^{3}} - \frac{b \log{\left(i \sqrt{c} + x \right)}}{6 c^{3}} + \frac{b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{6 c^{3}} & \text{for}\: c \neq 0 \\- \frac{a}{6 x^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(6*x**6) - b*atanh(c/x**2)/(6*x**6) - b/(12*c*x**4) + b*log(x)/(3*c**3) - b*log(-I*sqrt(c) + x)/(6*c**3) - b*log(I*sqrt(c) + x)/(6*c**3) + b*atanh(c/x**2)/(6*c**3), Ne(c, 0)), (-a/(6*x**6), True))","A",0
165,1,717,0,11.515147," ","integrate(x**4*(a+b*atanh(c/x**2)),x)","\begin{cases} \frac{a x^{5}}{5} & \text{for}\: c = 0 \\\frac{x^{5} \left(a - \infty b\right)}{5} & \text{for}\: c = - x^{2} \\\frac{x^{5} \left(a + \infty b\right)}{5} & \text{for}\: c = x^{2} \\- \frac{6 i a c^{\frac{5}{2}} x^{5}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{6 i a \sqrt{c} x^{9}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{4 i b c^{\frac{7}{2}} x^{3}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{6 i b c^{\frac{5}{2}} x^{5} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{4 i b c^{\frac{3}{2}} x^{7}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{6 i b \sqrt{c} x^{9} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{6 i b c^{5} \log{\left(- \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{3 b c^{5} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{3 i b c^{5} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{3 b c^{5} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{3 i b c^{5} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{6 i b c^{5} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{6 i b c^{3} x^{4} \log{\left(- \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{3 b c^{3} x^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{3 i b c^{3} x^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{3 b c^{3} x^{4} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} - \frac{3 i b c^{3} x^{4} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} + \frac{6 i b c^{3} x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{5}{2}} + 30 i \sqrt{c} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**5/5, Eq(c, 0)), (x**5*(a - oo*b)/5, Eq(c, -x**2)), (x**5*(a + oo*b)/5, Eq(c, x**2)), (-6*I*a*c**(5/2)*x**5/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 6*I*a*sqrt(c)*x**9/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 4*I*b*c**(7/2)*x**3/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 6*I*b*c**(5/2)*x**5*atanh(c/x**2)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 4*I*b*c**(3/2)*x**7/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 6*I*b*sqrt(c)*x**9*atanh(c/x**2)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 6*I*b*c**5*log(-sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 3*b*c**5*log(-I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 3*I*b*c**5*log(-I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 3*b*c**5*log(I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 3*I*b*c**5*log(I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 6*I*b*c**5*atanh(c/x**2)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 6*I*b*c**3*x**4*log(-sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 3*b*c**3*x**4*log(-I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 3*I*b*c**3*x**4*log(-I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 3*b*c**3*x**4*log(I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) - 3*I*b*c**3*x**4*log(I*sqrt(c) + x)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4) + 6*I*b*c**3*x**4*atanh(c/x**2)/(-30*I*c**(5/2) + 30*I*sqrt(c)*x**4), True))","A",0
166,1,702,0,7.790382," ","integrate(x**2*(a+b*atanh(c/x**2)),x)","\begin{cases} \frac{a x^{3}}{3} & \text{for}\: c = 0 \\\frac{x^{3} \left(a - \infty b\right)}{3} & \text{for}\: c = - x^{2} \\\frac{x^{3} \left(a + \infty b\right)}{3} & \text{for}\: c = x^{2} \\- \frac{2 i a c^{\frac{5}{2}} x^{3}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{2 i a \sqrt{c} x^{7}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{4 i b c^{\frac{7}{2}} x}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{2 i b c^{\frac{5}{2}} x^{3} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{4 i b c^{\frac{3}{2}} x^{5}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{2 i b \sqrt{c} x^{7} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{2 i b c^{4} \log{\left(- \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{b c^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{i b c^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{b c^{4} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{i b c^{4} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{2 i b c^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{2 i b c^{2} x^{4} \log{\left(- \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{b c^{2} x^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{i b c^{2} x^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{b c^{2} x^{4} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} - \frac{i b c^{2} x^{4} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} + \frac{2 i b c^{2} x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{\frac{5}{2}} + 6 i \sqrt{c} x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**3/3, Eq(c, 0)), (x**3*(a - oo*b)/3, Eq(c, -x**2)), (x**3*(a + oo*b)/3, Eq(c, x**2)), (-2*I*a*c**(5/2)*x**3/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + 2*I*a*sqrt(c)*x**7/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - 4*I*b*c**(7/2)*x/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - 2*I*b*c**(5/2)*x**3*atanh(c/x**2)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + 4*I*b*c**(3/2)*x**5/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + 2*I*b*sqrt(c)*x**7*atanh(c/x**2)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - 2*I*b*c**4*log(-sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + b*c**4*log(-I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + I*b*c**4*log(-I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - b*c**4*log(I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + I*b*c**4*log(I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - 2*I*b*c**4*atanh(c/x**2)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + 2*I*b*c**2*x**4*log(-sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - b*c**2*x**4*log(-I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - I*b*c**2*x**4*log(-I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + b*c**2*x**4*log(I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) - I*b*c**2*x**4*log(I*sqrt(c) + x)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4) + 2*I*b*c**2*x**4*atanh(c/x**2)/(-6*I*c**(5/2) + 6*I*sqrt(c)*x**4), True))","A",0
167,1,520,0,5.143140," ","integrate(a+b*atanh(c/x**2),x)","a x + b \left(\begin{cases} 0 & \text{for}\: c = 0 \\- \infty x & \text{for}\: c = - x^{2} \\\infty x & \text{for}\: c = x^{2} \\- \frac{2 i c^{\frac{5}{2}} x \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{2 i \sqrt{c} x^{5} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} - \frac{2 i c^{3} \log{\left(- \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} - \frac{c^{3} \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{i c^{3} \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{c^{3} \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{i c^{3} \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} - \frac{2 i c^{3} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{2 i c x^{4} \log{\left(- \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{c x^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} - \frac{i c x^{4} \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} - \frac{c x^{4} \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} - \frac{i c x^{4} \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} + \frac{2 i c x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{\frac{5}{2}} + 2 i \sqrt{c} x^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((0, Eq(c, 0)), (-oo*x, Eq(c, -x**2)), (oo*x, Eq(c, x**2)), (-2*I*c**(5/2)*x*atanh(c/x**2)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + 2*I*sqrt(c)*x**5*atanh(c/x**2)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) - 2*I*c**3*log(-sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) - c**3*log(-I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + I*c**3*log(-I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + c**3*log(I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + I*c**3*log(I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) - 2*I*c**3*atanh(c/x**2)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + 2*I*c*x**4*log(-sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + c*x**4*log(-I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) - I*c*x**4*log(-I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) - c*x**4*log(I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) - I*c*x**4*log(I*sqrt(c) + x)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4) + 2*I*c*x**4*atanh(c/x**2)/(-2*I*c**(5/2) + 2*I*sqrt(c)*x**4), True))","A",0
168,1,620,0,9.306873," ","integrate((a+b*atanh(c/x**2))/x**2,x)","\begin{cases} - \frac{a}{x} & \text{for}\: c = 0 \\- \frac{a - \infty b}{x} & \text{for}\: c = - x^{2} \\- \frac{a + \infty b}{x} & \text{for}\: c = x^{2} \\\frac{2 i a c^{4}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{2 i a c^{2} x^{4}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{2 i b c^{\frac{7}{2}} x \log{\left(- \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{b c^{\frac{7}{2}} x \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{i b c^{\frac{7}{2}} x \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{b c^{\frac{7}{2}} x \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{i b c^{\frac{7}{2}} x \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{2 i b c^{\frac{7}{2}} x \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{2 i b c^{\frac{3}{2}} x^{5} \log{\left(- \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{b c^{\frac{3}{2}} x^{5} \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{i b c^{\frac{3}{2}} x^{5} \log{\left(- i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{b c^{\frac{3}{2}} x^{5} \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{i b c^{\frac{3}{2}} x^{5} \log{\left(i \sqrt{c} + x \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{2 i b c^{\frac{3}{2}} x^{5} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} + \frac{2 i b c^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} - \frac{2 i b c^{2} x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 2 i c^{4} x + 2 i c^{2} x^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x, Eq(c, 0)), (-(a - oo*b)/x, Eq(c, -x**2)), (-(a + oo*b)/x, Eq(c, x**2)), (2*I*a*c**4/(-2*I*c**4*x + 2*I*c**2*x**5) - 2*I*a*c**2*x**4/(-2*I*c**4*x + 2*I*c**2*x**5) + 2*I*b*c**(7/2)*x*log(-sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) - b*c**(7/2)*x*log(-I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) - I*b*c**(7/2)*x*log(-I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) + b*c**(7/2)*x*log(I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) - I*b*c**(7/2)*x*log(I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) + 2*I*b*c**(7/2)*x*atanh(c/x**2)/(-2*I*c**4*x + 2*I*c**2*x**5) - 2*I*b*c**(3/2)*x**5*log(-sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) + b*c**(3/2)*x**5*log(-I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) + I*b*c**(3/2)*x**5*log(-I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) - b*c**(3/2)*x**5*log(I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) + I*b*c**(3/2)*x**5*log(I*sqrt(c) + x)/(-2*I*c**4*x + 2*I*c**2*x**5) - 2*I*b*c**(3/2)*x**5*atanh(c/x**2)/(-2*I*c**4*x + 2*I*c**2*x**5) + 2*I*b*c**4*atanh(c/x**2)/(-2*I*c**4*x + 2*I*c**2*x**5) - 2*I*b*c**2*x**4*atanh(c/x**2)/(-2*I*c**4*x + 2*I*c**2*x**5), True))","A",0
169,1,733,0,13.688562," ","integrate((a+b*atanh(c/x**2))/x**4,x)","\begin{cases} - \frac{a}{3 x^{3}} & \text{for}\: c = 0 \\- \frac{a - \infty b}{3 x^{3}} & \text{for}\: c = - x^{2} \\- \frac{a + \infty b}{3 x^{3}} & \text{for}\: c = x^{2} \\\frac{2 i a c^{9}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{2 i a c^{7} x^{4}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{2 i b c^{\frac{15}{2}} x^{3} \log{\left(- \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{b c^{\frac{15}{2}} x^{3} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{i b c^{\frac{15}{2}} x^{3} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{b c^{\frac{15}{2}} x^{3} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{i b c^{\frac{15}{2}} x^{3} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{2 i b c^{\frac{15}{2}} x^{3} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{2 i b c^{\frac{11}{2}} x^{7} \log{\left(- \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{b c^{\frac{11}{2}} x^{7} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{i b c^{\frac{11}{2}} x^{7} \log{\left(- i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{b c^{\frac{11}{2}} x^{7} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{i b c^{\frac{11}{2}} x^{7} \log{\left(i \sqrt{c} + x \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{2 i b c^{\frac{11}{2}} x^{7} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{2 i b c^{9} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} + \frac{4 i b c^{8} x^{2}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{2 i b c^{7} x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} - \frac{4 i b c^{6} x^{6}}{- 6 i c^{9} x^{3} + 6 i c^{7} x^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(3*x**3), Eq(c, 0)), (-(a - oo*b)/(3*x**3), Eq(c, -x**2)), (-(a + oo*b)/(3*x**3), Eq(c, x**2)), (2*I*a*c**9/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - 2*I*a*c**7*x**4/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + 2*I*b*c**(15/2)*x**3*log(-sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + b*c**(15/2)*x**3*log(-I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - I*b*c**(15/2)*x**3*log(-I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - b*c**(15/2)*x**3*log(I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - I*b*c**(15/2)*x**3*log(I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + 2*I*b*c**(15/2)*x**3*atanh(c/x**2)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - 2*I*b*c**(11/2)*x**7*log(-sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - b*c**(11/2)*x**7*log(-I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + I*b*c**(11/2)*x**7*log(-I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + b*c**(11/2)*x**7*log(I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + I*b*c**(11/2)*x**7*log(I*sqrt(c) + x)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - 2*I*b*c**(11/2)*x**7*atanh(c/x**2)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + 2*I*b*c**9*atanh(c/x**2)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) + 4*I*b*c**8*x**2/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - 2*I*b*c**7*x**4*atanh(c/x**2)/(-6*I*c**9*x**3 + 6*I*c**7*x**7) - 4*I*b*c**6*x**6/(-6*I*c**9*x**3 + 6*I*c**7*x**7), True))","A",0
170,1,797,0,20.044773," ","integrate((a+b*atanh(c/x**2))/x**6,x)","\begin{cases} - \frac{a}{5 x^{5}} & \text{for}\: c = 0 \\- \frac{a - \infty b}{5 x^{5}} & \text{for}\: c = - x^{2} \\- \frac{a + \infty b}{5 x^{5}} & \text{for}\: c = x^{2} \\\frac{6 i a c^{\frac{27}{2}}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{6 i a c^{\frac{23}{2}} x^{4}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{6 i b c^{\frac{27}{2}} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{4 i b c^{\frac{25}{2}} x^{2}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{6 i b c^{\frac{23}{2}} x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{4 i b c^{\frac{21}{2}} x^{6}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{6 i b c^{11} x^{5} \log{\left(- \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{3 b c^{11} x^{5} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{3 i b c^{11} x^{5} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{3 b c^{11} x^{5} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{3 i b c^{11} x^{5} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{6 i b c^{11} x^{5} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{6 i b c^{9} x^{9} \log{\left(- \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{3 b c^{9} x^{9} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{3 i b c^{9} x^{9} \log{\left(- i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{3 b c^{9} x^{9} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} + \frac{3 i b c^{9} x^{9} \log{\left(i \sqrt{c} + x \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} - \frac{6 i b c^{9} x^{9} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{- 30 i c^{\frac{27}{2}} x^{5} + 30 i c^{\frac{23}{2}} x^{9}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(5*x**5), Eq(c, 0)), (-(a - oo*b)/(5*x**5), Eq(c, -x**2)), (-(a + oo*b)/(5*x**5), Eq(c, x**2)), (6*I*a*c**(27/2)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 6*I*a*c**(23/2)*x**4/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 6*I*b*c**(27/2)*atanh(c/x**2)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 4*I*b*c**(25/2)*x**2/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 6*I*b*c**(23/2)*x**4*atanh(c/x**2)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 4*I*b*c**(21/2)*x**6/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 6*I*b*c**11*x**5*log(-sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 3*b*c**11*x**5*log(-I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 3*I*b*c**11*x**5*log(-I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 3*b*c**11*x**5*log(I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 3*I*b*c**11*x**5*log(I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 6*I*b*c**11*x**5*atanh(c/x**2)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 6*I*b*c**9*x**9*log(-sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 3*b*c**9*x**9*log(-I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 3*I*b*c**9*x**9*log(-I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 3*b*c**9*x**9*log(I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) + 3*I*b*c**9*x**9*log(I*sqrt(c) + x)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9) - 6*I*b*c**9*x**9*atanh(c/x**2)/(-30*I*c**(27/2)*x**5 + 30*I*c**(23/2)*x**9), True))","A",0
171,1,151,0,6.123883," ","integrate(x**3*(a+b*atanh(c/x**2))**2,x)","\frac{a^{2} x^{4}}{4} - \frac{a b c^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2} + \frac{a b c x^{2}}{2} + \frac{a b x^{4} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2} + \frac{b^{2} c^{2} \log{\left(- i \sqrt{c} + x \right)}}{2} + \frac{b^{2} c^{2} \log{\left(i \sqrt{c} + x \right)}}{2} - \frac{b^{2} c^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x^{2}} \right)}}{4} - \frac{b^{2} c^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2} + \frac{b^{2} c x^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2} + \frac{b^{2} x^{4} \operatorname{atanh}^{2}{\left(\frac{c}{x^{2}} \right)}}{4}"," ",0,"a**2*x**4/4 - a*b*c**2*atanh(c/x**2)/2 + a*b*c*x**2/2 + a*b*x**4*atanh(c/x**2)/2 + b**2*c**2*log(-I*sqrt(c) + x)/2 + b**2*c**2*log(I*sqrt(c) + x)/2 - b**2*c**2*atanh(c/x**2)**2/4 - b**2*c**2*atanh(c/x**2)/2 + b**2*c*x**2*atanh(c/x**2)/2 + b**2*x**4*atanh(c/x**2)**2/4","C",0
172,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c/x**2))**2,x)","\int x \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*atanh(c/x**2))**2, x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))**2/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))**2/x, x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))**2/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))**2/x**3, x)","F",0
175,1,172,0,16.628285," ","integrate((a+b*atanh(c/x**2))**2/x**5,x)","\begin{cases} - \frac{a^{2}}{4 x^{4}} - \frac{a b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2 x^{4}} - \frac{a b}{2 c x^{2}} + \frac{a b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2 c^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x^{2}} \right)}}{4 x^{4}} - \frac{b^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2 c x^{2}} + \frac{b^{2} \log{\left(x \right)}}{c^{2}} - \frac{b^{2} \log{\left(- i \sqrt{c} + x \right)}}{2 c^{2}} - \frac{b^{2} \log{\left(i \sqrt{c} + x \right)}}{2 c^{2}} + \frac{b^{2} \operatorname{atanh}^{2}{\left(\frac{c}{x^{2}} \right)}}{4 c^{2}} + \frac{b^{2} \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}{2 c^{2}} & \text{for}\: c \neq 0 \\- \frac{a^{2}}{4 x^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(4*x**4) - a*b*atanh(c/x**2)/(2*x**4) - a*b/(2*c*x**2) + a*b*atanh(c/x**2)/(2*c**2) - b**2*atanh(c/x**2)**2/(4*x**4) - b**2*atanh(c/x**2)/(2*c*x**2) + b**2*log(x)/c**2 - b**2*log(-I*sqrt(c) + x)/(2*c**2) - b**2*log(I*sqrt(c) + x)/(2*c**2) + b**2*atanh(c/x**2)**2/(4*c**2) + b**2*atanh(c/x**2)/(2*c**2), Ne(c, 0)), (-a**2/(4*x**4), True))","A",0
176,0,0,0,0.000000," ","integrate(x**4*(a+b*atanh(c/x**2))**2,x)","\int x^{4} \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}\, dx"," ",0,"Integral(x**4*(a + b*atanh(c/x**2))**2, x)","F",0
177,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c/x**2))**2,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c/x**2))**2, x)","F",0
178,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))**2,x)","\int \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))**2, x)","F",0
179,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))**2/x**2, x)","F",0
180,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))**2/x**4,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}}{x^{4}}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))**2/x**4, x)","F",0
181,0,0,0,0.000000," ","integrate((a+b*atanh(c/x**2))**2/x**6,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}}{x^{6}}\, dx"," ",0,"Integral((a + b*atanh(c/x**2))**2/x**6, x)","F",0
182,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c/x**2))**3,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{3}\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c/x**2))**3, x)","F",0
183,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c/x**2))**2,x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)^{2}\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c/x**2))**2, x)","F",0
184,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c/x**2)),x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}\right)\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c/x**2)), x)","F",0
185,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c/x**2)),x)","\int \frac{\left(d x\right)^{m}}{a + b \operatorname{atanh}{\left(\frac{c}{x^{2}} \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*atanh(c/x**2)), x)","F",0
186,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c/x**2))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**(1/2))),x)","\int x^{3} \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)\, dx"," ",0,"Integral(x**3*(a + b*atanh(c*sqrt(x))), x)","F",0
188,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(1/2))),x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*sqrt(x))), x)","F",0
189,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**(1/2))),x)","\int x \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)\, dx"," ",0,"Integral(x*(a + b*atanh(c*sqrt(x))), x)","F",0
190,0,0,0,0.000000," ","integrate(a+b*atanh(c*x**(1/2)),x)","\int \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)\, dx"," ",0,"Integral(a + b*atanh(c*sqrt(x)), x)","F",0
191,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x,x)","\int \frac{a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))/x, x)","F",0
192,1,231,0,21.866608," ","integrate((a+b*atanh(c*x**(1/2)))/x**2,x)","\begin{cases} - \frac{a}{x} + \frac{b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x} & \text{for}\: c = - \sqrt{\frac{1}{x}} \\- \frac{a}{x} - \frac{b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x} & \text{for}\: c = \sqrt{\frac{1}{x}} \\- \frac{a c^{2} x^{\frac{3}{2}}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{a \sqrt{x}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{b c^{4} x^{\frac{5}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{b c^{3} x^{2}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{2 b c^{2} x^{\frac{3}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{b c x}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{b \sqrt{x} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x + b*atanh(sqrt(x)*sqrt(1/x))/x, Eq(c, -sqrt(1/x))), (-a/x - b*atanh(sqrt(x)*sqrt(1/x))/x, Eq(c, sqrt(1/x))), (-a*c**2*x**(3/2)/(c**2*x**(5/2) - x**(3/2)) + a*sqrt(x)/(c**2*x**(5/2) - x**(3/2)) + b*c**4*x**(5/2)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) - b*c**3*x**2/(c**2*x**(5/2) - x**(3/2)) - 2*b*c**2*x**(3/2)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) + b*c*x/(c**2*x**(5/2) - x**(3/2)) + b*sqrt(x)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)), True))","A",0
193,1,342,0,89.353867," ","integrate((a+b*atanh(c*x**(1/2)))/x**3,x)","\begin{cases} - \frac{a}{2 x^{2}} + \frac{b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{2 x^{2}} & \text{for}\: c = - \sqrt{\frac{1}{x}} \\- \frac{a}{2 x^{2}} - \frac{b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{2 x^{2}} & \text{for}\: c = \sqrt{\frac{1}{x}} \\- \frac{3 a c^{2} x^{\frac{3}{2}}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{3 a \sqrt{x}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{3 b c^{6} x^{\frac{7}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{3 b c^{5} x^{3}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{3 b c^{4} x^{\frac{5}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{2 b c^{3} x^{2}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{3 b c^{2} x^{\frac{3}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{b c x}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{3 b \sqrt{x} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/(2*x**2) + b*atanh(sqrt(x)*sqrt(1/x))/(2*x**2), Eq(c, -sqrt(1/x))), (-a/(2*x**2) - b*atanh(sqrt(x)*sqrt(1/x))/(2*x**2), Eq(c, sqrt(1/x))), (-3*a*c**2*x**(3/2)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 3*a*sqrt(x)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 3*b*c**6*x**(7/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) - 3*b*c**5*x**3/(6*c**2*x**(7/2) - 6*x**(5/2)) - 3*b*c**4*x**(5/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) + 2*b*c**3*x**2/(6*c**2*x**(7/2) - 6*x**(5/2)) - 3*b*c**2*x**(3/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) + b*c*x/(6*c**2*x**(7/2) - 6*x**(5/2)) + 3*b*sqrt(x)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)), True))","A",0
194,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**(1/2)))**2,x)","\int x^{3} \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{2}\, dx"," ",0,"Integral(x**3*(a + b*atanh(c*sqrt(x)))**2, x)","F",0
196,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(1/2)))**2,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{2}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*sqrt(x)))**2, x)","F",0
197,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**(1/2)))**2,x)","\int x \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*atanh(c*sqrt(x)))**2, x)","F",0
198,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))**2, x)","F",0
199,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))**2/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))**2/x, x)","F",0
200,1,680,0,22.586498," ","integrate((a+b*atanh(c*x**(1/2)))**2/x**2,x)","\begin{cases} - \frac{a^{2}}{x} + \frac{2 a b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x} - \frac{b^{2} \operatorname{atanh}^{2}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x} & \text{for}\: c = - \sqrt{\frac{1}{x}} \\- \frac{a^{2}}{x} - \frac{2 a b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x} - \frac{b^{2} \operatorname{atanh}^{2}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x} & \text{for}\: c = \sqrt{\frac{1}{x}} \\- \frac{a^{2}}{x} & \text{for}\: c = 0 \\- \frac{a^{2} c^{2} x^{\frac{3}{2}}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{a^{2} \sqrt{x}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{2 a b c^{4} x^{\frac{5}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{2 a b c^{3} x^{2}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{4 a b c^{2} x^{\frac{3}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{2 a b c x}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{2 a b \sqrt{x} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{b^{2} c^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{2 b^{2} c^{4} x^{\frac{5}{2}} \log{\left(\sqrt{x} - \frac{1}{c} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{b^{2} c^{4} x^{\frac{5}{2}} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{2 b^{2} c^{4} x^{\frac{5}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{2 b^{2} c^{3} x^{2} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{b^{2} c^{2} x^{\frac{3}{2}} \log{\left(x \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{2 b^{2} c^{2} x^{\frac{3}{2}} \log{\left(\sqrt{x} - \frac{1}{c} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} - \frac{2 b^{2} c^{2} x^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{2 b^{2} c^{2} x^{\frac{3}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{2 b^{2} c x \operatorname{atanh}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} + \frac{b^{2} \sqrt{x} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{c^{2} x^{\frac{5}{2}} - x^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/x + 2*a*b*atanh(sqrt(x)*sqrt(1/x))/x - b**2*atanh(sqrt(x)*sqrt(1/x))**2/x, Eq(c, -sqrt(1/x))), (-a**2/x - 2*a*b*atanh(sqrt(x)*sqrt(1/x))/x - b**2*atanh(sqrt(x)*sqrt(1/x))**2/x, Eq(c, sqrt(1/x))), (-a**2/x, Eq(c, 0)), (-a**2*c**2*x**(3/2)/(c**2*x**(5/2) - x**(3/2)) + a**2*sqrt(x)/(c**2*x**(5/2) - x**(3/2)) + 2*a*b*c**4*x**(5/2)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) - 2*a*b*c**3*x**2/(c**2*x**(5/2) - x**(3/2)) - 4*a*b*c**2*x**(3/2)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) + 2*a*b*c*x/(c**2*x**(5/2) - x**(3/2)) + 2*a*b*sqrt(x)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) + b**2*c**4*x**(5/2)*log(x)/(c**2*x**(5/2) - x**(3/2)) - 2*b**2*c**4*x**(5/2)*log(sqrt(x) - 1/c)/(c**2*x**(5/2) - x**(3/2)) + b**2*c**4*x**(5/2)*atanh(c*sqrt(x))**2/(c**2*x**(5/2) - x**(3/2)) - 2*b**2*c**4*x**(5/2)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) - 2*b**2*c**3*x**2*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) - b**2*c**2*x**(3/2)*log(x)/(c**2*x**(5/2) - x**(3/2)) + 2*b**2*c**2*x**(3/2)*log(sqrt(x) - 1/c)/(c**2*x**(5/2) - x**(3/2)) - 2*b**2*c**2*x**(3/2)*atanh(c*sqrt(x))**2/(c**2*x**(5/2) - x**(3/2)) + 2*b**2*c**2*x**(3/2)*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) + 2*b**2*c*x*atanh(c*sqrt(x))/(c**2*x**(5/2) - x**(3/2)) + b**2*sqrt(x)*atanh(c*sqrt(x))**2/(c**2*x**(5/2) - x**(3/2)), True))","A",0
201,1,972,0,91.042726," ","integrate((a+b*atanh(c*x**(1/2)))**2/x**3,x)","\begin{cases} - \frac{a^{2}}{2 x^{2}} & \text{for}\: c = 0 \\- \frac{a^{2}}{2 x^{2}} + \frac{a b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{2 x^{2}} & \text{for}\: c = - \sqrt{\frac{1}{x}} \\- \frac{a^{2}}{2 x^{2}} - \frac{a b \operatorname{atanh}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{x^{2}} - \frac{b^{2} \operatorname{atanh}^{2}{\left(\sqrt{x} \sqrt{\frac{1}{x}} \right)}}{2 x^{2}} & \text{for}\: c = \sqrt{\frac{1}{x}} \\- \frac{3 a^{2} c^{2} x^{\frac{3}{2}}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{3 a^{2} \sqrt{x}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{6 a b c^{6} x^{\frac{7}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{6 a b c^{5} x^{3}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{6 a b c^{4} x^{\frac{5}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{4 a b c^{3} x^{2}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{6 a b c^{2} x^{\frac{3}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{2 a b c x}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{6 a b \sqrt{x} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{4 b^{2} c^{6} x^{\frac{7}{2}} \log{\left(x \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{8 b^{2} c^{6} x^{\frac{7}{2}} \log{\left(\sqrt{x} - \frac{1}{c} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{3 b^{2} c^{6} x^{\frac{7}{2}} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{8 b^{2} c^{6} x^{\frac{7}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{6 b^{2} c^{5} x^{3} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{4 b^{2} c^{4} x^{\frac{5}{2}} \log{\left(x \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{8 b^{2} c^{4} x^{\frac{5}{2}} \log{\left(\sqrt{x} - \frac{1}{c} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{3 b^{2} c^{4} x^{\frac{5}{2}} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{8 b^{2} c^{4} x^{\frac{5}{2}} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{b^{2} c^{4} x^{\frac{5}{2}}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{4 b^{2} c^{3} x^{2} \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} - \frac{3 b^{2} c^{2} x^{\frac{3}{2}} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{b^{2} c^{2} x^{\frac{3}{2}}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{2 b^{2} c x \operatorname{atanh}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} + \frac{3 b^{2} \sqrt{x} \operatorname{atanh}^{2}{\left(c \sqrt{x} \right)}}{6 c^{2} x^{\frac{7}{2}} - 6 x^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2/(2*x**2), Eq(c, 0)), (-a**2/(2*x**2) + a*b*atanh(sqrt(x)*sqrt(1/x))/x**2 - b**2*atanh(sqrt(x)*sqrt(1/x))**2/(2*x**2), Eq(c, -sqrt(1/x))), (-a**2/(2*x**2) - a*b*atanh(sqrt(x)*sqrt(1/x))/x**2 - b**2*atanh(sqrt(x)*sqrt(1/x))**2/(2*x**2), Eq(c, sqrt(1/x))), (-3*a**2*c**2*x**(3/2)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 3*a**2*sqrt(x)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 6*a*b*c**6*x**(7/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) - 6*a*b*c**5*x**3/(6*c**2*x**(7/2) - 6*x**(5/2)) - 6*a*b*c**4*x**(5/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) + 4*a*b*c**3*x**2/(6*c**2*x**(7/2) - 6*x**(5/2)) - 6*a*b*c**2*x**(3/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) + 2*a*b*c*x/(6*c**2*x**(7/2) - 6*x**(5/2)) + 6*a*b*sqrt(x)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) + 4*b**2*c**6*x**(7/2)*log(x)/(6*c**2*x**(7/2) - 6*x**(5/2)) - 8*b**2*c**6*x**(7/2)*log(sqrt(x) - 1/c)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 3*b**2*c**6*x**(7/2)*atanh(c*sqrt(x))**2/(6*c**2*x**(7/2) - 6*x**(5/2)) - 8*b**2*c**6*x**(7/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) - 6*b**2*c**5*x**3*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) - 4*b**2*c**4*x**(5/2)*log(x)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 8*b**2*c**4*x**(5/2)*log(sqrt(x) - 1/c)/(6*c**2*x**(7/2) - 6*x**(5/2)) - 3*b**2*c**4*x**(5/2)*atanh(c*sqrt(x))**2/(6*c**2*x**(7/2) - 6*x**(5/2)) + 8*b**2*c**4*x**(5/2)*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) - b**2*c**4*x**(5/2)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 4*b**2*c**3*x**2*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) - 3*b**2*c**2*x**(3/2)*atanh(c*sqrt(x))**2/(6*c**2*x**(7/2) - 6*x**(5/2)) + b**2*c**2*x**(3/2)/(6*c**2*x**(7/2) - 6*x**(5/2)) + 2*b**2*c*x*atanh(c*sqrt(x))/(6*c**2*x**(7/2) - 6*x**(5/2)) + 3*b**2*sqrt(x)*atanh(c*sqrt(x))**2/(6*c**2*x**(7/2) - 6*x**(5/2)), True))","A",0
202,0,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**(1/2)))**3,x)","\int x^{3} \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x**3*(a + b*atanh(c*sqrt(x)))**3, x)","F",0
203,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(1/2)))**3,x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*sqrt(x)))**3, x)","F",0
204,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**(1/2)))**3,x)","\int x \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}\, dx"," ",0,"Integral(x*(a + b*atanh(c*sqrt(x)))**3, x)","F",0
205,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))**3,x)","\int \left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))**3, x)","F",0
206,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))**3/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))**3/x, x)","F",0
207,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))**3/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))**3/x**2, x)","F",0
208,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**(1/2)))**3/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c \sqrt{x} \right)}\right)^{3}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*sqrt(x)))**3/x**3, x)","F",0
209,1,121,0,5.348836," ","integrate(x**(3/2)*atanh(x**(1/2)),x)","\frac{4 x^{\frac{7}{2}} \operatorname{atanh}{\left(\sqrt{x} \right)}}{10 x - 10} - \frac{4 x^{\frac{5}{2}} \operatorname{atanh}{\left(\sqrt{x} \right)}}{10 x - 10} + \frac{x^{3}}{10 x - 10} + \frac{x^{2}}{10 x - 10} + \frac{4 x \log{\left(\sqrt{x} + 1 \right)}}{10 x - 10} - \frac{4 x \operatorname{atanh}{\left(\sqrt{x} \right)}}{10 x - 10} - \frac{4 \log{\left(\sqrt{x} + 1 \right)}}{10 x - 10} + \frac{4 \operatorname{atanh}{\left(\sqrt{x} \right)}}{10 x - 10} - \frac{2}{10 x - 10}"," ",0,"4*x**(7/2)*atanh(sqrt(x))/(10*x - 10) - 4*x**(5/2)*atanh(sqrt(x))/(10*x - 10) + x**3/(10*x - 10) + x**2/(10*x - 10) + 4*x*log(sqrt(x) + 1)/(10*x - 10) - 4*x*atanh(sqrt(x))/(10*x - 10) - 4*log(sqrt(x) + 1)/(10*x - 10) + 4*atanh(sqrt(x))/(10*x - 10) - 2/(10*x - 10)","B",0
210,1,39,0,1.064737," ","integrate(atanh(x**(1/2))*x**(1/2),x)","\frac{2 x^{\frac{3}{2}} \operatorname{atanh}{\left(\sqrt{x} \right)}}{3} + \frac{x}{3} + \frac{2 \log{\left(\sqrt{x} + 1 \right)}}{3} - \frac{2 \operatorname{atanh}{\left(\sqrt{x} \right)}}{3}"," ",0,"2*x**(3/2)*atanh(sqrt(x))/3 + x/3 + 2*log(sqrt(x) + 1)/3 - 2*atanh(sqrt(x))/3","A",0
211,1,87,0,0.539294," ","integrate(atanh(x**(1/2))/x**(1/2),x)","\frac{2 x^{\frac{3}{2}} \operatorname{atanh}{\left(\sqrt{x} \right)}}{x - 1} - \frac{2 \sqrt{x} \operatorname{atanh}{\left(\sqrt{x} \right)}}{x - 1} + \frac{2 x \log{\left(\sqrt{x} + 1 \right)}}{x - 1} - \frac{2 x \operatorname{atanh}{\left(\sqrt{x} \right)}}{x - 1} - \frac{2 \log{\left(\sqrt{x} + 1 \right)}}{x - 1} + \frac{2 \operatorname{atanh}{\left(\sqrt{x} \right)}}{x - 1}"," ",0,"2*x**(3/2)*atanh(sqrt(x))/(x - 1) - 2*sqrt(x)*atanh(sqrt(x))/(x - 1) + 2*x*log(sqrt(x) + 1)/(x - 1) - 2*x*atanh(sqrt(x))/(x - 1) - 2*log(sqrt(x) + 1)/(x - 1) + 2*atanh(sqrt(x))/(x - 1)","B",0
212,1,126,0,1.375458," ","integrate(atanh(x**(1/2))/x**(3/2),x)","- \frac{2 x^{\frac{3}{2}} \operatorname{atanh}{\left(\sqrt{x} \right)}}{x^{2} - x} + \frac{2 \sqrt{x} \operatorname{atanh}{\left(\sqrt{x} \right)}}{x^{2} - x} + \frac{x^{2} \log{\left(x \right)}}{x^{2} - x} - \frac{2 x^{2} \log{\left(\sqrt{x} + 1 \right)}}{x^{2} - x} + \frac{2 x^{2} \operatorname{atanh}{\left(\sqrt{x} \right)}}{x^{2} - x} - \frac{x \log{\left(x \right)}}{x^{2} - x} + \frac{2 x \log{\left(\sqrt{x} + 1 \right)}}{x^{2} - x} - \frac{2 x \operatorname{atanh}{\left(\sqrt{x} \right)}}{x^{2} - x}"," ",0,"-2*x**(3/2)*atanh(sqrt(x))/(x**2 - x) + 2*sqrt(x)*atanh(sqrt(x))/(x**2 - x) + x**2*log(x)/(x**2 - x) - 2*x**2*log(sqrt(x) + 1)/(x**2 - x) + 2*x**2*atanh(sqrt(x))/(x**2 - x) - x*log(x)/(x**2 - x) + 2*x*log(sqrt(x) + 1)/(x**2 - x) - 2*x*atanh(sqrt(x))/(x**2 - x)","B",0
213,-1,0,0,0.000000," ","integrate(x**3*(a+b*atanh(c*x**(3/2))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(3/2))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**(3/2))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate(a+b*atanh(c*x**(3/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(3/2)))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(3/2)))/x**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(3/2)))/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(3/2)))/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**(3/2)))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(3/2)))**2/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((a+b*atanh(c*x**(3/2)))**2/x**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,0,0,0,0.000000," ","integrate(x**2*(a+b*atanh(c*x**n)),x)","\int x^{2} \left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)\, dx"," ",0,"Integral(x**2*(a + b*atanh(c*x**n)), x)","F",0
225,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**n)),x)","\int x \left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)\, dx"," ",0,"Integral(x*(a + b*atanh(c*x**n)), x)","F",0
226,0,0,0,0.000000," ","integrate(a+b*atanh(c*x**n),x)","\int \left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)\, dx"," ",0,"Integral(a + b*atanh(c*x**n), x)","F",0
227,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))/x,x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))/x, x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))/x**2,x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{n} \right)}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))/x**2, x)","F",0
229,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))/x**3,x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{n} \right)}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))/x**3, x)","F",0
230,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))/x**4,x)","\int \frac{a + b \operatorname{atanh}{\left(c x^{n} \right)}}{x^{4}}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))/x**4, x)","F",0
231,0,0,0,0.000000," ","integrate(x*(a+b*atanh(c*x**n))**2,x)","\int x \left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)^{2}\, dx"," ",0,"Integral(x*(a + b*atanh(c*x**n))**2, x)","F",0
232,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))**2,x)","\int \left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))**2, x)","F",0
233,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))**2/x,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)^{2}}{x}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))**2/x, x)","F",0
234,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))**2/x**2,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)^{2}}{x^{2}}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))**2/x**2, x)","F",0
235,0,0,0,0.000000," ","integrate((a+b*atanh(c*x**n))**2/x**3,x)","\int \frac{\left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)^{2}}{x^{3}}\, dx"," ",0,"Integral((a + b*atanh(c*x**n))**2/x**3, x)","F",0
236,0,0,0,0.000000," ","integrate(atanh(a*x**n)/x,x)","\int \frac{\operatorname{atanh}{\left(a x^{n} \right)}}{x}\, dx"," ",0,"Integral(atanh(a*x**n)/x, x)","F",0
237,-1,0,0,0.000000," ","integrate(atanh(a*x**5)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,1,15,0,0.193887," ","integrate(atanh(1/x),x)","x \operatorname{atanh}{\left(\frac{1}{x} \right)} + \log{\left(x + 1 \right)} - \operatorname{atanh}{\left(\frac{1}{x} \right)}"," ",0,"x*atanh(1/x) + log(x + 1) - atanh(1/x)","A",0
239,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**n))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,-1,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,0,0,0,0.000000," ","integrate((d*x)**m*(a+b*atanh(c*x**n)),x)","\int \left(d x\right)^{m} \left(a + b \operatorname{atanh}{\left(c x^{n} \right)}\right)\, dx"," ",0,"Integral((d*x)**m*(a + b*atanh(c*x**n)), x)","F",0
242,0,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x**n)),x)","\int \frac{\left(d x\right)^{m}}{a + b \operatorname{atanh}{\left(c x^{n} \right)}}\, dx"," ",0,"Integral((d*x)**m/(a + b*atanh(c*x**n)), x)","F",0
243,-1,0,0,0.000000," ","integrate((d*x)**m/(a+b*atanh(c*x**n))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
