1,1,624,0,0.356535," ","integrate((a+b*coth(d*x+c)^2)^5,x, algorithm=""maxima"")","\frac{1}{315} \, b^{5} {\left(315 \, x + \frac{315 \, c}{d} - \frac{2 \, {\left(3492 \, e^{\left(-2 \, d x - 2 \, c\right)} - 13968 \, e^{\left(-4 \, d x - 4 \, c\right)} + 26292 \, e^{\left(-6 \, d x - 6 \, c\right)} - 39438 \, e^{\left(-8 \, d x - 8 \, c\right)} + 31500 \, e^{\left(-10 \, d x - 10 \, c\right)} - 21000 \, e^{\left(-12 \, d x - 12 \, c\right)} + 6300 \, e^{\left(-14 \, d x - 14 \, c\right)} - 1575 \, e^{\left(-16 \, d x - 16 \, c\right)} - 563\right)}}{d {\left(9 \, e^{\left(-2 \, d x - 2 \, c\right)} - 36 \, e^{\left(-4 \, d x - 4 \, c\right)} + 84 \, e^{\left(-6 \, d x - 6 \, c\right)} - 126 \, e^{\left(-8 \, d x - 8 \, c\right)} + 126 \, e^{\left(-10 \, d x - 10 \, c\right)} - 84 \, e^{\left(-12 \, d x - 12 \, c\right)} + 36 \, e^{\left(-14 \, d x - 14 \, c\right)} - 9 \, e^{\left(-16 \, d x - 16 \, c\right)} + e^{\left(-18 \, d x - 18 \, c\right)} - 1\right)}}\right)} + \frac{1}{21} \, a b^{4} {\left(105 \, x + \frac{105 \, c}{d} - \frac{8 \, {\left(203 \, e^{\left(-2 \, d x - 2 \, c\right)} - 609 \, e^{\left(-4 \, d x - 4 \, c\right)} + 770 \, e^{\left(-6 \, d x - 6 \, c\right)} - 770 \, e^{\left(-8 \, d x - 8 \, c\right)} + 315 \, e^{\left(-10 \, d x - 10 \, c\right)} - 105 \, e^{\left(-12 \, d x - 12 \, c\right)} - 44\right)}}{d {\left(7 \, e^{\left(-2 \, d x - 2 \, c\right)} - 21 \, e^{\left(-4 \, d x - 4 \, c\right)} + 35 \, e^{\left(-6 \, d x - 6 \, c\right)} - 35 \, e^{\left(-8 \, d x - 8 \, c\right)} + 21 \, e^{\left(-10 \, d x - 10 \, c\right)} - 7 \, e^{\left(-12 \, d x - 12 \, c\right)} + e^{\left(-14 \, d x - 14 \, c\right)} - 1\right)}}\right)} + \frac{2}{3} \, a^{2} b^{3} {\left(15 \, x + \frac{15 \, c}{d} - \frac{2 \, {\left(70 \, e^{\left(-2 \, d x - 2 \, c\right)} - 140 \, e^{\left(-4 \, d x - 4 \, c\right)} + 90 \, e^{\left(-6 \, d x - 6 \, c\right)} - 45 \, e^{\left(-8 \, d x - 8 \, c\right)} - 23\right)}}{d {\left(5 \, e^{\left(-2 \, d x - 2 \, c\right)} - 10 \, e^{\left(-4 \, d x - 4 \, c\right)} + 10 \, e^{\left(-6 \, d x - 6 \, c\right)} - 5 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-10 \, d x - 10 \, c\right)} - 1\right)}}\right)} + \frac{10}{3} \, a^{3} b^{2} {\left(3 \, x + \frac{3 \, c}{d} - \frac{4 \, {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 2\right)}}{d {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)} - 1\right)}}\right)} + 5 \, a^{4} b {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + a^{5} x"," ",0,"1/315*b^5*(315*x + 315*c/d - 2*(3492*e^(-2*d*x - 2*c) - 13968*e^(-4*d*x - 4*c) + 26292*e^(-6*d*x - 6*c) - 39438*e^(-8*d*x - 8*c) + 31500*e^(-10*d*x - 10*c) - 21000*e^(-12*d*x - 12*c) + 6300*e^(-14*d*x - 14*c) - 1575*e^(-16*d*x - 16*c) - 563)/(d*(9*e^(-2*d*x - 2*c) - 36*e^(-4*d*x - 4*c) + 84*e^(-6*d*x - 6*c) - 126*e^(-8*d*x - 8*c) + 126*e^(-10*d*x - 10*c) - 84*e^(-12*d*x - 12*c) + 36*e^(-14*d*x - 14*c) - 9*e^(-16*d*x - 16*c) + e^(-18*d*x - 18*c) - 1))) + 1/21*a*b^4*(105*x + 105*c/d - 8*(203*e^(-2*d*x - 2*c) - 609*e^(-4*d*x - 4*c) + 770*e^(-6*d*x - 6*c) - 770*e^(-8*d*x - 8*c) + 315*e^(-10*d*x - 10*c) - 105*e^(-12*d*x - 12*c) - 44)/(d*(7*e^(-2*d*x - 2*c) - 21*e^(-4*d*x - 4*c) + 35*e^(-6*d*x - 6*c) - 35*e^(-8*d*x - 8*c) + 21*e^(-10*d*x - 10*c) - 7*e^(-12*d*x - 12*c) + e^(-14*d*x - 14*c) - 1))) + 2/3*a^2*b^3*(15*x + 15*c/d - 2*(70*e^(-2*d*x - 2*c) - 140*e^(-4*d*x - 4*c) + 90*e^(-6*d*x - 6*c) - 45*e^(-8*d*x - 8*c) - 23)/(d*(5*e^(-2*d*x - 2*c) - 10*e^(-4*d*x - 4*c) + 10*e^(-6*d*x - 6*c) - 5*e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c) - 1))) + 10/3*a^3*b^2*(3*x + 3*c/d - 4*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) - 2)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 5*a^4*b*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + a^5*x","B",0
2,1,410,0,0.335617," ","integrate((a+b*coth(d*x+c)^2)^4,x, algorithm=""maxima"")","\frac{1}{105} \, b^{4} {\left(105 \, x + \frac{105 \, c}{d} - \frac{8 \, {\left(203 \, e^{\left(-2 \, d x - 2 \, c\right)} - 609 \, e^{\left(-4 \, d x - 4 \, c\right)} + 770 \, e^{\left(-6 \, d x - 6 \, c\right)} - 770 \, e^{\left(-8 \, d x - 8 \, c\right)} + 315 \, e^{\left(-10 \, d x - 10 \, c\right)} - 105 \, e^{\left(-12 \, d x - 12 \, c\right)} - 44\right)}}{d {\left(7 \, e^{\left(-2 \, d x - 2 \, c\right)} - 21 \, e^{\left(-4 \, d x - 4 \, c\right)} + 35 \, e^{\left(-6 \, d x - 6 \, c\right)} - 35 \, e^{\left(-8 \, d x - 8 \, c\right)} + 21 \, e^{\left(-10 \, d x - 10 \, c\right)} - 7 \, e^{\left(-12 \, d x - 12 \, c\right)} + e^{\left(-14 \, d x - 14 \, c\right)} - 1\right)}}\right)} + \frac{4}{15} \, a b^{3} {\left(15 \, x + \frac{15 \, c}{d} - \frac{2 \, {\left(70 \, e^{\left(-2 \, d x - 2 \, c\right)} - 140 \, e^{\left(-4 \, d x - 4 \, c\right)} + 90 \, e^{\left(-6 \, d x - 6 \, c\right)} - 45 \, e^{\left(-8 \, d x - 8 \, c\right)} - 23\right)}}{d {\left(5 \, e^{\left(-2 \, d x - 2 \, c\right)} - 10 \, e^{\left(-4 \, d x - 4 \, c\right)} + 10 \, e^{\left(-6 \, d x - 6 \, c\right)} - 5 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-10 \, d x - 10 \, c\right)} - 1\right)}}\right)} + 2 \, a^{2} b^{2} {\left(3 \, x + \frac{3 \, c}{d} - \frac{4 \, {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 2\right)}}{d {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)} - 1\right)}}\right)} + 4 \, a^{3} b {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + a^{4} x"," ",0,"1/105*b^4*(105*x + 105*c/d - 8*(203*e^(-2*d*x - 2*c) - 609*e^(-4*d*x - 4*c) + 770*e^(-6*d*x - 6*c) - 770*e^(-8*d*x - 8*c) + 315*e^(-10*d*x - 10*c) - 105*e^(-12*d*x - 12*c) - 44)/(d*(7*e^(-2*d*x - 2*c) - 21*e^(-4*d*x - 4*c) + 35*e^(-6*d*x - 6*c) - 35*e^(-8*d*x - 8*c) + 21*e^(-10*d*x - 10*c) - 7*e^(-12*d*x - 12*c) + e^(-14*d*x - 14*c) - 1))) + 4/15*a*b^3*(15*x + 15*c/d - 2*(70*e^(-2*d*x - 2*c) - 140*e^(-4*d*x - 4*c) + 90*e^(-6*d*x - 6*c) - 45*e^(-8*d*x - 8*c) - 23)/(d*(5*e^(-2*d*x - 2*c) - 10*e^(-4*d*x - 4*c) + 10*e^(-6*d*x - 6*c) - 5*e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c) - 1))) + 2*a^2*b^2*(3*x + 3*c/d - 4*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) - 2)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 4*a^3*b*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + a^4*x","B",0
3,1,239,0,0.324447," ","integrate((a+b*coth(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{15} \, b^{3} {\left(15 \, x + \frac{15 \, c}{d} - \frac{2 \, {\left(70 \, e^{\left(-2 \, d x - 2 \, c\right)} - 140 \, e^{\left(-4 \, d x - 4 \, c\right)} + 90 \, e^{\left(-6 \, d x - 6 \, c\right)} - 45 \, e^{\left(-8 \, d x - 8 \, c\right)} - 23\right)}}{d {\left(5 \, e^{\left(-2 \, d x - 2 \, c\right)} - 10 \, e^{\left(-4 \, d x - 4 \, c\right)} + 10 \, e^{\left(-6 \, d x - 6 \, c\right)} - 5 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-10 \, d x - 10 \, c\right)} - 1\right)}}\right)} + a b^{2} {\left(3 \, x + \frac{3 \, c}{d} - \frac{4 \, {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 2\right)}}{d {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)} - 1\right)}}\right)} + 3 \, a^{2} b {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + a^{3} x"," ",0,"1/15*b^3*(15*x + 15*c/d - 2*(70*e^(-2*d*x - 2*c) - 140*e^(-4*d*x - 4*c) + 90*e^(-6*d*x - 6*c) - 45*e^(-8*d*x - 8*c) - 23)/(d*(5*e^(-2*d*x - 2*c) - 10*e^(-4*d*x - 4*c) + 10*e^(-6*d*x - 6*c) - 5*e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c) - 1))) + a*b^2*(3*x + 3*c/d - 4*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) - 2)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 3*a^2*b*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + a^3*x","B",0
4,1,114,0,0.317464," ","integrate((a+b*coth(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} {\left(3 \, x + \frac{3 \, c}{d} - \frac{4 \, {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 2\right)}}{d {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)} - 1\right)}}\right)} + 2 \, a b {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + a^{2} x"," ",0,"1/3*b^2*(3*x + 3*c/d - 4*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) - 2)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 2*a*b*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + a^2*x","B",0
5,1,56,0,0.423247," ","integrate(1/(a+b*coth(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - a + b}{2 \, \sqrt{a b}}\right)}{\sqrt{a b} {\left(a + b\right)} d} + \frac{d x + c}{{\left(a + b\right)} d}"," ",0,"b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) - a + b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) + (d*x + c)/((a + b)*d)","A",0
6,1,207,0,0.470875," ","integrate(1/(a+b*coth(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a b + b^{2}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - a + b}{2 \, \sqrt{a b}}\right)}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b} d} + \frac{a b + b^{2} - {\left(a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{d x + c}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"1/2*(3*a*b + b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) - a + b)/sqrt(a*b))/((a^3 + 2*a^2*b + a*b^2)*sqrt(a*b)*d) + (a*b + b^2 - (a*b - b^2)*e^(-2*d*x - 2*c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*e^(-2*d*x - 2*c) + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*e^(-4*d*x - 4*c))*d) + (d*x + c)/((a^2 + 2*a*b + b^2)*d)","B",0
7,1,509,0,0.558100," ","integrate(1/(a+b*coth(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(15 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - a + b}{2 \, \sqrt{a b}}\right)}{8 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b} d} + \frac{9 \, a^{3} b + 21 \, a^{2} b^{2} + 15 \, a b^{3} + 3 \, b^{4} - {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(9 \, a^{3} b - 3 \, a^{2} b^{2} + 7 \, a b^{3} + 3 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5} - 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{d x + c}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"1/8*(15*a^2*b + 10*a*b^2 + 3*b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) - a + b)/sqrt(a*b))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sqrt(a*b)*d) + 1/4*(9*a^3*b + 21*a^2*b^2 + 15*a*b^3 + 3*b^4 - (27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4)*e^(-2*d*x - 2*c) + 3*(9*a^3*b - 3*a^2*b^2 + 7*a*b^3 + 3*b^4)*e^(-4*d*x - 4*c) - (9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4)*e^(-6*d*x - 6*c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5 - 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*e^(-4*d*x - 4*c) - 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*e^(-6*d*x - 6*c) + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*e^(-8*d*x - 8*c))*d) + (d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
8,1,925,0,0.726089," ","integrate(1/(a+b*coth(d*x+c)^2)^4,x, algorithm=""maxima"")","\frac{{\left(35 \, a^{3} b + 35 \, a^{2} b^{2} + 21 \, a b^{3} + 5 \, b^{4}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - a + b}{2 \, \sqrt{a b}}\right)}{16 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{a b} d} + \frac{87 \, a^{5} b + 319 \, a^{4} b^{2} + 450 \, a^{3} b^{3} + 306 \, a^{2} b^{4} + 103 \, a b^{5} + 15 \, b^{6} - 3 \, {\left(145 \, a^{5} b + 267 \, a^{4} b^{2} + 34 \, a^{3} b^{3} - 178 \, a^{2} b^{4} - 115 \, a b^{5} - 25 \, b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, {\left(145 \, a^{5} b + 93 \, a^{4} b^{2} - 6 \, a^{3} b^{3} + 106 \, a^{2} b^{4} + 85 \, a b^{5} + 25 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(435 \, a^{5} b + 29 \, a^{4} b^{2} + 162 \, a^{3} b^{3} - 306 \, a^{2} b^{4} - 245 \, a b^{5} - 75 \, b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(145 \, a^{5} b + 17 \, a^{4} b^{2} - 58 \, a^{3} b^{3} + 150 \, a^{2} b^{4} + 105 \, a b^{5} + 25 \, b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - 3 \, {\left(29 \, a^{5} b + 23 \, a^{4} b^{2} - 62 \, a^{3} b^{3} - 82 \, a^{2} b^{4} - 31 \, a b^{5} - 5 \, b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)}}{24 \, {\left(a^{10} + 7 \, a^{9} b + 21 \, a^{8} b^{2} + 35 \, a^{7} b^{3} + 35 \, a^{6} b^{4} + 21 \, a^{5} b^{5} + 7 \, a^{4} b^{6} + a^{3} b^{7} - 6 \, {\left(a^{10} + 5 \, a^{9} b + 9 \, a^{8} b^{2} + 5 \, a^{7} b^{3} - 5 \, a^{6} b^{4} - 9 \, a^{5} b^{5} - 5 \, a^{4} b^{6} - a^{3} b^{7}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(5 \, a^{10} + 19 \, a^{9} b + 25 \, a^{8} b^{2} + 15 \, a^{7} b^{3} + 15 \, a^{6} b^{4} + 25 \, a^{5} b^{5} + 19 \, a^{4} b^{6} + 5 \, a^{3} b^{7}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(5 \, a^{10} + 17 \, a^{9} b + 21 \, a^{8} b^{2} + 9 \, a^{7} b^{3} - 9 \, a^{6} b^{4} - 21 \, a^{5} b^{5} - 17 \, a^{4} b^{6} - 5 \, a^{3} b^{7}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(5 \, a^{10} + 19 \, a^{9} b + 25 \, a^{8} b^{2} + 15 \, a^{7} b^{3} + 15 \, a^{6} b^{4} + 25 \, a^{5} b^{5} + 19 \, a^{4} b^{6} + 5 \, a^{3} b^{7}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - 6 \, {\left(a^{10} + 5 \, a^{9} b + 9 \, a^{8} b^{2} + 5 \, a^{7} b^{3} - 5 \, a^{6} b^{4} - 9 \, a^{5} b^{5} - 5 \, a^{4} b^{6} - a^{3} b^{7}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + {\left(a^{10} + 7 \, a^{9} b + 21 \, a^{8} b^{2} + 35 \, a^{7} b^{3} + 35 \, a^{6} b^{4} + 21 \, a^{5} b^{5} + 7 \, a^{4} b^{6} + a^{3} b^{7}\right)} e^{\left(-12 \, d x - 12 \, c\right)}\right)} d} + \frac{d x + c}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d}"," ",0,"1/16*(35*a^3*b + 35*a^2*b^2 + 21*a*b^3 + 5*b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) - a + b)/sqrt(a*b))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*sqrt(a*b)*d) + 1/24*(87*a^5*b + 319*a^4*b^2 + 450*a^3*b^3 + 306*a^2*b^4 + 103*a*b^5 + 15*b^6 - 3*(145*a^5*b + 267*a^4*b^2 + 34*a^3*b^3 - 178*a^2*b^4 - 115*a*b^5 - 25*b^6)*e^(-2*d*x - 2*c) + 6*(145*a^5*b + 93*a^4*b^2 - 6*a^3*b^3 + 106*a^2*b^4 + 85*a*b^5 + 25*b^6)*e^(-4*d*x - 4*c) - 2*(435*a^5*b + 29*a^4*b^2 + 162*a^3*b^3 - 306*a^2*b^4 - 245*a*b^5 - 75*b^6)*e^(-6*d*x - 6*c) + 3*(145*a^5*b + 17*a^4*b^2 - 58*a^3*b^3 + 150*a^2*b^4 + 105*a*b^5 + 25*b^6)*e^(-8*d*x - 8*c) - 3*(29*a^5*b + 23*a^4*b^2 - 62*a^3*b^3 - 82*a^2*b^4 - 31*a*b^5 - 5*b^6)*e^(-10*d*x - 10*c))/((a^10 + 7*a^9*b + 21*a^8*b^2 + 35*a^7*b^3 + 35*a^6*b^4 + 21*a^5*b^5 + 7*a^4*b^6 + a^3*b^7 - 6*(a^10 + 5*a^9*b + 9*a^8*b^2 + 5*a^7*b^3 - 5*a^6*b^4 - 9*a^5*b^5 - 5*a^4*b^6 - a^3*b^7)*e^(-2*d*x - 2*c) + 3*(5*a^10 + 19*a^9*b + 25*a^8*b^2 + 15*a^7*b^3 + 15*a^6*b^4 + 25*a^5*b^5 + 19*a^4*b^6 + 5*a^3*b^7)*e^(-4*d*x - 4*c) - 4*(5*a^10 + 17*a^9*b + 21*a^8*b^2 + 9*a^7*b^3 - 9*a^6*b^4 - 21*a^5*b^5 - 17*a^4*b^6 - 5*a^3*b^7)*e^(-6*d*x - 6*c) + 3*(5*a^10 + 19*a^9*b + 25*a^8*b^2 + 15*a^7*b^3 + 15*a^6*b^4 + 25*a^5*b^5 + 19*a^4*b^6 + 5*a^3*b^7)*e^(-8*d*x - 8*c) - 6*(a^10 + 5*a^9*b + 9*a^8*b^2 + 5*a^7*b^3 - 5*a^6*b^4 - 9*a^5*b^5 - 5*a^4*b^6 - a^3*b^7)*e^(-10*d*x - 10*c) + (a^10 + 7*a^9*b + 21*a^8*b^2 + 35*a^7*b^3 + 35*a^6*b^4 + 21*a^5*b^5 + 7*a^4*b^6 + a^3*b^7)*e^(-12*d*x - 12*c))*d) + (d*x + c)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d)","B",0
9,1,38,0,0.405766," ","integrate(1/(1-2*coth(x)^2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(-2 \, x\right)} - 3}{2 \, \sqrt{2} + e^{\left(-2 \, x\right)} + 3}\right) - x"," ",0,"-1/2*sqrt(2)*log(-(2*sqrt(2) - e^(-2*x) - 3)/(2*sqrt(2) + e^(-2*x) + 3)) - x","B",0
10,1,19,0,0.423931," ","integrate((1-coth(x)^2)^(1/2),x, algorithm=""maxima"")","i \, \log\left(e^{\left(-x\right)} + 1\right) - i \, \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"I*log(e^(-x) + 1) - I*log(e^(-x) - 1)","C",0
11,1,17,0,0.422904," ","integrate((-1+coth(x)^2)^(1/2),x, algorithm=""maxima"")","\log\left(e^{\left(-x\right)} + 1\right) - \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"log(e^(-x) + 1) - log(e^(-x) - 1)","A",0
12,1,49,0,0.420721," ","integrate((1-coth(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{i \, e^{\left(-x\right)} + i \, e^{\left(-3 \, x\right)}}{2 \, e^{\left(-2 \, x\right)} - e^{\left(-4 \, x\right)} - 1} + \frac{1}{2} i \, \log\left(e^{\left(-x\right)} + 1\right) - \frac{1}{2} i \, \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"(I*e^(-x) + I*e^(-3*x))/(2*e^(-2*x) - e^(-4*x) - 1) + 1/2*I*log(e^(-x) + 1) - 1/2*I*log(e^(-x) - 1)","C",0
13,1,46,0,0.412932," ","integrate((-1+coth(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{e^{\left(-x\right)} + e^{\left(-3 \, x\right)}}{2 \, e^{\left(-2 \, x\right)} - e^{\left(-4 \, x\right)} - 1} - \frac{1}{2} \, \log\left(e^{\left(-x\right)} + 1\right) + \frac{1}{2} \, \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"-(e^(-x) + e^(-3*x))/(2*e^(-2*x) - e^(-4*x) - 1) - 1/2*log(e^(-x) + 1) + 1/2*log(e^(-x) - 1)","A",0
14,1,11,0,0.418946," ","integrate(1/(1-coth(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} i \, e^{\left(-x\right)} + \frac{1}{2} i \, e^{x}"," ",0,"1/2*I*e^(-x) + 1/2*I*e^x","C",0
15,1,11,0,0.417206," ","integrate(1/(-1+coth(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, e^{\left(-x\right)} - \frac{1}{2} \, e^{x}"," ",0,"-1/2*e^(-x) - 1/2*e^x","A",0
16,0,0,0,0.000000," ","integrate(coth(x)^3*(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{2} + a} \coth\left(x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^2 + a)*coth(x)^3, x)","F",0
17,0,0,0,0.000000," ","integrate(coth(x)^2*(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{2} + a} \coth\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^2 + a)*coth(x)^2, x)","F",0
18,0,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{2} + a} \coth\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^2 + a)*coth(x), x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^2 + a), x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(1/2)*tanh(x),x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{2} + a} \tanh\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^2 + a)*tanh(x), x)","F",0
21,0,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(1/2)*tanh(x)^2,x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{2} + a} \tanh\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^2 + a)*tanh(x)^2, x)","F",0
22,0,0,0,0.000000," ","integrate(coth(x)^3*(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)^{3}\,{d x}"," ",0,"integrate((b*coth(x)^2 + a)^(3/2)*coth(x)^3, x)","F",0
23,0,0,0,0.000000," ","integrate(coth(x)^2*(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*coth(x)^2 + a)^(3/2)*coth(x)^2, x)","F",0
24,0,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)\,{d x}"," ",0,"integrate((b*coth(x)^2 + a)^(3/2)*coth(x), x)","F",0
25,0,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*coth(x)^2 + a)^(3/2), x)","F",0
26,0,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(3/2)*tanh(x),x, algorithm=""maxima"")","\int {\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)\,{d x}"," ",0,"integrate((b*coth(x)^2 + a)^(3/2)*tanh(x), x)","F",0
27,0,0,0,0.000000," ","integrate((a+b*coth(x)^2)^(3/2)*tanh(x)^2,x, algorithm=""maxima"")","\int {\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*coth(x)^2 + a)^(3/2)*tanh(x)^2, x)","F",0
28,0,0,0,0.000000," ","integrate((1+coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\coth\left(x\right)^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(coth(x)^2 + 1), x)","F",0
29,0,0,0,0.000000," ","integrate((-1-coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-\coth\left(x\right)^{2} - 1}\,{d x}"," ",0,"integrate(sqrt(-coth(x)^2 - 1), x)","F",0
30,0,0,0,0.000000," ","integrate((1+coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\coth\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((coth(x)^2 + 1)^(3/2), x)","F",0
31,0,0,0,0.000000," ","integrate((-1-coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(-\coth\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-coth(x)^2 - 1)^(3/2), x)","F",0
32,0,0,0,0.000000," ","integrate(coth(x)^3/(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{3}}{\sqrt{b \coth\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)^3/sqrt(b*coth(x)^2 + a), x)","F",0
33,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{\sqrt{b \coth\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)^2/sqrt(b*coth(x)^2 + a), x)","F",0
34,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{\sqrt{b \coth\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)/sqrt(b*coth(x)^2 + a), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \coth\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*coth(x)^2 + a), x)","F",0
36,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{\sqrt{b \coth\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)/sqrt(b*coth(x)^2 + a), x)","F",0
37,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{\sqrt{b \coth\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^2/sqrt(b*coth(x)^2 + a), x)","F",0
38,0,0,0,0.000000," ","integrate(coth(x)^3/(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{3}}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)^3/(b*coth(x)^2 + a)^(3/2), x)","F",0
39,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)^2/(b*coth(x)^2 + a)^(3/2), x)","F",0
40,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*coth(x)^2 + a)^(3/2), x)","F",0
41,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*coth(x)^2 + a)^(3/2), x)","F",0
42,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*coth(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^2/(b*coth(x)^2 + a)^(3/2), x)","F",0
43,0,0,0,0.000000," ","integrate(coth(x)^3/(a+b*coth(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{3}}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)^3/(b*coth(x)^2 + a)^(5/2), x)","F",0
44,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*coth(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)^2/(b*coth(x)^2 + a)^(5/2), x)","F",0
45,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*coth(x)^2 + a)^(5/2), x)","F",0
46,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*coth(x)^2 + a)^(5/2), x)","F",0
47,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*coth(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{{\left(b \coth\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^2/(b*coth(x)^2 + a)^(5/2), x)","F",0
48,0,0,0,0.000000," ","integrate(1/(1+coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\coth\left(x\right)^{2} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(coth(x)^2 + 1), x)","F",0
49,0,0,0,0.000000," ","integrate(1/(-1-coth(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\coth\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-coth(x)^2 - 1), x)","F",0
50,1,73,0,0.412908," ","integrate(1/(1+coth(x)^3),x, algorithm=""maxima"")","-\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, \sqrt{3} e^{\left(-x\right)} + 3^{\frac{1}{4}} \sqrt{2}\right)}\right) + \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, \sqrt{3} e^{\left(-x\right)} - 3^{\frac{1}{4}} \sqrt{2}\right)}\right) + \frac{1}{2} \, x + \frac{1}{12} \, e^{\left(-2 \, x\right)}"," ",0,"-2/9*sqrt(3)*arctan(1/6*3^(3/4)*sqrt(2)*(2*sqrt(3)*e^(-x) + 3^(1/4)*sqrt(2))) + 2/9*sqrt(3)*arctan(1/6*3^(3/4)*sqrt(2)*(2*sqrt(3)*e^(-x) - 3^(1/4)*sqrt(2))) + 1/2*x + 1/12*e^(-2*x)","B",0
51,0,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(x)^4)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \coth\left(x\right)^{4} + a} \coth\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*coth(x)^4 + a)*coth(x), x)","F",0
52,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{\sqrt{b \coth\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(coth(x)/sqrt(b*coth(x)^4 + a), x)","F",0
53,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)^4)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \coth\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*coth(x)^4 + a)^(3/2), x)","F",0
