1,1,154,0,1.130431," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{64} \, a {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{64} \, b {\left(\frac{120 \, {\left(d x + c\right)}}{d} + \frac{16 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} - \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)} + 144 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)}"," ",0,"1/64*a*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/64*b*(120*(d*x + c)/d + (16*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (15*e^(-2*d*x - 2*c) + 144*e^(-4*d*x - 4*c) - 1)/(d*(e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))))","B",0
2,1,136,0,0.391223," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{1}{24} \, b {\left(\frac{21 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{20 \, e^{\left(-2 \, d x - 2 \, c\right)} + 69 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} + \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"-1/24*b*((21*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (20*e^(-2*d*x - 2*c) + 69*e^(-4*d*x - 4*c) - 1)/(d*(e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + 1/24*a*(e^(3*d*x + 3*c)/d - 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d + e^(-3*d*x - 3*c)/d)","B",0
3,1,101,0,1.383995," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{8} \, b {\left(\frac{12 \, {\left(d x + c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{17 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)}\right)}}\right)}"," ",0,"-1/8*a*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/8*b*(12*(d*x + c)/d + e^(-2*d*x - 2*c)/d - (17*e^(-2*d*x - 2*c) + 1)/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c))))","B",0
4,1,67,0,0.366737," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{e^{\left(-d x - c\right)}}{d} + \frac{5 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}\right)} + \frac{a \cosh\left(d x + c\right)}{d}"," ",0,"1/2*b*(e^(-d*x - c)/d + (5*e^(-2*d*x - 2*c) + 1)/(d*(e^(-d*x - c) + e^(-3*d*x - 3*c)))) + a*cosh(d*x + c)/d","B",0
5,1,40,0,0.347845," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{a \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{2 \, b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}}"," ",0,"a*log(tanh(1/2*d*x + 1/2*c))/d - 2*b/(d*(e^(d*x + c) + e^(-d*x - c)))","A",0
6,1,39,0,0.339770," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}} + \frac{2 \, a}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}"," ",0,"2*b/(d*(e^(-2*d*x - 2*c) + 1)) + 2*a/(d*(e^(-2*d*x - 2*c) - 1))","A",0
7,1,152,0,0.383707," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} - b {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, e^{\left(-d x - c\right)}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)}"," ",0,"1/2*a*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) - b*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d - 2*e^(-d*x - c)/(d*(e^(-2*d*x - 2*c) + 1)))","B",0
8,1,113,0,0.357541," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{4}{3} \, a {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{1}{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)} + \frac{4 \, b}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"4/3*a*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)) - 1/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 4*b/(d*(e^(-4*d*x - 4*c) - 1))","B",0
9,1,295,0,0.358342," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{64} \, a^{2} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{192} \, b^{2} {\left(\frac{840 \, {\left(d x + c\right)}}{d} + \frac{3 \, {\left(24 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}\right)}}{d} - \frac{63 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1487 \, e^{\left(-4 \, d x - 4 \, c\right)} + 2517 \, e^{\left(-6 \, d x - 6 \, c\right)} + 1608 \, e^{\left(-8 \, d x - 8 \, c\right)} - 3}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-10 \, d x - 10 \, c\right)}\right)}}\right)} + \frac{1}{32} \, a b {\left(\frac{120 \, {\left(d x + c\right)}}{d} + \frac{16 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} - \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)} + 144 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)}"," ",0,"1/64*a^2*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/192*b^2*(840*(d*x + c)/d + 3*(24*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (63*e^(-2*d*x - 2*c) + 1487*e^(-4*d*x - 4*c) + 2517*e^(-6*d*x - 6*c) + 1608*e^(-8*d*x - 8*c) - 3)/(d*(e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) + 3*e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c)))) + 1/32*a*b*(120*(d*x + c)/d + (16*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (15*e^(-2*d*x - 2*c) + 144*e^(-4*d*x - 4*c) - 1)/(d*(e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))))","B",0
10,1,265,0,0.365385," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{1}{24} \, b^{2} {\left(\frac{33 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{30 \, e^{\left(-2 \, d x - 2 \, c\right)} + 240 \, e^{\left(-4 \, d x - 4 \, c\right)} + 322 \, e^{\left(-6 \, d x - 6 \, c\right)} + 177 \, e^{\left(-8 \, d x - 8 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)} + 3 \, e^{\left(-7 \, d x - 7 \, c\right)} + e^{\left(-9 \, d x - 9 \, c\right)}\right)}}\right)} - \frac{1}{12} \, a b {\left(\frac{21 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{20 \, e^{\left(-2 \, d x - 2 \, c\right)} + 69 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a^{2} {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} + \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"-1/24*b^2*((33*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (30*e^(-2*d*x - 2*c) + 240*e^(-4*d*x - 4*c) + 322*e^(-6*d*x - 6*c) + 177*e^(-8*d*x - 8*c) - 1)/(d*(e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c) + 3*e^(-7*d*x - 7*c) + e^(-9*d*x - 9*c)))) - 1/12*a*b*((21*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (20*e^(-2*d*x - 2*c) + 69*e^(-4*d*x - 4*c) - 1)/(d*(e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + 1/24*a^2*(e^(3*d*x + 3*c)/d - 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d + e^(-3*d*x - 3*c)/d)","B",0
11,1,217,0,0.346579," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{24} \, b^{2} {\left(\frac{60 \, {\left(d x + c\right)}}{d} + \frac{3 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{121 \, e^{\left(-2 \, d x - 2 \, c\right)} + 201 \, e^{\left(-4 \, d x - 4 \, c\right)} + 147 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)}\right)}}\right)} - \frac{1}{4} \, a b {\left(\frac{12 \, {\left(d x + c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{17 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)}\right)}}\right)}"," ",0,"-1/8*a^2*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/24*b^2*(60*(d*x + c)/d + 3*e^(-2*d*x - 2*c)/d - (121*e^(-2*d*x - 2*c) + 201*e^(-4*d*x - 4*c) + 147*e^(-6*d*x - 6*c) + 3)/(d*(e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c)))) - 1/4*a*b*(12*(d*x + c)/d + e^(-2*d*x - 2*c)/d - (17*e^(-2*d*x - 2*c) + 1)/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c))))","B",0
12,1,171,0,0.354109," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} {\left(\frac{3 \, e^{\left(-d x - c\right)}}{d} + \frac{33 \, e^{\left(-2 \, d x - 2 \, c\right)} + 41 \, e^{\left(-4 \, d x - 4 \, c\right)} + 27 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3}{d {\left(e^{\left(-d x - c\right)} + 3 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)} + e^{\left(-7 \, d x - 7 \, c\right)}\right)}}\right)} + a b {\left(\frac{e^{\left(-d x - c\right)}}{d} + \frac{5 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}\right)} + \frac{a^{2} \cosh\left(d x + c\right)}{d}"," ",0,"1/6*b^2*(3*e^(-d*x - c)/d + (33*e^(-2*d*x - 2*c) + 41*e^(-4*d*x - 4*c) + 27*e^(-6*d*x - 6*c) + 3)/(d*(e^(-d*x - c) + 3*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c) + e^(-7*d*x - 7*c)))) + a*b*(e^(-d*x - c)/d + (5*e^(-2*d*x - 2*c) + 1)/(d*(e^(-d*x - c) + e^(-3*d*x - 3*c)))) + a^2*cosh(d*x + c)/d","B",0
13,1,196,0,0.348614," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{2}{3} \, b^{2} {\left(\frac{3 \, e^{\left(-d x - c\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)}} + \frac{2 \, e^{\left(-3 \, d x - 3 \, c\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)}} + \frac{3 \, e^{\left(-5 \, d x - 5 \, c\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)} + \frac{a^{2} \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{4 \, a b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}}"," ",0,"-2/3*b^2*(3*e^(-d*x - c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 2*e^(-3*d*x - 3*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 3*e^(-5*d*x - 5*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1))) + a^2*log(tanh(1/2*d*x + 1/2*c))/d - 4*a*b/(d*(e^(d*x + c) + e^(-d*x - c)))","B",0
14,1,136,0,0.338834," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2}{3} \, b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{1}{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)} + \frac{4 \, a b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}} + \frac{2 \, a^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}"," ",0,"2/3*b^2*(3*e^(-4*d*x - 4*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1))) + 4*a*b/(d*(e^(-2*d*x - 2*c) + 1)) + 2*a^2/(d*(e^(-2*d*x - 2*c) - 1))","B",0
15,1,181,0,0.316132," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} - 2 \, a b {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, e^{\left(-d x - c\right)}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} - \frac{8 \, b^{2}}{3 \, d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{3}}"," ",0,"1/2*a^2*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) - 2*a*b*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d - 2*e^(-d*x - c)/(d*(e^(-2*d*x - 2*c) + 1))) - 8/3*b^2/(d*(e^(d*x + c) + e^(-d*x - c))^3)","B",0
16,1,210,0,0.318526," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{4}{3} \, b^{2} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} + \frac{1}{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)} + \frac{4}{3} \, a^{2} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{1}{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)} + \frac{8 \, a b}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"4/3*b^2*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1))) + 4/3*a^2*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)) - 1/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 8*a*b/(d*(e^(-4*d*x - 4*c) - 1))","B",0
17,1,480,0,0.339738," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{64} \, a^{3} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{320} \, b^{3} {\left(\frac{2520 \, {\left(d x + c\right)}}{d} + \frac{5 \, {\left(32 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}\right)}}{d} - \frac{135 \, e^{\left(-2 \, d x - 2 \, c\right)} + 5358 \, e^{\left(-4 \, d x - 4 \, c\right)} + 18190 \, e^{\left(-6 \, d x - 6 \, c\right)} + 28455 \, e^{\left(-8 \, d x - 8 \, c\right)} + 19995 \, e^{\left(-10 \, d x - 10 \, c\right)} + 6560 \, e^{\left(-12 \, d x - 12 \, c\right)} - 5}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 5 \, e^{\left(-6 \, d x - 6 \, c\right)} + 10 \, e^{\left(-8 \, d x - 8 \, c\right)} + 10 \, e^{\left(-10 \, d x - 10 \, c\right)} + 5 \, e^{\left(-12 \, d x - 12 \, c\right)} + e^{\left(-14 \, d x - 14 \, c\right)}\right)}}\right)} + \frac{1}{64} \, a b^{2} {\left(\frac{840 \, {\left(d x + c\right)}}{d} + \frac{3 \, {\left(24 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}\right)}}{d} - \frac{63 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1487 \, e^{\left(-4 \, d x - 4 \, c\right)} + 2517 \, e^{\left(-6 \, d x - 6 \, c\right)} + 1608 \, e^{\left(-8 \, d x - 8 \, c\right)} - 3}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-10 \, d x - 10 \, c\right)}\right)}}\right)} + \frac{3}{64} \, a^{2} b {\left(\frac{120 \, {\left(d x + c\right)}}{d} + \frac{16 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} - \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)} + 144 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)}"," ",0,"1/64*a^3*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/320*b^3*(2520*(d*x + c)/d + 5*(32*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (135*e^(-2*d*x - 2*c) + 5358*e^(-4*d*x - 4*c) + 18190*e^(-6*d*x - 6*c) + 28455*e^(-8*d*x - 8*c) + 19995*e^(-10*d*x - 10*c) + 6560*e^(-12*d*x - 12*c) - 5)/(d*(e^(-4*d*x - 4*c) + 5*e^(-6*d*x - 6*c) + 10*e^(-8*d*x - 8*c) + 10*e^(-10*d*x - 10*c) + 5*e^(-12*d*x - 12*c) + e^(-14*d*x - 14*c)))) + 1/64*a*b^2*(840*(d*x + c)/d + 3*(24*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (63*e^(-2*d*x - 2*c) + 1487*e^(-4*d*x - 4*c) + 2517*e^(-6*d*x - 6*c) + 1608*e^(-8*d*x - 8*c) - 3)/(d*(e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) + 3*e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c)))) + 3/64*a^2*b*(120*(d*x + c)/d + (16*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (15*e^(-2*d*x - 2*c) + 144*e^(-4*d*x - 4*c) - 1)/(d*(e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))))","B",0
18,1,439,0,0.349512," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{120} \, b^{3} {\left(\frac{5 \, {\left(45 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d} + \frac{200 \, e^{\left(-2 \, d x - 2 \, c\right)} + 2515 \, e^{\left(-4 \, d x - 4 \, c\right)} + 6680 \, e^{\left(-6 \, d x - 6 \, c\right)} + 9073 \, e^{\left(-8 \, d x - 8 \, c\right)} + 5600 \, e^{\left(-10 \, d x - 10 \, c\right)} + 1665 \, e^{\left(-12 \, d x - 12 \, c\right)} - 5}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 5 \, e^{\left(-5 \, d x - 5 \, c\right)} + 10 \, e^{\left(-7 \, d x - 7 \, c\right)} + 10 \, e^{\left(-9 \, d x - 9 \, c\right)} + 5 \, e^{\left(-11 \, d x - 11 \, c\right)} + e^{\left(-13 \, d x - 13 \, c\right)}\right)}}\right)} - \frac{1}{8} \, a b^{2} {\left(\frac{33 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{30 \, e^{\left(-2 \, d x - 2 \, c\right)} + 240 \, e^{\left(-4 \, d x - 4 \, c\right)} + 322 \, e^{\left(-6 \, d x - 6 \, c\right)} + 177 \, e^{\left(-8 \, d x - 8 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)} + 3 \, e^{\left(-7 \, d x - 7 \, c\right)} + e^{\left(-9 \, d x - 9 \, c\right)}\right)}}\right)} - \frac{1}{8} \, a^{2} b {\left(\frac{21 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{20 \, e^{\left(-2 \, d x - 2 \, c\right)} + 69 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a^{3} {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} + \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"-1/120*b^3*(5*(45*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (200*e^(-2*d*x - 2*c) + 2515*e^(-4*d*x - 4*c) + 6680*e^(-6*d*x - 6*c) + 9073*e^(-8*d*x - 8*c) + 5600*e^(-10*d*x - 10*c) + 1665*e^(-12*d*x - 12*c) - 5)/(d*(e^(-3*d*x - 3*c) + 5*e^(-5*d*x - 5*c) + 10*e^(-7*d*x - 7*c) + 10*e^(-9*d*x - 9*c) + 5*e^(-11*d*x - 11*c) + e^(-13*d*x - 13*c)))) - 1/8*a*b^2*((33*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (30*e^(-2*d*x - 2*c) + 240*e^(-4*d*x - 4*c) + 322*e^(-6*d*x - 6*c) + 177*e^(-8*d*x - 8*c) - 1)/(d*(e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c) + 3*e^(-7*d*x - 7*c) + e^(-9*d*x - 9*c)))) - 1/8*a^2*b*((21*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (20*e^(-2*d*x - 2*c) + 69*e^(-4*d*x - 4*c) - 1)/(d*(e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + 1/24*a^3*(e^(3*d*x + 3*c)/d - 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d + e^(-3*d*x - 3*c)/d)","B",0
19,1,377,0,0.329443," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{3} {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{120} \, b^{3} {\left(\frac{420 \, {\left(d x + c\right)}}{d} + \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{1003 \, e^{\left(-2 \, d x - 2 \, c\right)} + 3350 \, e^{\left(-4 \, d x - 4 \, c\right)} + 5590 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3915 \, e^{\left(-8 \, d x - 8 \, c\right)} + 1455 \, e^{\left(-10 \, d x - 10 \, c\right)} + 15}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 5 \, e^{\left(-4 \, d x - 4 \, c\right)} + 10 \, e^{\left(-6 \, d x - 6 \, c\right)} + 10 \, e^{\left(-8 \, d x - 8 \, c\right)} + 5 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)}\right)}}\right)} - \frac{1}{8} \, a b^{2} {\left(\frac{60 \, {\left(d x + c\right)}}{d} + \frac{3 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{121 \, e^{\left(-2 \, d x - 2 \, c\right)} + 201 \, e^{\left(-4 \, d x - 4 \, c\right)} + 147 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)}\right)}}\right)} - \frac{3}{8} \, a^{2} b {\left(\frac{12 \, {\left(d x + c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{17 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)}\right)}}\right)}"," ",0,"-1/8*a^3*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/120*b^3*(420*(d*x + c)/d + 15*e^(-2*d*x - 2*c)/d - (1003*e^(-2*d*x - 2*c) + 3350*e^(-4*d*x - 4*c) + 5590*e^(-6*d*x - 6*c) + 3915*e^(-8*d*x - 8*c) + 1455*e^(-10*d*x - 10*c) + 15)/(d*(e^(-2*d*x - 2*c) + 5*e^(-4*d*x - 4*c) + 10*e^(-6*d*x - 6*c) + 10*e^(-8*d*x - 8*c) + 5*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c)))) - 1/8*a*b^2*(60*(d*x + c)/d + 3*e^(-2*d*x - 2*c)/d - (121*e^(-2*d*x - 2*c) + 201*e^(-4*d*x - 4*c) + 147*e^(-6*d*x - 6*c) + 3)/(d*(e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c)))) - 3/8*a^2*b*(12*(d*x + c)/d + e^(-2*d*x - 2*c)/d - (17*e^(-2*d*x - 2*c) + 1)/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c))))","B",0
20,1,321,0,0.326307," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{10} \, b^{3} {\left(\frac{5 \, e^{\left(-d x - c\right)}}{d} + \frac{85 \, e^{\left(-2 \, d x - 2 \, c\right)} + 210 \, e^{\left(-4 \, d x - 4 \, c\right)} + 314 \, e^{\left(-6 \, d x - 6 \, c\right)} + 185 \, e^{\left(-8 \, d x - 8 \, c\right)} + 65 \, e^{\left(-10 \, d x - 10 \, c\right)} + 5}{d {\left(e^{\left(-d x - c\right)} + 5 \, e^{\left(-3 \, d x - 3 \, c\right)} + 10 \, e^{\left(-5 \, d x - 5 \, c\right)} + 10 \, e^{\left(-7 \, d x - 7 \, c\right)} + 5 \, e^{\left(-9 \, d x - 9 \, c\right)} + e^{\left(-11 \, d x - 11 \, c\right)}\right)}}\right)} + \frac{1}{2} \, a b^{2} {\left(\frac{3 \, e^{\left(-d x - c\right)}}{d} + \frac{33 \, e^{\left(-2 \, d x - 2 \, c\right)} + 41 \, e^{\left(-4 \, d x - 4 \, c\right)} + 27 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3}{d {\left(e^{\left(-d x - c\right)} + 3 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)} + e^{\left(-7 \, d x - 7 \, c\right)}\right)}}\right)} + \frac{3}{2} \, a^{2} b {\left(\frac{e^{\left(-d x - c\right)}}{d} + \frac{5 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}\right)} + \frac{a^{3} \cosh\left(d x + c\right)}{d}"," ",0,"1/10*b^3*(5*e^(-d*x - c)/d + (85*e^(-2*d*x - 2*c) + 210*e^(-4*d*x - 4*c) + 314*e^(-6*d*x - 6*c) + 185*e^(-8*d*x - 8*c) + 65*e^(-10*d*x - 10*c) + 5)/(d*(e^(-d*x - c) + 5*e^(-3*d*x - 3*c) + 10*e^(-5*d*x - 5*c) + 10*e^(-7*d*x - 7*c) + 5*e^(-9*d*x - 9*c) + e^(-11*d*x - 11*c)))) + 1/2*a*b^2*(3*e^(-d*x - c)/d + (33*e^(-2*d*x - 2*c) + 41*e^(-4*d*x - 4*c) + 27*e^(-6*d*x - 6*c) + 3)/(d*(e^(-d*x - c) + 3*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c) + e^(-7*d*x - 7*c)))) + 3/2*a^2*b*(e^(-d*x - c)/d + (5*e^(-2*d*x - 2*c) + 1)/(d*(e^(-d*x - c) + e^(-3*d*x - 3*c)))) + a^3*cosh(d*x + c)/d","B",0
21,1,560,0,0.325412," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{2}{15} \, b^{3} {\left(\frac{15 \, e^{\left(-d x - c\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)}} + \frac{20 \, e^{\left(-3 \, d x - 3 \, c\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)}} + \frac{58 \, e^{\left(-5 \, d x - 5 \, c\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)}} + \frac{20 \, e^{\left(-7 \, d x - 7 \, c\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)}} + \frac{15 \, e^{\left(-9 \, d x - 9 \, c\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 b^{2} {\left(\frac{3 \, e^{\left(-d x - c\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)}} + \frac{2 \, e^{\left(-3 \, d x - 3 \, c\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)}} + \frac{3 \, e^{\left(-5 \, d x - 5 \, c\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)} + \frac{a^{3} \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d} - \frac{6 \, a^{2} b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}}"," ",0,"-2/15*b^3*(15*e^(-d*x - c)/(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)) + 20*e^(-3*d*x - 3*c)/(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)) + 58*e^(-5*d*x - 5*c)/(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)) + 20*e^(-7*d*x - 7*c)/(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)) + 15*e^(-9*d*x - 9*c)/(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*b^2*(3*e^(-d*x - c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 2*e^(-3*d*x - 3*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 3*e^(-5*d*x - 5*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1))) + a^3*log(tanh(1/2*d*x + 1/2*c))/d - 6*a^2*b/(d*(e^(d*x + c) + e^(-d*x - c)))","B",0
22,1,348,0,0.326422," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{2}{5} \, b^{3} {\left(\frac{10 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{5 \, e^{\left(-8 \, d x - 8 \, c\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)}} + \frac{1}{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 b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{1}{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)} + \frac{6 \, a^{2} b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}} + \frac{2 \, a^{3}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}"," ",0,"2/5*b^3*(10*e^(-4*d*x - 4*c)/(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)) + 5*e^(-8*d*x - 8*c)/(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)) + 1/(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*b^2*(3*e^(-4*d*x - 4*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1))) + 6*a^2*b/(d*(e^(-2*d*x - 2*c) + 1)) + 2*a^3/(d*(e^(-2*d*x - 2*c) - 1))","B",0
23,1,403,0,0.332380," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} - 3 \, a^{2} b {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, e^{\left(-d x - c\right)}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} - \frac{8}{15} \, b^{3} {\left(\frac{5 \, e^{\left(-3 \, d x - 3 \, c\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)}} - \frac{2 \, e^{\left(-5 \, d x - 5 \, c\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)}} + \frac{5 \, e^{\left(-7 \, d x - 7 \, c\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{8 \, a b^{2}}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{3}}"," ",0,"1/2*a^3*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) - 3*a^2*b*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d - 2*e^(-d*x - c)/(d*(e^(-2*d*x - 2*c) + 1))) - 8/15*b^3*(5*e^(-3*d*x - 3*c)/(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*e^(-5*d*x - 5*c)/(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)) + 5*e^(-7*d*x - 7*c)/(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))) - 8*a*b^2/(d*(e^(d*x + c) + e^(-d*x - c))^3)","B",0
24,1,493,0,0.343884," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{4}{15} \, b^{3} {\left(\frac{5 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{5 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{15 \, e^{\left(-6 \, d x - 6 \, c\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)}} + \frac{1}{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)} + 4 \, a b^{2} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} + \frac{1}{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)} + \frac{4}{3} \, a^{3} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{1}{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)} + \frac{12 \, a^{2} b}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"4/15*b^3*(5*e^(-2*d*x - 2*c)/(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)) - 5*e^(-4*d*x - 4*c)/(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)) + 15*e^(-6*d*x - 6*c)/(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)) + 1/(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))) + 4*a*b^2*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1))) + 4/3*a^3*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)) - 1/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) + 12*a^2*b/(d*(e^(-4*d*x - 4*c) - 1))","B",0
25,1,514,0,0.510027," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a b - b^{2}\right)} {\left(d x + c\right)}}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(8 \, b e^{\left(-2 \, d x - 2 \, c\right)} + a + b\right)} e^{\left(4 \, d x + 4 \, c\right)}}{64 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} - \frac{{\left(a^{2} b - 6 \, a b^{2} + 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^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b} d} - \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} - \frac{3 \, b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} {\left(a + b\right)} d} - \frac{8 \, b e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{3 \, {\left(d x + c\right)}}{8 \, {\left(a + b\right)} d} - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a + b\right)} d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a + b\right)} d}"," ",0,"-1/2*(a*b - b^2)*(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/64*(8*b*e^(-2*d*x - 2*c) + a + b)*e^(4*d*x + 4*c)/((a^2 + 2*a*b + b^2)*d) - 1/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*d) + 1/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d) + 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) - 1/8*(a^2*b - 6*a*b^2 + b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)*d) - 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) - 3/8*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) - 1/64*(8*b*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c))/((a^2 + 2*a*b + b^2)*d) + 3/8*(d*x + c)/((a + b)*d) - 1/8*e^(2*d*x + 2*c)/((a + b)*d) + 1/8*e^(-2*d*x - 2*c)/((a + b)*d)","B",0
26,0,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left({\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - 3 \, {\left(3 \, a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - 3 \, {\left(3 \, a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a + b\right)} e^{\left(-3 \, d x\right)}}{24 \, {\left(a^{2} d e^{\left(3 \, c\right)} + 2 \, a b d e^{\left(3 \, c\right)} + b^{2} d e^{\left(3 \, c\right)}\right)}} - \frac{1}{8} \, \int \frac{16 \, {\left(a b e^{\left(3 \, d x + 3 \, c\right)} - a b e^{\left(d x + c\right)}\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/24*((a*e^(6*c) + b*e^(6*c))*e^(6*d*x) - 3*(3*a*e^(4*c) - b*e^(4*c))*e^(4*d*x) - 3*(3*a*e^(2*c) - b*e^(2*c))*e^(2*d*x) + a + b)*e^(-3*d*x)/(a^2*d*e^(3*c) + 2*a*b*d*e^(3*c) + b^2*d*e^(3*c)) - 1/8*integrate(16*(a*b*e^(3*d*x + 3*c) - a*b*e^(d*x + c))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3 + (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))*e^(2*d*x)), x)","F",0
27,1,316,0,0.461082," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} + \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} + \frac{b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} {\left(a + b\right)} d} - \frac{d x + c}{2 \, {\left(a + b\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a + b\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a + b\right)} d}"," ",0,"1/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) + 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) + 1/2*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) - 1/2*(d*x + c)/((a + b)*d) + 1/8*e^(2*d*x + 2*c)/((a + b)*d) - 1/8*e^(-2*d*x - 2*c)/((a + b)*d)","B",0
28,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)} e^{\left(-d x\right)}}{2 \, {\left(a d e^{c} + b d e^{c}\right)}} + \frac{1}{2} \, \int \frac{4 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}\right)}}{a^{2} + 2 \, a b + b^{2} + {\left(a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/2*(e^(2*d*x + 2*c) + 1)*e^(-d*x)/(a*d*e^c + b*d*e^c) + 1/2*integrate(4*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^2 + 2*a*b + b^2 + (a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))*e^(4*d*x) + 2*(a^2*e^(2*c) - b^2*e^(2*c))*e^(2*d*x)), x)","F",0
29,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{a d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a d} - 2 \, \int \frac{b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}}{a^{2} + a b + {\left(a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-log((e^(d*x + c) + 1)*e^(-c))/(a*d) + log((e^(d*x + c) - 1)*e^(-c))/(a*d) - 2*integrate((b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^2 + a*b + (a^2*e^(4*c) + a*b*e^(4*c))*e^(4*d*x) + 2*(a^2*e^(2*c) - a*b*e^(2*c))*e^(2*d*x)), x)","F",0
30,1,62,0,0.433090," ","integrate(csch(d*x+c)^2/(a+b*tanh(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} a d} + \frac{2}{{\left(a e^{\left(-2 \, d x - 2 \, c\right)} - a\right)} d}"," ",0,"b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*d) + 2/((a*e^(-2*d*x - 2*c) - a)*d)","A",0
31,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}}{a d e^{\left(4 \, d x + 4 \, c\right)} - 2 \, a d e^{\left(2 \, d x + 2 \, c\right)} + a d} + \frac{{\left(a + 2 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, a^{2} d} - \frac{{\left(a + 2 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, a^{2} d} + 8 \, \int \frac{{\left(a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(a b e^{c} + b^{2} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{3} + a^{2} b + {\left(a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-(e^(3*d*x + 3*c) + e^(d*x + c))/(a*d*e^(4*d*x + 4*c) - 2*a*d*e^(2*d*x + 2*c) + a*d) + 1/2*(a + 2*b)*log((e^(d*x + c) + 1)*e^(-c))/(a^2*d) - 1/2*(a + 2*b)*log((e^(d*x + c) - 1)*e^(-c))/(a^2*d) + 8*integrate(1/4*((a*b*e^(3*c) + b^2*e^(3*c))*e^(3*d*x) - (a*b*e^c + b^2*e^c)*e^(d*x))/(a^3 + a^2*b + (a^3*e^(4*c) + a^2*b*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) - a^2*b*e^(2*c))*e^(2*d*x)), x)","F",0
32,1,134,0,0.462620," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(6 \, {\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, b e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, a - 3 \, b\right)}}{3 \, {\left(3 \, a^{2} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, a^{2} e^{\left(-4 \, d x - 4 \, c\right)} + a^{2} e^{\left(-6 \, d x - 6 \, c\right)} - a^{2}\right)} d} - \frac{{\left(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)}{\sqrt{a b} a^{2} d}"," ",0,"2/3*(6*(a + b)*e^(-2*d*x - 2*c) - 3*b*e^(-4*d*x - 4*c) - 2*a - 3*b)/((3*a^2*e^(-2*d*x - 2*c) - 3*a^2*e^(-4*d*x - 4*c) + a^2*e^(-6*d*x - 6*c) - a^2)*d) - (a*b + b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d)","B",0
33,1,1690,0,0.717655," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(a b - 2 \, b^{2}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(a b - 2 \, b^{2}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} + \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(3 \, a^{3} b - 33 \, a^{2} b^{2} + 13 \, a b^{3} + 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)}{32 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a b} d} + \frac{{\left(3 \, a^{2} b - 6 \, a b^{2} - 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} - \frac{{\left(3 \, a^{3} b - 33 \, a^{2} b^{2} + 13 \, a b^{3} + 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)}{32 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} \sqrt{a b} d} - \frac{{\left(3 \, a^{2} b - 6 \, a b^{2} - 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} - \frac{3 \, {\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)}{16 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b} d} - \frac{a^{3} b - 5 \, a^{2} b^{2} - 5 \, a b^{3} + b^{4} + {\left(a^{3} b - 15 \, a^{2} b^{2} + 15 \, a b^{3} - b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{3} b - 5 \, a^{2} b^{2} - 5 \, a b^{3} + b^{4} + {\left(a^{3} b - 15 \, a^{2} b^{2} + 15 \, a b^{3} - b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{16 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5} + 2 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{a^{2} b - b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{2} b - b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{3 \, {\left(a b + b^{2} + {\left(a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}\right)}}{8 \, {\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{3 \, {\left(d x + c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{{\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 16 \, b e^{\left(2 \, d x + 2 \, c\right)}}{64 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{16 \, b e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"-1/4*(a*b - 2*b^2)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 1/2*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/4*(a*b - 2*b^2)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) + 1/2*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/32*(3*a^3*b - 33*a^2*b^2 + 13*a*b^3 + b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sqrt(a*b)*d) + 1/8*(3*a^2*b - 6*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)*d) - 1/32*(3*a^3*b - 33*a^2*b^2 + 13*a*b^3 + b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*sqrt(a*b)*d) - 1/8*(3*a^2*b - 6*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)*d) - 3/16*(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) - 1/16*(a^3*b - 5*a^2*b^2 - 5*a*b^3 + b^4 + (a^3*b - 15*a^2*b^2 + 15*a*b^3 - b^4)*e^(2*d*x + 2*c))/((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*e^(4*d*x + 4*c) + 2*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*e^(2*d*x + 2*c))*d) + 1/16*(a^3*b - 5*a^2*b^2 - 5*a*b^3 + b^4 + (a^3*b - 15*a^2*b^2 + 15*a*b^3 - b^4)*e^(-2*d*x - 2*c))/((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5 + 2*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*e^(-2*d*x - 2*c) + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*e^(-4*d*x - 4*c))*d) - 1/4*(a^2*b - b^3 + (a^2*b - 6*a*b^2 + b^3)*e^(2*d*x + 2*c))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*e^(4*d*x + 4*c) + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*e^(2*d*x + 2*c))*d) + 1/4*(a^2*b - b^3 + (a^2*b - 6*a*b^2 + b^3)*e^(-2*d*x - 2*c))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*e^(-2*d*x - 2*c) + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*e^(-4*d*x - 4*c))*d) + 3/8*(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) + 3/8*(d*x + c)/((a^2 + 2*a*b + b^2)*d) + 1/64*((a + b)*e^(4*d*x + 4*c) + 16*b*e^(2*d*x + 2*c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/64*(16*b*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/8*e^(2*d*x + 2*c)/((a^2 + 2*a*b + b^2)*d) + 1/8*e^(-2*d*x - 2*c)/((a^2 + 2*a*b + b^2)*d)","B",0
34,0,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{a^{2} + 2 \, a b + b^{2} + {\left(a^{2} e^{\left(10 \, c\right)} + 2 \, a b e^{\left(10 \, c\right)} + b^{2} e^{\left(10 \, c\right)}\right)} e^{\left(10 \, d x\right)} - {\left(7 \, a^{2} e^{\left(8 \, c\right)} - 6 \, a b e^{\left(8 \, c\right)} - 13 \, b^{2} e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - 2 \, {\left(13 \, a^{2} e^{\left(6 \, c\right)} - 40 \, a b e^{\left(6 \, c\right)} + 7 \, b^{2} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - 2 \, {\left(13 \, a^{2} e^{\left(4 \, c\right)} - 40 \, a b e^{\left(4 \, c\right)} + 7 \, b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - {\left(7 \, a^{2} e^{\left(2 \, c\right)} - 6 \, a b e^{\left(2 \, c\right)} - 13 \, b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{24 \, {\left({\left(a^{4} d e^{\left(7 \, c\right)} + 4 \, a^{3} b d e^{\left(7 \, c\right)} + 6 \, a^{2} b^{2} d e^{\left(7 \, c\right)} + 4 \, a b^{3} d e^{\left(7 \, c\right)} + b^{4} d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(a^{4} d e^{\left(5 \, c\right)} + 2 \, a^{3} b d e^{\left(5 \, c\right)} - 2 \, a b^{3} d e^{\left(5 \, c\right)} - b^{4} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(a^{4} d e^{\left(3 \, c\right)} + 4 \, a^{3} b d e^{\left(3 \, c\right)} + 6 \, a^{2} b^{2} d e^{\left(3 \, c\right)} + 4 \, a b^{3} d e^{\left(3 \, c\right)} + b^{4} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)}\right)}} - \frac{1}{8} \, \int \frac{8 \, {\left({\left(3 \, a b e^{\left(3 \, c\right)} - 2 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(3 \, a b e^{c} - 2 \, b^{2} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + {\left(a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/24*(a^2 + 2*a*b + b^2 + (a^2*e^(10*c) + 2*a*b*e^(10*c) + b^2*e^(10*c))*e^(10*d*x) - (7*a^2*e^(8*c) - 6*a*b*e^(8*c) - 13*b^2*e^(8*c))*e^(8*d*x) - 2*(13*a^2*e^(6*c) - 40*a*b*e^(6*c) + 7*b^2*e^(6*c))*e^(6*d*x) - 2*(13*a^2*e^(4*c) - 40*a*b*e^(4*c) + 7*b^2*e^(4*c))*e^(4*d*x) - (7*a^2*e^(2*c) - 6*a*b*e^(2*c) - 13*b^2*e^(2*c))*e^(2*d*x))/((a^4*d*e^(7*c) + 4*a^3*b*d*e^(7*c) + 6*a^2*b^2*d*e^(7*c) + 4*a*b^3*d*e^(7*c) + b^4*d*e^(7*c))*e^(7*d*x) + 2*(a^4*d*e^(5*c) + 2*a^3*b*d*e^(5*c) - 2*a*b^3*d*e^(5*c) - b^4*d*e^(5*c))*e^(5*d*x) + (a^4*d*e^(3*c) + 4*a^3*b*d*e^(3*c) + 6*a^2*b^2*d*e^(3*c) + 4*a*b^3*d*e^(3*c) + b^4*d*e^(3*c))*e^(3*d*x)) - 1/8*integrate(8*((3*a*b*e^(3*c) - 2*b^2*e^(3*c))*e^(3*d*x) - (3*a*b*e^c - 2*b^2*e^c)*e^(d*x))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + (a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))*e^(4*d*x) + 2*(a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c))*e^(2*d*x)), x)","F",0
35,1,840,0,0.586024," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{{\left(3 \, a^{2} b - 6 \, a b^{2} - 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} + \frac{{\left(3 \, a^{2} b - 6 \, a b^{2} - 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} + \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)}{4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b} d} + \frac{a^{2} b - b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{2} b - b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{a b + b^{2} + {\left(a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{2 \, {\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}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"1/2*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/2*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/8*(3*a^2*b - 6*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)*d) + 1/8*(3*a^2*b - 6*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)*d) + 1/4*(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) + 1/4*(a^2*b - b^3 + (a^2*b - 6*a*b^2 + b^3)*e^(2*d*x + 2*c))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*e^(4*d*x + 4*c) + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*e^(2*d*x + 2*c))*d) - 1/4*(a^2*b - b^3 + (a^2*b - 6*a*b^2 + b^3)*e^(-2*d*x - 2*c))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*e^(-2*d*x - 2*c) + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*e^(-4*d*x - 4*c))*d) - 1/2*(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) - 1/2*(d*x + c)/((a^2 + 2*a*b + b^2)*d) + 1/8*e^(2*d*x + 2*c)/((a^2 + 2*a*b + b^2)*d) - 1/8*e^(-2*d*x - 2*c)/((a^2 + 2*a*b + b^2)*d)","B",0
36,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a + b}{2 \, {\left({\left(a^{3} d e^{\left(5 \, c\right)} + 3 \, a^{2} b d e^{\left(5 \, c\right)} + 3 \, a b^{2} d e^{\left(5 \, c\right)} + b^{3} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(3 \, c\right)} + a^{2} b d e^{\left(3 \, c\right)} - a b^{2} d e^{\left(3 \, c\right)} - b^{3} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{3} d e^{c} + 3 \, a^{2} b d e^{c} + 3 \, a b^{2} d e^{c} + b^{3} d e^{c}\right)} e^{\left(d x\right)}\right)}} + \frac{1}{2} \, \int \frac{6 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/2*((a*e^(6*c) + b*e^(6*c))*e^(6*d*x) + 3*(a*e^(4*c) - b*e^(4*c))*e^(4*d*x) + 3*(a*e^(2*c) - b*e^(2*c))*e^(2*d*x) + a + b)/((a^3*d*e^(5*c) + 3*a^2*b*d*e^(5*c) + 3*a*b^2*d*e^(5*c) + b^3*d*e^(5*c))*e^(5*d*x) + 2*(a^3*d*e^(3*c) + a^2*b*d*e^(3*c) - a*b^2*d*e^(3*c) - b^3*d*e^(3*c))*e^(3*d*x) + (a^3*d*e^c + 3*a^2*b*d*e^c + 3*a*b^2*d*e^c + b^3*d*e^c)*e^(d*x)) + 1/2*integrate(6*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3 + (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))*e^(2*d*x)), x)","F",0
37,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{b e^{\left(3 \, d x + 3 \, c\right)} + b e^{\left(d x + c\right)}}{a^{3} d + 2 \, a^{2} b d + a b^{2} d + {\left(a^{3} d e^{\left(4 \, c\right)} + 2 \, a^{2} b d e^{\left(4 \, c\right)} + a b^{2} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(2 \, c\right)} - a b^{2} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} - \frac{\log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{a^{2} d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a^{2} d} - 2 \, \int \frac{{\left(3 \, a b e^{\left(3 \, c\right)} + 2 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(3 \, a b e^{c} + 2 \, b^{2} e^{c}\right)} e^{\left(d x\right)}}{2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"(b*e^(3*d*x + 3*c) + b*e^(d*x + c))/(a^3*d + 2*a^2*b*d + a*b^2*d + (a^3*d*e^(4*c) + 2*a^2*b*d*e^(4*c) + a*b^2*d*e^(4*c))*e^(4*d*x) + 2*(a^3*d*e^(2*c) - a*b^2*d*e^(2*c))*e^(2*d*x)) - log((e^(d*x + c) + 1)*e^(-c))/(a^2*d) + log((e^(d*x + c) - 1)*e^(-c))/(a^2*d) - 2*integrate(1/2*((3*a*b*e^(3*c) + 2*b^2*e^(3*c))*e^(3*d*x) - (3*a*b*e^c + 2*b^2*e^c)*e^(d*x))/(a^4 + 2*a^3*b + a^2*b^2 + (a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))*e^(4*d*x) + 2*(a^4*e^(2*c) - a^2*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
38,1,212,0,0.504723," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} + 5 \, a b + 3 \, b^{2} + 2 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{3 \, b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2} d}"," ",0,"-(2*a^2 + 5*a*b + 3*b^2 + 2*(2*a^2 - 3*b^2)*e^(-2*d*x - 2*c) + (2*a^2 + 3*a*b + 3*b^2)*e^(-4*d*x - 4*c))/((a^4 + 2*a^3*b + a^2*b^2 + (a^4 - 2*a^3*b - 3*a^2*b^2)*e^(-2*d*x - 2*c) - (a^4 - 2*a^3*b - 3*a^2*b^2)*e^(-4*d*x - 4*c) - (a^4 + 2*a^3*b + a^2*b^2)*e^(-6*d*x - 6*c))*d) + 3/2*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d)","B",0
39,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a e^{\left(7 \, c\right)} + 2 \, b e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(3 \, a e^{\left(5 \, c\right)} - 2 \, b e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(3 \, a e^{\left(3 \, c\right)} - 2 \, b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a e^{c} + 2 \, b e^{c}\right)} e^{\left(d x\right)}}{4 \, a^{2} b d e^{\left(6 \, d x + 6 \, c\right)} + 4 \, a^{2} b d e^{\left(2 \, d x + 2 \, c\right)} - a^{3} d - a^{2} b d - {\left(a^{3} d e^{\left(8 \, c\right)} + a^{2} b d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(4 \, c\right)} - 3 \, a^{2} b d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)}} + \frac{{\left(a + 4 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, a^{3} d} - \frac{{\left(a + 4 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, a^{3} d} + 8 \, \int \frac{{\left(3 \, a b e^{\left(3 \, c\right)} + 4 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(3 \, a b e^{c} + 4 \, b^{2} e^{c}\right)} e^{\left(d x\right)}}{8 \, {\left(a^{4} + a^{3} b + {\left(a^{4} e^{\left(4 \, c\right)} + a^{3} b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} - a^{3} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"((a*e^(7*c) + 2*b*e^(7*c))*e^(7*d*x) + (3*a*e^(5*c) - 2*b*e^(5*c))*e^(5*d*x) + (3*a*e^(3*c) - 2*b*e^(3*c))*e^(3*d*x) + (a*e^c + 2*b*e^c)*e^(d*x))/(4*a^2*b*d*e^(6*d*x + 6*c) + 4*a^2*b*d*e^(2*d*x + 2*c) - a^3*d - a^2*b*d - (a^3*d*e^(8*c) + a^2*b*d*e^(8*c))*e^(8*d*x) + 2*(a^3*d*e^(4*c) - 3*a^2*b*d*e^(4*c))*e^(4*d*x)) + 1/2*(a + 4*b)*log((e^(d*x + c) + 1)*e^(-c))/(a^3*d) - 1/2*(a + 4*b)*log((e^(d*x + c) - 1)*e^(-c))/(a^3*d) + 8*integrate(1/8*((3*a*b*e^(3*c) + 4*b^2*e^(3*c))*e^(3*d*x) - (3*a*b*e^c + 4*b^2*e^c)*e^(d*x))/(a^4 + a^3*b + (a^4*e^(4*c) + a^3*b*e^(4*c))*e^(4*d*x) + 2*(a^4*e^(2*c) - a^3*b*e^(2*c))*e^(2*d*x)), x)","F",0
40,1,282,0,0.550072," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{4 \, a^{2} + 19 \, a b + 15 \, b^{2} - 2 \, {\left(2 \, a^{2} + 13 \, a b + 30 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(3 \, a b + 5 \, b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{3 \, {\left(a^{4} + a^{3} b - {\left(a^{4} + 5 \, a^{3} b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{4} + 5 \, a^{3} b\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{4} + a^{3} b\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} - \frac{{\left(3 \, a b + 5 \, 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 \, \sqrt{a b} a^{3} d}"," ",0,"1/3*(4*a^2 + 19*a*b + 15*b^2 - 2*(2*a^2 + 13*a*b + 30*b^2)*e^(-2*d*x - 2*c) - 2*(10*a^2 - 2*a*b - 45*b^2)*e^(-4*d*x - 4*c) - 6*(2*a^2 + a*b + 10*b^2)*e^(-6*d*x - 6*c) + 3*(3*a*b + 5*b^2)*e^(-8*d*x - 8*c))/((a^4 + a^3*b - (a^4 + 5*a^3*b)*e^(-2*d*x - 2*c) - 2*(a^4 - 5*a^3*b)*e^(-4*d*x - 4*c) + 2*(a^4 - 5*a^3*b)*e^(-6*d*x - 6*c) + (a^4 + 5*a^3*b)*e^(-8*d*x - 8*c) - (a^4 + a^3*b)*e^(-10*d*x - 10*c))*d) - 1/2*(3*a*b + 5*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3*d)","B",0
41,1,3392,0,1.119503," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(a b - 3 \, b^{2}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d} - \frac{3 \, b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} + \frac{3 \, {\left(a b - 3 \, b^{2}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d} + \frac{3 \, b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} + \frac{3 \, {\left(5 \, a^{4} b - 80 \, a^{3} b^{2} + 50 \, a^{2} b^{3} + 8 \, a b^{4} + b^{5}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{128 \, {\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)} \sqrt{a b} d} + \frac{3 \, {\left(5 \, a^{3} b - 15 \, a^{2} b^{2} - 5 \, a b^{3} - 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)}{32 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} - \frac{3 \, {\left(5 \, a^{4} b - 80 \, a^{3} b^{2} + 50 \, a^{2} b^{3} + 8 \, a b^{4} + b^{5}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{128 \, {\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)} \sqrt{a b} d} - \frac{3 \, {\left(5 \, a^{3} b - 15 \, a^{2} b^{2} - 5 \, a b^{3} - 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)}{32 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} - \frac{3 \, {\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)}{64 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b} d} - \frac{9 \, a^{5} b - 65 \, a^{4} b^{2} - 134 \, a^{3} b^{3} - 34 \, a^{2} b^{4} + 29 \, a b^{5} + 3 \, b^{6} + {\left(9 \, a^{5} b - 183 \, a^{4} b^{2} + 98 \, a^{3} b^{3} + 266 \, a^{2} b^{4} - 27 \, a b^{5} - 3 \, b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{5} b - 459 \, a^{4} b^{2} + 710 \, a^{3} b^{3} - 542 \, a^{2} b^{4} + 63 \, a b^{5} + 9 \, b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{5} b - 341 \, a^{4} b^{2} + 86 \, a^{3} b^{3} + 398 \, a^{2} b^{4} - 65 \, a b^{5} - 9 \, b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{64 \, {\left(a^{9} + 7 \, a^{8} b + 21 \, a^{7} b^{2} + 35 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 21 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + a^{2} b^{7} + {\left(a^{9} + 7 \, a^{8} b + 21 \, a^{7} b^{2} + 35 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 21 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + a^{2} b^{7}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 5 \, a^{6} b^{3} - 5 \, a^{5} b^{4} - 9 \, a^{4} b^{5} - 5 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{9} + 13 \, a^{8} b + 23 \, a^{7} b^{2} + 25 \, a^{6} b^{3} + 25 \, a^{5} b^{4} + 23 \, a^{4} b^{5} + 13 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 5 \, a^{6} b^{3} - 5 \, a^{5} b^{4} - 9 \, a^{4} b^{5} - 5 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{9 \, a^{5} b - 65 \, a^{4} b^{2} - 134 \, a^{3} b^{3} - 34 \, a^{2} b^{4} + 29 \, a b^{5} + 3 \, b^{6} + {\left(27 \, a^{5} b - 341 \, a^{4} b^{2} + 86 \, a^{3} b^{3} + 398 \, a^{2} b^{4} - 65 \, a b^{5} - 9 \, b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{5} b - 459 \, a^{4} b^{2} + 710 \, a^{3} b^{3} - 542 \, a^{2} b^{4} + 63 \, a b^{5} + 9 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(9 \, a^{5} b - 183 \, a^{4} b^{2} + 98 \, a^{3} b^{3} + 266 \, a^{2} b^{4} - 27 \, a b^{5} - 3 \, b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{64 \, {\left(a^{9} + 7 \, a^{8} b + 21 \, a^{7} b^{2} + 35 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 21 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + a^{2} b^{7} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 5 \, a^{6} b^{3} - 5 \, a^{5} b^{4} - 9 \, a^{4} b^{5} - 5 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{9} + 13 \, a^{8} b + 23 \, a^{7} b^{2} + 25 \, a^{6} b^{3} + 25 \, a^{5} b^{4} + 23 \, a^{4} b^{5} + 13 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{9} + 5 \, a^{8} b + 9 \, a^{7} b^{2} + 5 \, a^{6} b^{3} - 5 \, a^{5} b^{4} - 9 \, a^{4} b^{5} - 5 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{9} + 7 \, a^{8} b + 21 \, a^{7} b^{2} + 35 \, a^{6} b^{3} + 35 \, a^{5} b^{4} + 21 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + a^{2} b^{7}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{9 \, a^{4} b + 4 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 20 \, a b^{4} - 3 \, b^{5} + 3 \, {\left(3 \, a^{4} b - 22 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{4} b - 156 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 36 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{4} b - 86 \, a^{3} b^{2} - 84 \, a^{2} b^{3} + 38 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{9 \, a^{4} b + 4 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 20 \, a b^{4} - 3 \, b^{5} + {\left(27 \, a^{4} b - 86 \, a^{3} b^{2} - 84 \, a^{2} b^{3} + 38 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{4} b - 156 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 36 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(3 \, a^{4} b - 22 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{3 \, {\left(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)}\right)}}{32 \, {\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{3 \, {\left(d x + c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 24 \, b e^{\left(2 \, d x + 2 \, c\right)}}{64 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{24 \, b e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"-3/8*(a*b - 3*b^2)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d) - 3/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) + 3/8*(a*b - 3*b^2)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d) + 3/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) + 3/128*(5*a^4*b - 80*a^3*b^2 + 50*a^2*b^3 + 8*a*b^4 + b^5)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((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)*sqrt(a*b)*d) + 3/32*(5*a^3*b - 15*a^2*b^2 - 5*a*b^3 - b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) - 3/128*(5*a^4*b - 80*a^3*b^2 + 50*a^2*b^3 + 8*a*b^4 + b^5)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((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)*sqrt(a*b)*d) - 3/32*(5*a^3*b - 15*a^2*b^2 - 5*a*b^3 - b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) - 3/64*(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) - 1/64*(9*a^5*b - 65*a^4*b^2 - 134*a^3*b^3 - 34*a^2*b^4 + 29*a*b^5 + 3*b^6 + (9*a^5*b - 183*a^4*b^2 + 98*a^3*b^3 + 266*a^2*b^4 - 27*a*b^5 - 3*b^6)*e^(6*d*x + 6*c) + (27*a^5*b - 459*a^4*b^2 + 710*a^3*b^3 - 542*a^2*b^4 + 63*a*b^5 + 9*b^6)*e^(4*d*x + 4*c) + (27*a^5*b - 341*a^4*b^2 + 86*a^3*b^3 + 398*a^2*b^4 - 65*a*b^5 - 9*b^6)*e^(2*d*x + 2*c))/((a^9 + 7*a^8*b + 21*a^7*b^2 + 35*a^6*b^3 + 35*a^5*b^4 + 21*a^4*b^5 + 7*a^3*b^6 + a^2*b^7 + (a^9 + 7*a^8*b + 21*a^7*b^2 + 35*a^6*b^3 + 35*a^5*b^4 + 21*a^4*b^5 + 7*a^3*b^6 + a^2*b^7)*e^(8*d*x + 8*c) + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 5*a^6*b^3 - 5*a^5*b^4 - 9*a^4*b^5 - 5*a^3*b^6 - a^2*b^7)*e^(6*d*x + 6*c) + 2*(3*a^9 + 13*a^8*b + 23*a^7*b^2 + 25*a^6*b^3 + 25*a^5*b^4 + 23*a^4*b^5 + 13*a^3*b^6 + 3*a^2*b^7)*e^(4*d*x + 4*c) + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 5*a^6*b^3 - 5*a^5*b^4 - 9*a^4*b^5 - 5*a^3*b^6 - a^2*b^7)*e^(2*d*x + 2*c))*d) + 1/64*(9*a^5*b - 65*a^4*b^2 - 134*a^3*b^3 - 34*a^2*b^4 + 29*a*b^5 + 3*b^6 + (27*a^5*b - 341*a^4*b^2 + 86*a^3*b^3 + 398*a^2*b^4 - 65*a*b^5 - 9*b^6)*e^(-2*d*x - 2*c) + (27*a^5*b - 459*a^4*b^2 + 710*a^3*b^3 - 542*a^2*b^4 + 63*a*b^5 + 9*b^6)*e^(-4*d*x - 4*c) + (9*a^5*b - 183*a^4*b^2 + 98*a^3*b^3 + 266*a^2*b^4 - 27*a*b^5 - 3*b^6)*e^(-6*d*x - 6*c))/((a^9 + 7*a^8*b + 21*a^7*b^2 + 35*a^6*b^3 + 35*a^5*b^4 + 21*a^4*b^5 + 7*a^3*b^6 + a^2*b^7 + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 5*a^6*b^3 - 5*a^5*b^4 - 9*a^4*b^5 - 5*a^3*b^6 - a^2*b^7)*e^(-2*d*x - 2*c) + 2*(3*a^9 + 13*a^8*b + 23*a^7*b^2 + 25*a^6*b^3 + 25*a^5*b^4 + 23*a^4*b^5 + 13*a^3*b^6 + 3*a^2*b^7)*e^(-4*d*x - 4*c) + 4*(a^9 + 5*a^8*b + 9*a^7*b^2 + 5*a^6*b^3 - 5*a^5*b^4 - 9*a^4*b^5 - 5*a^3*b^6 - a^2*b^7)*e^(-6*d*x - 6*c) + (a^9 + 7*a^8*b + 21*a^7*b^2 + 35*a^6*b^3 + 35*a^5*b^4 + 21*a^4*b^5 + 7*a^3*b^6 + a^2*b^7)*e^(-8*d*x - 8*c))*d) - 1/16*(9*a^4*b + 4*a^3*b^2 - 22*a^2*b^3 - 20*a*b^4 - 3*b^5 + 3*(3*a^4*b - 22*a^3*b^2 - 20*a^2*b^3 + 6*a*b^4 + b^5)*e^(6*d*x + 6*c) + (27*a^4*b - 156*a^3*b^2 + 110*a^2*b^3 - 36*a*b^4 - 9*b^5)*e^(4*d*x + 4*c) + (27*a^4*b - 86*a^3*b^2 - 84*a^2*b^3 + 38*a*b^4 + 9*b^5)*e^(2*d*x + 2*c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*e^(8*d*x + 8*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(6*d*x + 6*c) + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*e^(4*d*x + 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(2*d*x + 2*c))*d) + 1/16*(9*a^4*b + 4*a^3*b^2 - 22*a^2*b^3 - 20*a*b^4 - 3*b^5 + (27*a^4*b - 86*a^3*b^2 - 84*a^2*b^3 + 38*a*b^4 + 9*b^5)*e^(-2*d*x - 2*c) + (27*a^4*b - 156*a^3*b^2 + 110*a^2*b^3 - 36*a*b^4 - 9*b^5)*e^(-4*d*x - 4*c) + 3*(3*a^4*b - 22*a^3*b^2 - 20*a^2*b^3 + 6*a*b^4 + b^5)*e^(-6*d*x - 6*c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(-2*d*x - 2*c) + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*e^(-4*d*x - 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(-6*d*x - 6*c) + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*e^(-8*d*x - 8*c))*d) + 3/32*(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) + 3/8*(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/64*((a + b)*e^(4*d*x + 4*c) + 24*b*e^(2*d*x + 2*c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 1/64*(24*b*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 1/8*e^(2*d*x + 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/8*e^(-2*d*x - 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
42,-2,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
43,1,1806,0,0.817005," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{3 \, b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{3 \, b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{3 \, {\left(5 \, a^{3} b - 15 \, a^{2} b^{2} - 5 \, a b^{3} - 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)}{32 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} + \frac{3 \, {\left(5 \, a^{3} b - 15 \, a^{2} b^{2} - 5 \, a b^{3} - 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)}{32 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} + \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)}{16 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b} d} + \frac{9 \, a^{4} b + 4 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 20 \, a b^{4} - 3 \, b^{5} + 3 \, {\left(3 \, a^{4} b - 22 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{4} b - 156 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 36 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{4} b - 86 \, a^{3} b^{2} - 84 \, a^{2} b^{3} + 38 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{9 \, a^{4} b + 4 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 20 \, a b^{4} - 3 \, b^{5} + {\left(27 \, a^{4} b - 86 \, a^{3} b^{2} - 84 \, a^{2} b^{3} + 38 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{4} b - 156 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 36 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(3 \, a^{4} b - 22 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} 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)}}{8 \, {\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}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"3/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 3/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 3/32*(5*a^3*b - 15*a^2*b^2 - 5*a*b^3 - b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) + 3/32*(5*a^3*b - 15*a^2*b^2 - 5*a*b^3 - b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) + 1/16*(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) + 1/16*(9*a^4*b + 4*a^3*b^2 - 22*a^2*b^3 - 20*a*b^4 - 3*b^5 + 3*(3*a^4*b - 22*a^3*b^2 - 20*a^2*b^3 + 6*a*b^4 + b^5)*e^(6*d*x + 6*c) + (27*a^4*b - 156*a^3*b^2 + 110*a^2*b^3 - 36*a*b^4 - 9*b^5)*e^(4*d*x + 4*c) + (27*a^4*b - 86*a^3*b^2 - 84*a^2*b^3 + 38*a*b^4 + 9*b^5)*e^(2*d*x + 2*c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*e^(8*d*x + 8*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(6*d*x + 6*c) + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*e^(4*d*x + 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(2*d*x + 2*c))*d) - 1/16*(9*a^4*b + 4*a^3*b^2 - 22*a^2*b^3 - 20*a*b^4 - 3*b^5 + (27*a^4*b - 86*a^3*b^2 - 84*a^2*b^3 + 38*a*b^4 + 9*b^5)*e^(-2*d*x - 2*c) + (27*a^4*b - 156*a^3*b^2 + 110*a^2*b^3 - 36*a*b^4 - 9*b^5)*e^(-4*d*x - 4*c) + 3*(3*a^4*b - 22*a^3*b^2 - 20*a^2*b^3 + 6*a*b^4 + b^5)*e^(-6*d*x - 6*c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(-2*d*x - 2*c) + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*e^(-4*d*x - 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(-6*d*x - 6*c) + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*e^(-8*d*x - 8*c))*d) - 1/8*(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) - 1/2*(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/8*e^(2*d*x + 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/8*e^(-2*d*x - 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
44,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{2 \, a^{2} + 4 \, a b + 2 \, b^{2} + 2 \, {\left(a^{2} e^{\left(10 \, c\right)} + 2 \, a b e^{\left(10 \, c\right)} + b^{2} e^{\left(10 \, c\right)}\right)} e^{\left(10 \, d x\right)} + 5 \, {\left(2 \, a^{2} e^{\left(8 \, c\right)} - a b e^{\left(8 \, c\right)} - 3 \, b^{2} e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 5 \, {\left(4 \, a^{2} e^{\left(6 \, c\right)} - 7 \, a b e^{\left(6 \, c\right)} + b^{2} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 5 \, {\left(4 \, a^{2} e^{\left(4 \, c\right)} - 7 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 5 \, {\left(2 \, a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)} - 3 \, b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{4 \, {\left({\left(a^{5} d e^{\left(9 \, c\right)} + 5 \, a^{4} b d e^{\left(9 \, c\right)} + 10 \, a^{3} b^{2} d e^{\left(9 \, c\right)} + 10 \, a^{2} b^{3} d e^{\left(9 \, c\right)} + 5 \, a b^{4} d e^{\left(9 \, c\right)} + b^{5} d e^{\left(9 \, c\right)}\right)} e^{\left(9 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(7 \, c\right)} + 3 \, a^{4} b d e^{\left(7 \, c\right)} + 2 \, a^{3} b^{2} d e^{\left(7 \, c\right)} - 2 \, a^{2} b^{3} d e^{\left(7 \, c\right)} - 3 \, a b^{4} d e^{\left(7 \, c\right)} - b^{5} d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(3 \, a^{5} d e^{\left(5 \, c\right)} + 7 \, a^{4} b d e^{\left(5 \, c\right)} + 6 \, a^{3} b^{2} d e^{\left(5 \, c\right)} + 6 \, a^{2} b^{3} d e^{\left(5 \, c\right)} + 7 \, a b^{4} d e^{\left(5 \, c\right)} + 3 \, b^{5} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(3 \, c\right)} + 3 \, a^{4} b d e^{\left(3 \, c\right)} + 2 \, a^{3} b^{2} d e^{\left(3 \, c\right)} - 2 \, a^{2} b^{3} d e^{\left(3 \, c\right)} - 3 \, a b^{4} d e^{\left(3 \, c\right)} - b^{5} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{5} d e^{c} + 5 \, a^{4} b d e^{c} + 10 \, a^{3} b^{2} d e^{c} + 10 \, a^{2} b^{3} d e^{c} + 5 \, a b^{4} d e^{c} + b^{5} d e^{c}\right)} e^{\left(d x\right)}\right)}} + \frac{1}{2} \, \int \frac{15 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}\right)}}{2 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + {\left(a^{4} e^{\left(4 \, c\right)} + 4 \, a^{3} b e^{\left(4 \, c\right)} + 6 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 4 \, a b^{3} e^{\left(4 \, c\right)} + b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)} - 2 \, a b^{3} e^{\left(2 \, c\right)} - b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*(2*a^2 + 4*a*b + 2*b^2 + 2*(a^2*e^(10*c) + 2*a*b*e^(10*c) + b^2*e^(10*c))*e^(10*d*x) + 5*(2*a^2*e^(8*c) - a*b*e^(8*c) - 3*b^2*e^(8*c))*e^(8*d*x) + 5*(4*a^2*e^(6*c) - 7*a*b*e^(6*c) + b^2*e^(6*c))*e^(6*d*x) + 5*(4*a^2*e^(4*c) - 7*a*b*e^(4*c) + b^2*e^(4*c))*e^(4*d*x) + 5*(2*a^2*e^(2*c) - a*b*e^(2*c) - 3*b^2*e^(2*c))*e^(2*d*x))/((a^5*d*e^(9*c) + 5*a^4*b*d*e^(9*c) + 10*a^3*b^2*d*e^(9*c) + 10*a^2*b^3*d*e^(9*c) + 5*a*b^4*d*e^(9*c) + b^5*d*e^(9*c))*e^(9*d*x) + 4*(a^5*d*e^(7*c) + 3*a^4*b*d*e^(7*c) + 2*a^3*b^2*d*e^(7*c) - 2*a^2*b^3*d*e^(7*c) - 3*a*b^4*d*e^(7*c) - b^5*d*e^(7*c))*e^(7*d*x) + 2*(3*a^5*d*e^(5*c) + 7*a^4*b*d*e^(5*c) + 6*a^3*b^2*d*e^(5*c) + 6*a^2*b^3*d*e^(5*c) + 7*a*b^4*d*e^(5*c) + 3*b^5*d*e^(5*c))*e^(5*d*x) + 4*(a^5*d*e^(3*c) + 3*a^4*b*d*e^(3*c) + 2*a^3*b^2*d*e^(3*c) - 2*a^2*b^3*d*e^(3*c) - 3*a*b^4*d*e^(3*c) - b^5*d*e^(3*c))*e^(3*d*x) + (a^5*d*e^c + 5*a^4*b*d*e^c + 10*a^3*b^2*d*e^c + 10*a^2*b^3*d*e^c + 5*a*b^4*d*e^c + b^5*d*e^c)*e^(d*x)) + 1/2*integrate(15/2*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + (a^4*e^(4*c) + 4*a^3*b*e^(4*c) + 6*a^2*b^2*e^(4*c) + 4*a*b^3*e^(4*c) + b^4*e^(4*c))*e^(4*d*x) + 2*(a^4*e^(2*c) + 2*a^3*b*e^(2*c) - 2*a*b^3*e^(2*c) - b^4*e^(2*c))*e^(2*d*x)), x)","F",0
45,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(9 \, a^{2} b e^{\left(7 \, c\right)} + 13 \, a b^{2} e^{\left(7 \, c\right)} + 4 \, b^{3} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(27 \, a^{2} b e^{\left(5 \, c\right)} + 11 \, a b^{2} e^{\left(5 \, c\right)} - 4 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(27 \, a^{2} b e^{\left(3 \, c\right)} + 11 \, a b^{2} e^{\left(3 \, c\right)} - 4 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(9 \, a^{2} b e^{c} + 13 \, a b^{2} e^{c} + 4 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{6} d + 4 \, a^{5} b d + 6 \, a^{4} b^{2} d + 4 \, a^{3} b^{3} d + a^{2} b^{4} d + {\left(a^{6} d e^{\left(8 \, c\right)} + 4 \, a^{5} b d e^{\left(8 \, c\right)} + 6 \, a^{4} b^{2} d e^{\left(8 \, c\right)} + 4 \, a^{3} b^{3} d e^{\left(8 \, c\right)} + a^{2} b^{4} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{6} d e^{\left(6 \, c\right)} + 2 \, a^{5} b d e^{\left(6 \, c\right)} - 2 \, a^{3} b^{3} d e^{\left(6 \, c\right)} - a^{2} b^{4} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{6} d e^{\left(4 \, c\right)} + 4 \, a^{5} b d e^{\left(4 \, c\right)} + 2 \, a^{4} b^{2} d e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} d e^{\left(4 \, c\right)} + 3 \, a^{2} b^{4} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{6} d e^{\left(2 \, c\right)} + 2 \, a^{5} b d e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} d e^{\left(2 \, c\right)} - a^{2} b^{4} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} - \frac{\log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{a^{3} d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a^{3} d} - 2 \, \int \frac{{\left(15 \, a^{2} b e^{\left(3 \, c\right)} + 20 \, a b^{2} e^{\left(3 \, c\right)} + 8 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(15 \, a^{2} b e^{c} + 20 \, a b^{2} e^{c} + 8 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{8 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3} + {\left(a^{6} e^{\left(4 \, c\right)} + 3 \, a^{5} b e^{\left(4 \, c\right)} + 3 \, a^{4} b^{2} e^{\left(4 \, c\right)} + a^{3} b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{6} e^{\left(2 \, c\right)} + a^{5} b e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)} - a^{3} b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*((9*a^2*b*e^(7*c) + 13*a*b^2*e^(7*c) + 4*b^3*e^(7*c))*e^(7*d*x) + (27*a^2*b*e^(5*c) + 11*a*b^2*e^(5*c) - 4*b^3*e^(5*c))*e^(5*d*x) + (27*a^2*b*e^(3*c) + 11*a*b^2*e^(3*c) - 4*b^3*e^(3*c))*e^(3*d*x) + (9*a^2*b*e^c + 13*a*b^2*e^c + 4*b^3*e^c)*e^(d*x))/(a^6*d + 4*a^5*b*d + 6*a^4*b^2*d + 4*a^3*b^3*d + a^2*b^4*d + (a^6*d*e^(8*c) + 4*a^5*b*d*e^(8*c) + 6*a^4*b^2*d*e^(8*c) + 4*a^3*b^3*d*e^(8*c) + a^2*b^4*d*e^(8*c))*e^(8*d*x) + 4*(a^6*d*e^(6*c) + 2*a^5*b*d*e^(6*c) - 2*a^3*b^3*d*e^(6*c) - a^2*b^4*d*e^(6*c))*e^(6*d*x) + 2*(3*a^6*d*e^(4*c) + 4*a^5*b*d*e^(4*c) + 2*a^4*b^2*d*e^(4*c) + 4*a^3*b^3*d*e^(4*c) + 3*a^2*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^6*d*e^(2*c) + 2*a^5*b*d*e^(2*c) - 2*a^3*b^3*d*e^(2*c) - a^2*b^4*d*e^(2*c))*e^(2*d*x)) - log((e^(d*x + c) + 1)*e^(-c))/(a^3*d) + log((e^(d*x + c) - 1)*e^(-c))/(a^3*d) - 2*integrate(1/8*((15*a^2*b*e^(3*c) + 20*a*b^2*e^(3*c) + 8*b^3*e^(3*c))*e^(3*d*x) - (15*a^2*b*e^c + 20*a*b^2*e^c + 8*b^3*e^c)*e^(d*x))/(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3 + (a^6*e^(4*c) + 3*a^5*b*e^(4*c) + 3*a^4*b^2*e^(4*c) + a^3*b^3*e^(4*c))*e^(4*d*x) + 2*(a^6*e^(2*c) + a^5*b*e^(2*c) - a^4*b^2*e^(2*c) - a^3*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
46,1,478,0,0.618791," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{8 \, a^{4} + 41 \, a^{3} b + 73 \, a^{2} b^{2} + 55 \, a b^{3} + 15 \, b^{4} + 2 \, {\left(16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{4 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{15 \, b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3} d}"," ",0,"-1/4*(8*a^4 + 41*a^3*b + 73*a^2*b^2 + 55*a*b^3 + 15*b^4 + 2*(16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4)*e^(-2*d*x - 2*c) + 2*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*e^(-4*d*x - 4*c) + 2*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*e^(-6*d*x - 6*c) + (8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*e^(-8*d*x - 8*c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*e^(-2*d*x - 2*c) + 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*e^(-4*d*x - 4*c) - 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*e^(-6*d*x - 6*c) - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*e^(-8*d*x - 8*c) - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*e^(-10*d*x - 10*c))*d) + 15/8*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3*d)","B",0
47,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, a^{3} e^{\left(11 \, c\right)} + 21 \, a^{2} b e^{\left(11 \, c\right)} + 29 \, a b^{2} e^{\left(11 \, c\right)} + 12 \, b^{3} e^{\left(11 \, c\right)}\right)} e^{\left(11 \, d x\right)} + {\left(20 \, a^{3} e^{\left(9 \, c\right)} + 37 \, a^{2} b e^{\left(9 \, c\right)} - 15 \, a b^{2} e^{\left(9 \, c\right)} - 36 \, b^{3} e^{\left(9 \, c\right)}\right)} e^{\left(9 \, d x\right)} + 2 \, {\left(20 \, a^{3} e^{\left(7 \, c\right)} + 3 \, a^{2} b e^{\left(7 \, c\right)} - 7 \, a b^{2} e^{\left(7 \, c\right)} + 12 \, b^{3} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(20 \, a^{3} e^{\left(5 \, c\right)} + 3 \, a^{2} b e^{\left(5 \, c\right)} - 7 \, a b^{2} e^{\left(5 \, c\right)} + 12 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(20 \, a^{3} e^{\left(3 \, c\right)} + 37 \, a^{2} b e^{\left(3 \, c\right)} - 15 \, a b^{2} e^{\left(3 \, c\right)} - 36 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a^{3} e^{c} + 21 \, a^{2} b e^{c} + 29 \, a b^{2} e^{c} + 12 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{6} d + 3 \, a^{5} b d + 3 \, a^{4} b^{2} d + a^{3} b^{3} d + {\left(a^{6} d e^{\left(12 \, c\right)} + 3 \, a^{5} b d e^{\left(12 \, c\right)} + 3 \, a^{4} b^{2} d e^{\left(12 \, c\right)} + a^{3} b^{3} d e^{\left(12 \, c\right)}\right)} e^{\left(12 \, d x\right)} + 2 \, {\left(a^{6} d e^{\left(10 \, c\right)} - a^{5} b d e^{\left(10 \, c\right)} - 5 \, a^{4} b^{2} d e^{\left(10 \, c\right)} - 3 \, a^{3} b^{3} d e^{\left(10 \, c\right)}\right)} e^{\left(10 \, d x\right)} - {\left(a^{6} d e^{\left(8 \, c\right)} + 3 \, a^{5} b d e^{\left(8 \, c\right)} - 13 \, a^{4} b^{2} d e^{\left(8 \, c\right)} - 15 \, a^{3} b^{3} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - 4 \, {\left(a^{6} d e^{\left(6 \, c\right)} - a^{5} b d e^{\left(6 \, c\right)} + 3 \, a^{4} b^{2} d e^{\left(6 \, c\right)} + 5 \, a^{3} b^{3} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - {\left(a^{6} d e^{\left(4 \, c\right)} + 3 \, a^{5} b d e^{\left(4 \, c\right)} - 13 \, a^{4} b^{2} d e^{\left(4 \, c\right)} - 15 \, a^{3} b^{3} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{6} d e^{\left(2 \, c\right)} - a^{5} b d e^{\left(2 \, c\right)} - 5 \, a^{4} b^{2} d e^{\left(2 \, c\right)} - 3 \, a^{3} b^{3} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} + \frac{{\left(a + 6 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, a^{4} d} - \frac{{\left(a + 6 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, a^{4} d} + 8 \, \int \frac{{\left(15 \, a^{2} b e^{\left(3 \, c\right)} + 40 \, a b^{2} e^{\left(3 \, c\right)} + 24 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(15 \, a^{2} b e^{c} + 40 \, a b^{2} e^{c} + 24 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{32 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2} + {\left(a^{6} e^{\left(4 \, c\right)} + 2 \, a^{5} b e^{\left(4 \, c\right)} + a^{4} b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{6} e^{\left(2 \, c\right)} - a^{4} b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-1/4*((4*a^3*e^(11*c) + 21*a^2*b*e^(11*c) + 29*a*b^2*e^(11*c) + 12*b^3*e^(11*c))*e^(11*d*x) + (20*a^3*e^(9*c) + 37*a^2*b*e^(9*c) - 15*a*b^2*e^(9*c) - 36*b^3*e^(9*c))*e^(9*d*x) + 2*(20*a^3*e^(7*c) + 3*a^2*b*e^(7*c) - 7*a*b^2*e^(7*c) + 12*b^3*e^(7*c))*e^(7*d*x) + 2*(20*a^3*e^(5*c) + 3*a^2*b*e^(5*c) - 7*a*b^2*e^(5*c) + 12*b^3*e^(5*c))*e^(5*d*x) + (20*a^3*e^(3*c) + 37*a^2*b*e^(3*c) - 15*a*b^2*e^(3*c) - 36*b^3*e^(3*c))*e^(3*d*x) + (4*a^3*e^c + 21*a^2*b*e^c + 29*a*b^2*e^c + 12*b^3*e^c)*e^(d*x))/(a^6*d + 3*a^5*b*d + 3*a^4*b^2*d + a^3*b^3*d + (a^6*d*e^(12*c) + 3*a^5*b*d*e^(12*c) + 3*a^4*b^2*d*e^(12*c) + a^3*b^3*d*e^(12*c))*e^(12*d*x) + 2*(a^6*d*e^(10*c) - a^5*b*d*e^(10*c) - 5*a^4*b^2*d*e^(10*c) - 3*a^3*b^3*d*e^(10*c))*e^(10*d*x) - (a^6*d*e^(8*c) + 3*a^5*b*d*e^(8*c) - 13*a^4*b^2*d*e^(8*c) - 15*a^3*b^3*d*e^(8*c))*e^(8*d*x) - 4*(a^6*d*e^(6*c) - a^5*b*d*e^(6*c) + 3*a^4*b^2*d*e^(6*c) + 5*a^3*b^3*d*e^(6*c))*e^(6*d*x) - (a^6*d*e^(4*c) + 3*a^5*b*d*e^(4*c) - 13*a^4*b^2*d*e^(4*c) - 15*a^3*b^3*d*e^(4*c))*e^(4*d*x) + 2*(a^6*d*e^(2*c) - a^5*b*d*e^(2*c) - 5*a^4*b^2*d*e^(2*c) - 3*a^3*b^3*d*e^(2*c))*e^(2*d*x)) + 1/2*(a + 6*b)*log((e^(d*x + c) + 1)*e^(-c))/(a^4*d) - 1/2*(a + 6*b)*log((e^(d*x + c) - 1)*e^(-c))/(a^4*d) + 8*integrate(1/32*((15*a^2*b*e^(3*c) + 40*a*b^2*e^(3*c) + 24*b^3*e^(3*c))*e^(3*d*x) - (15*a^2*b*e^c + 40*a*b^2*e^c + 24*b^3*e^c)*e^(d*x))/(a^6 + 2*a^5*b + a^4*b^2 + (a^6*e^(4*c) + 2*a^5*b*e^(4*c) + a^4*b^2*e^(4*c))*e^(4*d*x) + 2*(a^6*e^(2*c) - a^4*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
48,1,615,0,0.699952," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{16 \, a^{4} + 147 \, a^{3} b + 351 \, a^{2} b^{2} + 325 \, a b^{3} + 105 \, b^{4} + 2 \, {\left(8 \, a^{4} + 32 \, a^{3} b - 251 \, a^{2} b^{2} - 590 \, a b^{3} - 315 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(96 \, a^{4} + 313 \, a^{3} b + 19 \, a^{2} b^{2} - 1725 \, a b^{3} - 1575 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(56 \, a^{4} + 80 \, a^{3} b - 65 \, a^{2} b^{2} + 400 \, a b^{3} + 525 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(176 \, a^{4} + 135 \, a^{3} b + 15 \, a^{2} b^{2} - 1375 \, a b^{3} - 1575 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - 6 \, {\left(8 \, a^{4} + 45 \, a^{2} b^{2} + 150 \, a b^{3} + 105 \, b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + 15 \, {\left(3 \, a^{3} b + 13 \, a^{2} b^{2} + 17 \, a b^{3} + 7 \, b^{4}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{12 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3} + {\left(a^{7} - 5 \, a^{6} b - 13 \, a^{5} b^{2} - 7 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{7} + a^{6} b - 23 \, a^{5} b^{2} - 21 \, a^{4} b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{7} - 7 \, a^{6} b + 25 \, a^{5} b^{2} + 35 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{7} - 7 \, a^{6} b + 25 \, a^{5} b^{2} + 35 \, a^{4} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{7} + a^{6} b - 23 \, a^{5} b^{2} - 21 \, a^{4} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{7} - 5 \, a^{6} b - 13 \, a^{5} b^{2} - 7 \, a^{4} b^{3}\right)} e^{\left(-12 \, d x - 12 \, c\right)} - {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} e^{\left(-14 \, d x - 14 \, c\right)}\right)} d} - \frac{5 \, {\left(3 \, a b + 7 \, 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)}{8 \, \sqrt{a b} a^{4} d}"," ",0,"1/12*(16*a^4 + 147*a^3*b + 351*a^2*b^2 + 325*a*b^3 + 105*b^4 + 2*(8*a^4 + 32*a^3*b - 251*a^2*b^2 - 590*a*b^3 - 315*b^4)*e^(-2*d*x - 2*c) - (96*a^4 + 313*a^3*b + 19*a^2*b^2 - 1725*a*b^3 - 1575*b^4)*e^(-4*d*x - 4*c) - 4*(56*a^4 + 80*a^3*b - 65*a^2*b^2 + 400*a*b^3 + 525*b^4)*e^(-6*d*x - 6*c) - (176*a^4 + 135*a^3*b + 15*a^2*b^2 - 1375*a*b^3 - 1575*b^4)*e^(-8*d*x - 8*c) - 6*(8*a^4 + 45*a^2*b^2 + 150*a*b^3 + 105*b^4)*e^(-10*d*x - 10*c) + 15*(3*a^3*b + 13*a^2*b^2 + 17*a*b^3 + 7*b^4)*e^(-12*d*x - 12*c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3 + (a^7 - 5*a^6*b - 13*a^5*b^2 - 7*a^4*b^3)*e^(-2*d*x - 2*c) - (3*a^7 + a^6*b - 23*a^5*b^2 - 21*a^4*b^3)*e^(-4*d*x - 4*c) - (3*a^7 - 7*a^6*b + 25*a^5*b^2 + 35*a^4*b^3)*e^(-6*d*x - 6*c) + (3*a^7 - 7*a^6*b + 25*a^5*b^2 + 35*a^4*b^3)*e^(-8*d*x - 8*c) + (3*a^7 + a^6*b - 23*a^5*b^2 - 21*a^4*b^3)*e^(-10*d*x - 10*c) - (a^7 - 5*a^6*b - 13*a^5*b^2 - 7*a^4*b^3)*e^(-12*d*x - 12*c) - (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*e^(-14*d*x - 14*c))*d) - 5/8*(3*a*b + 7*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^4*d)","B",0
49,1,194,0,0.418288," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","\frac{1}{64} \, a {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{64} \, b {\left(\frac{192 \, {\left(d x + c\right)}}{d} - \frac{20 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} + \frac{192 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{18 \, e^{\left(-2 \, d x - 2 \, c\right)} + 39 \, e^{\left(-4 \, d x - 4 \, c\right)} - 108 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)}\right)}}\right)}"," ",0,"1/64*a*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/64*b*(192*(d*x + c)/d - (20*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d + 192*log(e^(-2*d*x - 2*c) + 1)/d - (18*e^(-2*d*x - 2*c) + 39*e^(-4*d*x - 4*c) - 108*e^(-6*d*x - 6*c) - 1)/(d*(e^(-4*d*x - 4*c) + 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c))))","A",0
50,1,174,0,0.412375," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","\frac{1}{24} \, b {\left(\frac{27 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} - \frac{120 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{25 \, e^{\left(-2 \, d x - 2 \, c\right)} + 77 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 2 \, e^{\left(-5 \, d x - 5 \, c\right)} + e^{\left(-7 \, d x - 7 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} + \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"1/24*b*((27*e^(-d*x - c) - e^(-3*d*x - 3*c))/d - 120*arctan(e^(-d*x - c))/d - (25*e^(-2*d*x - 2*c) + 77*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) - 1)/(d*(e^(-3*d*x - 3*c) + 2*e^(-5*d*x - 5*c) + e^(-7*d*x - 7*c)))) + 1/24*a*(e^(3*d*x + 3*c)/d - 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d + e^(-3*d*x - 3*c)/d)","A",0
51,1,141,0,0.410287," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{8} \, b {\left(\frac{16 \, {\left(d x + c\right)}}{d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} + \frac{16 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)}"," ",0,"-1/8*a*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/8*b*(16*(d*x + c)/d - e^(-2*d*x - 2*c)/d + 16*log(e^(-2*d*x - 2*c) + 1)/d - (2*e^(-2*d*x - 2*c) - 15*e^(-4*d*x - 4*c) + 1)/(d*(e^(-2*d*x - 2*c) + 2*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))))","A",0
52,1,105,0,0.413967," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{6 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)}}{d} + \frac{4 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{a \cosh\left(d x + c\right)}{d}"," ",0,"1/2*b*(6*arctan(e^(-d*x - c))/d - e^(-d*x - c)/d + (4*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + 1)/(d*(e^(-d*x - c) + 2*e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + a*cosh(d*x + c)/d","A",0
53,1,83,0,0.407878," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-b*(arctan(e^(-d*x - c))/d + (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a*log(tanh(1/2*d*x + 1/2*c))/d","A",0
54,1,44,0,0.301637," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","\frac{2 \, a}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} - \frac{2 \, b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{2}}"," ",0,"2*a/(d*(e^(-2*d*x - 2*c) - 1)) - 2*b/(d*(e^(d*x + c) + e^(-d*x - c))^2)","A",0
55,1,156,0,0.420743," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{1}{2} \, a {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)}"," ",0,"-b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 1/2*a*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1)))","B",0
56,1,184,0,0.401213," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","b {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{4}{3} \, a {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{1}{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)}"," ",0,"b*(log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d - log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 4/3*a*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)) - 1/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)))","B",0
57,1,379,0,0.408224," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{1}{64} \, a^{2} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{320} \, b^{2} {\left(\frac{2520 \, {\left(d x + c\right)}}{d} + \frac{5 \, {\left(32 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}\right)}}{d} - \frac{135 \, e^{\left(-2 \, d x - 2 \, c\right)} + 5358 \, e^{\left(-4 \, d x - 4 \, c\right)} + 18190 \, e^{\left(-6 \, d x - 6 \, c\right)} + 28455 \, e^{\left(-8 \, d x - 8 \, c\right)} + 19995 \, e^{\left(-10 \, d x - 10 \, c\right)} + 6560 \, e^{\left(-12 \, d x - 12 \, c\right)} - 5}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 5 \, e^{\left(-6 \, d x - 6 \, c\right)} + 10 \, e^{\left(-8 \, d x - 8 \, c\right)} + 10 \, e^{\left(-10 \, d x - 10 \, c\right)} + 5 \, e^{\left(-12 \, d x - 12 \, c\right)} + e^{\left(-14 \, d x - 14 \, c\right)}\right)}}\right)} + \frac{1}{32} \, a b {\left(\frac{192 \, {\left(d x + c\right)}}{d} - \frac{20 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} + \frac{192 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{18 \, e^{\left(-2 \, d x - 2 \, c\right)} + 39 \, e^{\left(-4 \, d x - 4 \, c\right)} - 108 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)}\right)}}\right)}"," ",0,"1/64*a^2*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/320*b^2*(2520*(d*x + c)/d + 5*(32*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (135*e^(-2*d*x - 2*c) + 5358*e^(-4*d*x - 4*c) + 18190*e^(-6*d*x - 6*c) + 28455*e^(-8*d*x - 8*c) + 19995*e^(-10*d*x - 10*c) + 6560*e^(-12*d*x - 12*c) - 5)/(d*(e^(-4*d*x - 4*c) + 5*e^(-6*d*x - 6*c) + 10*e^(-8*d*x - 8*c) + 10*e^(-10*d*x - 10*c) + 5*e^(-12*d*x - 12*c) + e^(-14*d*x - 14*c)))) + 1/32*a*b*(192*(d*x + c)/d - (20*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d + 192*log(e^(-2*d*x - 2*c) + 1)/d - (18*e^(-2*d*x - 2*c) + 39*e^(-4*d*x - 4*c) - 108*e^(-6*d*x - 6*c) - 1)/(d*(e^(-4*d*x - 4*c) + 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c))))","B",0
58,1,348,0,0.407081," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","-\frac{1}{120} \, b^{2} {\left(\frac{5 \, {\left(45 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d} + \frac{200 \, e^{\left(-2 \, d x - 2 \, c\right)} + 2515 \, e^{\left(-4 \, d x - 4 \, c\right)} + 6680 \, e^{\left(-6 \, d x - 6 \, c\right)} + 9073 \, e^{\left(-8 \, d x - 8 \, c\right)} + 5600 \, e^{\left(-10 \, d x - 10 \, c\right)} + 1665 \, e^{\left(-12 \, d x - 12 \, c\right)} - 5}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 5 \, e^{\left(-5 \, d x - 5 \, c\right)} + 10 \, e^{\left(-7 \, d x - 7 \, c\right)} + 10 \, e^{\left(-9 \, d x - 9 \, c\right)} + 5 \, e^{\left(-11 \, d x - 11 \, c\right)} + e^{\left(-13 \, d x - 13 \, c\right)}\right)}}\right)} + \frac{1}{12} \, a b {\left(\frac{27 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} - \frac{120 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{25 \, e^{\left(-2 \, d x - 2 \, c\right)} + 77 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 2 \, e^{\left(-5 \, d x - 5 \, c\right)} + e^{\left(-7 \, d x - 7 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a^{2} {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} + \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"-1/120*b^2*(5*(45*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (200*e^(-2*d*x - 2*c) + 2515*e^(-4*d*x - 4*c) + 6680*e^(-6*d*x - 6*c) + 9073*e^(-8*d*x - 8*c) + 5600*e^(-10*d*x - 10*c) + 1665*e^(-12*d*x - 12*c) - 5)/(d*(e^(-3*d*x - 3*c) + 5*e^(-5*d*x - 5*c) + 10*e^(-7*d*x - 7*c) + 10*e^(-9*d*x - 9*c) + 5*e^(-11*d*x - 11*c) + e^(-13*d*x - 13*c)))) + 1/12*a*b*((27*e^(-d*x - c) - e^(-3*d*x - 3*c))/d - 120*arctan(e^(-d*x - c))/d - (25*e^(-2*d*x - 2*c) + 77*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) - 1)/(d*(e^(-3*d*x - 3*c) + 2*e^(-5*d*x - 5*c) + e^(-7*d*x - 7*c)))) + 1/24*a^2*(e^(3*d*x + 3*c)/d - 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d + e^(-3*d*x - 3*c)/d)","B",0
59,1,301,0,0.411349," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{120} \, b^{2} {\left(\frac{420 \, {\left(d x + c\right)}}{d} + \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{1003 \, e^{\left(-2 \, d x - 2 \, c\right)} + 3350 \, e^{\left(-4 \, d x - 4 \, c\right)} + 5590 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3915 \, e^{\left(-8 \, d x - 8 \, c\right)} + 1455 \, e^{\left(-10 \, d x - 10 \, c\right)} + 15}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 5 \, e^{\left(-4 \, d x - 4 \, c\right)} + 10 \, e^{\left(-6 \, d x - 6 \, c\right)} + 10 \, e^{\left(-8 \, d x - 8 \, c\right)} + 5 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)}\right)}}\right)} - \frac{1}{4} \, a b {\left(\frac{16 \, {\left(d x + c\right)}}{d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} + \frac{16 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)}"," ",0,"-1/8*a^2*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/120*b^2*(420*(d*x + c)/d + 15*e^(-2*d*x - 2*c)/d - (1003*e^(-2*d*x - 2*c) + 3350*e^(-4*d*x - 4*c) + 5590*e^(-6*d*x - 6*c) + 3915*e^(-8*d*x - 8*c) + 1455*e^(-10*d*x - 10*c) + 15)/(d*(e^(-2*d*x - 2*c) + 5*e^(-4*d*x - 4*c) + 10*e^(-6*d*x - 6*c) + 10*e^(-8*d*x - 8*c) + 5*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c)))) - 1/4*a*b*(16*(d*x + c)/d - e^(-2*d*x - 2*c)/d + 16*log(e^(-2*d*x - 2*c) + 1)/d - (2*e^(-2*d*x - 2*c) - 15*e^(-4*d*x - 4*c) + 1)/(d*(e^(-2*d*x - 2*c) + 2*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))))","B",0
60,1,253,0,0.408851," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","a b {\left(\frac{6 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)}}{d} + \frac{4 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{1}{10} \, b^{2} {\left(\frac{5 \, e^{\left(-d x - c\right)}}{d} + \frac{85 \, e^{\left(-2 \, d x - 2 \, c\right)} + 210 \, e^{\left(-4 \, d x - 4 \, c\right)} + 314 \, e^{\left(-6 \, d x - 6 \, c\right)} + 185 \, e^{\left(-8 \, d x - 8 \, c\right)} + 65 \, e^{\left(-10 \, d x - 10 \, c\right)} + 5}{d {\left(e^{\left(-d x - c\right)} + 5 \, e^{\left(-3 \, d x - 3 \, c\right)} + 10 \, e^{\left(-5 \, d x - 5 \, c\right)} + 10 \, e^{\left(-7 \, d x - 7 \, c\right)} + 5 \, e^{\left(-9 \, d x - 9 \, c\right)} + e^{\left(-11 \, d x - 11 \, c\right)}\right)}}\right)} + \frac{a^{2} \cosh\left(d x + c\right)}{d}"," ",0,"a*b*(6*arctan(e^(-d*x - c))/d - e^(-d*x - c)/d + (4*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + 1)/(d*(e^(-d*x - c) + 2*e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + 1/10*b^2*(5*e^(-d*x - c)/d + (85*e^(-2*d*x - 2*c) + 210*e^(-4*d*x - 4*c) + 314*e^(-6*d*x - 6*c) + 185*e^(-8*d*x - 8*c) + 65*e^(-10*d*x - 10*c) + 5)/(d*(e^(-d*x - c) + 5*e^(-3*d*x - 3*c) + 10*e^(-5*d*x - 5*c) + 10*e^(-7*d*x - 7*c) + 5*e^(-9*d*x - 9*c) + e^(-11*d*x - 11*c)))) + a^2*cosh(d*x + c)/d","B",0
61,1,447,0,0.406711," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","-2 \, a b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} - \frac{2}{15} \, b^{2} {\left(\frac{15 \, e^{\left(-d x - c\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)}} + \frac{20 \, e^{\left(-3 \, d x - 3 \, c\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)}} + \frac{58 \, e^{\left(-5 \, d x - 5 \, c\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)}} + \frac{20 \, e^{\left(-7 \, d x - 7 \, c\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)}} + \frac{15 \, e^{\left(-9 \, d x - 9 \, c\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{a^{2} \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-2*a*b*(arctan(e^(-d*x - c))/d + (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) - 2/15*b^2*(15*e^(-d*x - c)/(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)) + 20*e^(-3*d*x - 3*c)/(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)) + 58*e^(-5*d*x - 5*c)/(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)) + 20*e^(-7*d*x - 7*c)/(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)) + 15*e^(-9*d*x - 9*c)/(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^2*log(tanh(1/2*d*x + 1/2*c))/d","B",0
62,1,256,0,0.314604," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{2}{5} \, b^{2} {\left(\frac{10 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{5 \, e^{\left(-8 \, d x - 8 \, c\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)}} + \frac{1}{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{2 \, a^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} - \frac{4 \, a b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{2}}"," ",0,"2/5*b^2*(10*e^(-4*d*x - 4*c)/(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)) + 5*e^(-8*d*x - 8*c)/(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)) + 1/(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/(d*(e^(-2*d*x - 2*c) - 1)) - 4*a*b/(d*(e^(d*x + c) + e^(-d*x - c))^2)","B",0
63,1,378,0,0.411073," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","-2 \, a b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{1}{2} \, a^{2} {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} - \frac{8}{15} \, b^{2} {\left(\frac{5 \, e^{\left(-3 \, d x - 3 \, c\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)}} - \frac{2 \, e^{\left(-5 \, d x - 5 \, c\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)}} + \frac{5 \, e^{\left(-7 \, d x - 7 \, c\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)}"," ",0,"-2*a*b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 1/2*a^2*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) - 8/15*b^2*(5*e^(-3*d*x - 3*c)/(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*e^(-5*d*x - 5*c)/(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)) + 5*e^(-7*d*x - 7*c)/(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)))","B",0
64,1,468,0,0.409549," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","2 \, a b {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{4}{15} \, b^{2} {\left(\frac{5 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{5 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{15 \, e^{\left(-6 \, d x - 6 \, c\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)}} + \frac{1}{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{4}{3} \, a^{2} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{1}{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)}"," ",0,"2*a*b*(log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d - log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 4/15*b^2*(5*e^(-2*d*x - 2*c)/(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)) - 5*e^(-4*d*x - 4*c)/(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)) + 15*e^(-6*d*x - 6*c)/(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)) + 1/(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))) + 4/3*a^2*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)) - 1/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)))","B",0
65,1,647,0,0.432337," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","\frac{1}{64} \, a^{3} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{3}{320} \, a b^{2} {\left(\frac{2520 \, {\left(d x + c\right)}}{d} + \frac{5 \, {\left(32 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}\right)}}{d} - \frac{135 \, e^{\left(-2 \, d x - 2 \, c\right)} + 5358 \, e^{\left(-4 \, d x - 4 \, c\right)} + 18190 \, e^{\left(-6 \, d x - 6 \, c\right)} + 28455 \, e^{\left(-8 \, d x - 8 \, c\right)} + 19995 \, e^{\left(-10 \, d x - 10 \, c\right)} + 6560 \, e^{\left(-12 \, d x - 12 \, c\right)} - 5}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 5 \, e^{\left(-6 \, d x - 6 \, c\right)} + 10 \, e^{\left(-8 \, d x - 8 \, c\right)} + 10 \, e^{\left(-10 \, d x - 10 \, c\right)} + 5 \, e^{\left(-12 \, d x - 12 \, c\right)} + e^{\left(-14 \, d x - 14 \, c\right)}\right)}}\right)} + \frac{1}{64} \, b^{3} {\left(\frac{960 \, {\left(d x + c\right)}}{d} - \frac{44 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} + \frac{960 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{36 \, e^{\left(-2 \, d x - 2 \, c\right)} + 324 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1384 \, e^{\left(-6 \, d x - 6 \, c\right)} - 9126 \, e^{\left(-8 \, d x - 8 \, c\right)} - 24112 \, e^{\left(-10 \, d x - 10 \, c\right)} - 31868 \, e^{\left(-12 \, d x - 12 \, c\right)} - 25912 \, e^{\left(-14 \, d x - 14 \, c\right)} - 11169 \, e^{\left(-16 \, d x - 16 \, c\right)} - 2516 \, e^{\left(-18 \, d x - 18 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 8 \, e^{\left(-6 \, d x - 6 \, c\right)} + 28 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 70 \, e^{\left(-12 \, d x - 12 \, c\right)} + 56 \, e^{\left(-14 \, d x - 14 \, c\right)} + 28 \, e^{\left(-16 \, d x - 16 \, c\right)} + 8 \, e^{\left(-18 \, d x - 18 \, c\right)} + e^{\left(-20 \, d x - 20 \, c\right)}\right)}}\right)} + \frac{3}{64} \, a^{2} b {\left(\frac{192 \, {\left(d x + c\right)}}{d} - \frac{20 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} + \frac{192 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{18 \, e^{\left(-2 \, d x - 2 \, c\right)} + 39 \, e^{\left(-4 \, d x - 4 \, c\right)} - 108 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)}\right)}}\right)}"," ",0,"1/64*a^3*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 3/320*a*b^2*(2520*(d*x + c)/d + 5*(32*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (135*e^(-2*d*x - 2*c) + 5358*e^(-4*d*x - 4*c) + 18190*e^(-6*d*x - 6*c) + 28455*e^(-8*d*x - 8*c) + 19995*e^(-10*d*x - 10*c) + 6560*e^(-12*d*x - 12*c) - 5)/(d*(e^(-4*d*x - 4*c) + 5*e^(-6*d*x - 6*c) + 10*e^(-8*d*x - 8*c) + 10*e^(-10*d*x - 10*c) + 5*e^(-12*d*x - 12*c) + e^(-14*d*x - 14*c)))) + 1/64*b^3*(960*(d*x + c)/d - (44*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d + 960*log(e^(-2*d*x - 2*c) + 1)/d - (36*e^(-2*d*x - 2*c) + 324*e^(-4*d*x - 4*c) - 1384*e^(-6*d*x - 6*c) - 9126*e^(-8*d*x - 8*c) - 24112*e^(-10*d*x - 10*c) - 31868*e^(-12*d*x - 12*c) - 25912*e^(-14*d*x - 14*c) - 11169*e^(-16*d*x - 16*c) - 2516*e^(-18*d*x - 18*c) - 1)/(d*(e^(-4*d*x - 4*c) + 8*e^(-6*d*x - 6*c) + 28*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 70*e^(-12*d*x - 12*c) + 56*e^(-14*d*x - 14*c) + 28*e^(-16*d*x - 16*c) + 8*e^(-18*d*x - 18*c) + e^(-20*d*x - 20*c)))) + 3/64*a^2*b*(192*(d*x + c)/d - (20*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d + 192*log(e^(-2*d*x - 2*c) + 1)/d - (18*e^(-2*d*x - 2*c) + 39*e^(-4*d*x - 4*c) - 108*e^(-6*d*x - 6*c) - 1)/(d*(e^(-4*d*x - 4*c) + 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c))))","B",0
66,1,604,0,0.428616," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","\frac{1}{192} \, b^{3} {\left(\frac{8 \, {\left(63 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d} - \frac{3465 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{440 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6103 \, e^{\left(-4 \, d x - 4 \, c\right)} + 21019 \, e^{\left(-6 \, d x - 6 \, c\right)} + 41207 \, e^{\left(-8 \, d x - 8 \, c\right)} + 40243 \, e^{\left(-10 \, d x - 10 \, c\right)} + 22589 \, e^{\left(-12 \, d x - 12 \, c\right)} + 505 \, e^{\left(-14 \, d x - 14 \, c\right)} - 3331 \, e^{\left(-16 \, d x - 16 \, c\right)} - 1791 \, e^{\left(-18 \, d x - 18 \, c\right)} - 8}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 8 \, e^{\left(-5 \, d x - 5 \, c\right)} + 28 \, e^{\left(-7 \, d x - 7 \, c\right)} + 56 \, e^{\left(-9 \, d x - 9 \, c\right)} + 70 \, e^{\left(-11 \, d x - 11 \, c\right)} + 56 \, e^{\left(-13 \, d x - 13 \, c\right)} + 28 \, e^{\left(-15 \, d x - 15 \, c\right)} + 8 \, e^{\left(-17 \, d x - 17 \, c\right)} + e^{\left(-19 \, d x - 19 \, c\right)}\right)}}\right)} - \frac{1}{40} \, a b^{2} {\left(\frac{5 \, {\left(45 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d} + \frac{200 \, e^{\left(-2 \, d x - 2 \, c\right)} + 2515 \, e^{\left(-4 \, d x - 4 \, c\right)} + 6680 \, e^{\left(-6 \, d x - 6 \, c\right)} + 9073 \, e^{\left(-8 \, d x - 8 \, c\right)} + 5600 \, e^{\left(-10 \, d x - 10 \, c\right)} + 1665 \, e^{\left(-12 \, d x - 12 \, c\right)} - 5}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 5 \, e^{\left(-5 \, d x - 5 \, c\right)} + 10 \, e^{\left(-7 \, d x - 7 \, c\right)} + 10 \, e^{\left(-9 \, d x - 9 \, c\right)} + 5 \, e^{\left(-11 \, d x - 11 \, c\right)} + e^{\left(-13 \, d x - 13 \, c\right)}\right)}}\right)} + \frac{1}{8} \, a^{2} b {\left(\frac{27 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} - \frac{120 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{25 \, e^{\left(-2 \, d x - 2 \, c\right)} + 77 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 2 \, e^{\left(-5 \, d x - 5 \, c\right)} + e^{\left(-7 \, d x - 7 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a^{3} {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} + \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"1/192*b^3*(8*(63*e^(-d*x - c) - e^(-3*d*x - 3*c))/d - 3465*arctan(e^(-d*x - c))/d - (440*e^(-2*d*x - 2*c) + 6103*e^(-4*d*x - 4*c) + 21019*e^(-6*d*x - 6*c) + 41207*e^(-8*d*x - 8*c) + 40243*e^(-10*d*x - 10*c) + 22589*e^(-12*d*x - 12*c) + 505*e^(-14*d*x - 14*c) - 3331*e^(-16*d*x - 16*c) - 1791*e^(-18*d*x - 18*c) - 8)/(d*(e^(-3*d*x - 3*c) + 8*e^(-5*d*x - 5*c) + 28*e^(-7*d*x - 7*c) + 56*e^(-9*d*x - 9*c) + 70*e^(-11*d*x - 11*c) + 56*e^(-13*d*x - 13*c) + 28*e^(-15*d*x - 15*c) + 8*e^(-17*d*x - 17*c) + e^(-19*d*x - 19*c)))) - 1/40*a*b^2*(5*(45*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + (200*e^(-2*d*x - 2*c) + 2515*e^(-4*d*x - 4*c) + 6680*e^(-6*d*x - 6*c) + 9073*e^(-8*d*x - 8*c) + 5600*e^(-10*d*x - 10*c) + 1665*e^(-12*d*x - 12*c) - 5)/(d*(e^(-3*d*x - 3*c) + 5*e^(-5*d*x - 5*c) + 10*e^(-7*d*x - 7*c) + 10*e^(-9*d*x - 9*c) + 5*e^(-11*d*x - 11*c) + e^(-13*d*x - 13*c)))) + 1/8*a^2*b*((27*e^(-d*x - c) - e^(-3*d*x - 3*c))/d - 120*arctan(e^(-d*x - c))/d - (25*e^(-2*d*x - 2*c) + 77*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) - 1)/(d*(e^(-3*d*x - 3*c) + 2*e^(-5*d*x - 5*c) + e^(-7*d*x - 7*c)))) + 1/24*a^3*(e^(3*d*x + 3*c)/d - 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d + e^(-3*d*x - 3*c)/d)","A",0
67,1,544,0,0.425050," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{3} {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{40} \, a b^{2} {\left(\frac{420 \, {\left(d x + c\right)}}{d} + \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{1003 \, e^{\left(-2 \, d x - 2 \, c\right)} + 3350 \, e^{\left(-4 \, d x - 4 \, c\right)} + 5590 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3915 \, e^{\left(-8 \, d x - 8 \, c\right)} + 1455 \, e^{\left(-10 \, d x - 10 \, c\right)} + 15}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 5 \, e^{\left(-4 \, d x - 4 \, c\right)} + 10 \, e^{\left(-6 \, d x - 6 \, c\right)} + 10 \, e^{\left(-8 \, d x - 8 \, c\right)} + 5 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)}\right)}}\right)} - \frac{1}{24} \, b^{3} {\left(\frac{120 \, {\left(d x + c\right)}}{d} - \frac{3 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} + \frac{120 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{24 \, e^{\left(-2 \, d x - 2 \, c\right)} - 396 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1752 \, e^{\left(-6 \, d x - 6 \, c\right)} - 4430 \, e^{\left(-8 \, d x - 8 \, c\right)} - 5464 \, e^{\left(-10 \, d x - 10 \, c\right)} - 4556 \, e^{\left(-12 \, d x - 12 \, c\right)} - 1896 \, e^{\left(-14 \, d x - 14 \, c\right)} - 477 \, e^{\left(-16 \, d x - 16 \, c\right)} + 3}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 8 \, e^{\left(-4 \, d x - 4 \, c\right)} + 28 \, e^{\left(-6 \, d x - 6 \, c\right)} + 56 \, e^{\left(-8 \, d x - 8 \, c\right)} + 70 \, e^{\left(-10 \, d x - 10 \, c\right)} + 56 \, e^{\left(-12 \, d x - 12 \, c\right)} + 28 \, e^{\left(-14 \, d x - 14 \, c\right)} + 8 \, e^{\left(-16 \, d x - 16 \, c\right)} + e^{\left(-18 \, d x - 18 \, c\right)}\right)}}\right)} - \frac{3}{8} \, a^{2} b {\left(\frac{16 \, {\left(d x + c\right)}}{d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} + \frac{16 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)}"," ",0,"-1/8*a^3*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/40*a*b^2*(420*(d*x + c)/d + 15*e^(-2*d*x - 2*c)/d - (1003*e^(-2*d*x - 2*c) + 3350*e^(-4*d*x - 4*c) + 5590*e^(-6*d*x - 6*c) + 3915*e^(-8*d*x - 8*c) + 1455*e^(-10*d*x - 10*c) + 15)/(d*(e^(-2*d*x - 2*c) + 5*e^(-4*d*x - 4*c) + 10*e^(-6*d*x - 6*c) + 10*e^(-8*d*x - 8*c) + 5*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c)))) - 1/24*b^3*(120*(d*x + c)/d - 3*e^(-2*d*x - 2*c)/d + 120*log(e^(-2*d*x - 2*c) + 1)/d - (24*e^(-2*d*x - 2*c) - 396*e^(-4*d*x - 4*c) - 1752*e^(-6*d*x - 6*c) - 4430*e^(-8*d*x - 8*c) - 5464*e^(-10*d*x - 10*c) - 4556*e^(-12*d*x - 12*c) - 1896*e^(-14*d*x - 14*c) - 477*e^(-16*d*x - 16*c) + 3)/(d*(e^(-2*d*x - 2*c) + 8*e^(-4*d*x - 4*c) + 28*e^(-6*d*x - 6*c) + 56*e^(-8*d*x - 8*c) + 70*e^(-10*d*x - 10*c) + 56*e^(-12*d*x - 12*c) + 28*e^(-14*d*x - 14*c) + 8*e^(-16*d*x - 16*c) + e^(-18*d*x - 18*c)))) - 3/8*a^2*b*(16*(d*x + c)/d - e^(-2*d*x - 2*c)/d + 16*log(e^(-2*d*x - 2*c) + 1)/d - (2*e^(-2*d*x - 2*c) - 15*e^(-4*d*x - 4*c) + 1)/(d*(e^(-2*d*x - 2*c) + 2*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))))","B",0
68,1,484,0,0.424451," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","\frac{1}{64} \, b^{3} {\left(\frac{315 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{32 \, e^{\left(-d x - c\right)}}{d} + \frac{581 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1681 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3605 \, e^{\left(-6 \, d x - 6 \, c\right)} + 2569 \, e^{\left(-8 \, d x - 8 \, c\right)} + 1463 \, e^{\left(-10 \, d x - 10 \, c\right)} - 917 \, e^{\left(-12 \, d x - 12 \, c\right)} - 529 \, e^{\left(-14 \, d x - 14 \, c\right)} - 293 \, e^{\left(-16 \, d x - 16 \, c\right)} + 32}{d {\left(e^{\left(-d x - c\right)} + 8 \, e^{\left(-3 \, d x - 3 \, c\right)} + 28 \, e^{\left(-5 \, d x - 5 \, c\right)} + 56 \, e^{\left(-7 \, d x - 7 \, c\right)} + 70 \, e^{\left(-9 \, d x - 9 \, c\right)} + 56 \, e^{\left(-11 \, d x - 11 \, c\right)} + 28 \, e^{\left(-13 \, d x - 13 \, c\right)} + 8 \, e^{\left(-15 \, d x - 15 \, c\right)} + e^{\left(-17 \, d x - 17 \, c\right)}\right)}}\right)} + \frac{3}{2} \, a^{2} b {\left(\frac{6 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)}}{d} + \frac{4 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{3}{10} \, a b^{2} {\left(\frac{5 \, e^{\left(-d x - c\right)}}{d} + \frac{85 \, e^{\left(-2 \, d x - 2 \, c\right)} + 210 \, e^{\left(-4 \, d x - 4 \, c\right)} + 314 \, e^{\left(-6 \, d x - 6 \, c\right)} + 185 \, e^{\left(-8 \, d x - 8 \, c\right)} + 65 \, e^{\left(-10 \, d x - 10 \, c\right)} + 5}{d {\left(e^{\left(-d x - c\right)} + 5 \, e^{\left(-3 \, d x - 3 \, c\right)} + 10 \, e^{\left(-5 \, d x - 5 \, c\right)} + 10 \, e^{\left(-7 \, d x - 7 \, c\right)} + 5 \, e^{\left(-9 \, d x - 9 \, c\right)} + e^{\left(-11 \, d x - 11 \, c\right)}\right)}}\right)} + \frac{a^{3} \cosh\left(d x + c\right)}{d}"," ",0,"1/64*b^3*(315*arctan(e^(-d*x - c))/d - 32*e^(-d*x - c)/d + (581*e^(-2*d*x - 2*c) + 1681*e^(-4*d*x - 4*c) + 3605*e^(-6*d*x - 6*c) + 2569*e^(-8*d*x - 8*c) + 1463*e^(-10*d*x - 10*c) - 917*e^(-12*d*x - 12*c) - 529*e^(-14*d*x - 14*c) - 293*e^(-16*d*x - 16*c) + 32)/(d*(e^(-d*x - c) + 8*e^(-3*d*x - 3*c) + 28*e^(-5*d*x - 5*c) + 56*e^(-7*d*x - 7*c) + 70*e^(-9*d*x - 9*c) + 56*e^(-11*d*x - 11*c) + 28*e^(-13*d*x - 13*c) + 8*e^(-15*d*x - 15*c) + e^(-17*d*x - 17*c)))) + 3/2*a^2*b*(6*arctan(e^(-d*x - c))/d - e^(-d*x - c)/d + (4*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + 1)/(d*(e^(-d*x - c) + 2*e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + 3/10*a*b^2*(5*e^(-d*x - c)/d + (85*e^(-2*d*x - 2*c) + 210*e^(-4*d*x - 4*c) + 314*e^(-6*d*x - 6*c) + 185*e^(-8*d*x - 8*c) + 65*e^(-10*d*x - 10*c) + 5)/(d*(e^(-d*x - c) + 5*e^(-3*d*x - 3*c) + 10*e^(-5*d*x - 5*c) + 10*e^(-7*d*x - 7*c) + 5*e^(-9*d*x - 9*c) + e^(-11*d*x - 11*c)))) + a^3*cosh(d*x + c)/d","A",0
69,1,654,0,0.432949," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","-\frac{1}{192} \, b^{3} {\left(\frac{105 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{279 \, e^{\left(-d x - c\right)} + 91 \, e^{\left(-3 \, d x - 3 \, c\right)} + 1799 \, e^{\left(-5 \, d x - 5 \, c\right)} - 1085 \, e^{\left(-7 \, d x - 7 \, c\right)} + 1085 \, e^{\left(-9 \, d x - 9 \, c\right)} - 1799 \, e^{\left(-11 \, d x - 11 \, c\right)} - 91 \, e^{\left(-13 \, d x - 13 \, c\right)} - 279 \, e^{\left(-15 \, d x - 15 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)} - 3 \, a^{2} b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} - \frac{2}{5} \, a b^{2} {\left(\frac{15 \, e^{\left(-d x - c\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)}} + \frac{20 \, e^{\left(-3 \, d x - 3 \, c\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)}} + \frac{58 \, e^{\left(-5 \, d x - 5 \, c\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)}} + \frac{20 \, e^{\left(-7 \, d x - 7 \, c\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)}} + \frac{15 \, e^{\left(-9 \, d x - 9 \, c\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{a^{3} \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-1/192*b^3*(105*arctan(e^(-d*x - c))/d + (279*e^(-d*x - c) + 91*e^(-3*d*x - 3*c) + 1799*e^(-5*d*x - 5*c) - 1085*e^(-7*d*x - 7*c) + 1085*e^(-9*d*x - 9*c) - 1799*e^(-11*d*x - 11*c) - 91*e^(-13*d*x - 13*c) - 279*e^(-15*d*x - 15*c))/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1))) - 3*a^2*b*(arctan(e^(-d*x - c))/d + (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) - 2/5*a*b^2*(15*e^(-d*x - c)/(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)) + 20*e^(-3*d*x - 3*c)/(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)) + 58*e^(-5*d*x - 5*c)/(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)) + 20*e^(-7*d*x - 7*c)/(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)) + 15*e^(-9*d*x - 9*c)/(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^3*log(tanh(1/2*d*x + 1/2*c))/d","B",0
70,1,679,0,0.335765," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","-2 \, b^{3} {\left(\frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} + \frac{7 \, e^{\left(-6 \, d x - 6 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} + \frac{7 \, e^{\left(-10 \, d x - 10 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} + \frac{e^{\left(-14 \, d x - 14 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)} + \frac{6}{5} \, a b^{2} {\left(\frac{10 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{5 \, e^{\left(-8 \, d x - 8 \, c\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)}} + \frac{1}{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{2 \, a^{3}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} - \frac{6 \, a^{2} b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{2}}"," ",0,"-2*b^3*(e^(-2*d*x - 2*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) + 7*e^(-6*d*x - 6*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) + 7*e^(-10*d*x - 10*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) + e^(-14*d*x - 14*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1))) + 6/5*a*b^2*(10*e^(-4*d*x - 4*c)/(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)) + 5*e^(-8*d*x - 8*c)/(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)) + 1/(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^3/(d*(e^(-2*d*x - 2*c) - 1)) - 6*a^2*b/(d*(e^(d*x + c) + e^(-d*x - c))^2)","B",0
71,1,586,0,0.427432," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","-\frac{1}{192} \, b^{3} {\left(\frac{15 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{15 \, e^{\left(-d x - c\right)} - 397 \, e^{\left(-3 \, d x - 3 \, c\right)} + 895 \, e^{\left(-5 \, d x - 5 \, c\right)} - 1765 \, e^{\left(-7 \, d x - 7 \, c\right)} + 1765 \, e^{\left(-9 \, d x - 9 \, c\right)} - 895 \, e^{\left(-11 \, d x - 11 \, c\right)} + 397 \, e^{\left(-13 \, d x - 13 \, c\right)} - 15 \, e^{\left(-15 \, d x - 15 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)} - 3 \, a^{2} b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{1}{2} \, a^{3} {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(e^{\left(-d x - c\right)} + e^{\left(-3 \, d x - 3 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} - \frac{8}{5} \, a b^{2} {\left(\frac{5 \, e^{\left(-3 \, d x - 3 \, c\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)}} - \frac{2 \, e^{\left(-5 \, d x - 5 \, c\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)}} + \frac{5 \, e^{\left(-7 \, d x - 7 \, c\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)}"," ",0,"-1/192*b^3*(15*arctan(e^(-d*x - c))/d - (15*e^(-d*x - c) - 397*e^(-3*d*x - 3*c) + 895*e^(-5*d*x - 5*c) - 1765*e^(-7*d*x - 7*c) + 1765*e^(-9*d*x - 9*c) - 895*e^(-11*d*x - 11*c) + 397*e^(-13*d*x - 13*c) - 15*e^(-15*d*x - 15*c))/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1))) - 3*a^2*b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 1/2*a^3*(log(e^(-d*x - c) + 1)/d - log(e^(-d*x - c) - 1)/d + 2*(e^(-d*x - c) + e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) - 8/5*a*b^2*(5*e^(-3*d*x - 3*c)/(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*e^(-5*d*x - 5*c)/(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)) + 5*e^(-7*d*x - 7*c)/(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)))","B",0
72,1,997,0,0.425785," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""maxima"")","3 \, a^{2} b {\left(\frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{4}{5} \, a b^{2} {\left(\frac{5 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{5 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{15 \, e^{\left(-6 \, d x - 6 \, c\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)}} + \frac{1}{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{4}{3} \, a^{3} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{1}{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)} - \frac{4}{3} \, b^{3} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} - \frac{4 \, e^{\left(-6 \, d x - 6 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} + \frac{10 \, e^{\left(-8 \, d x - 8 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} - \frac{4 \, e^{\left(-10 \, d x - 10 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} + \frac{3 \, e^{\left(-12 \, d x - 12 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)}"," ",0,"3*a^2*b*(log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d - log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 4/5*a*b^2*(5*e^(-2*d*x - 2*c)/(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)) - 5*e^(-4*d*x - 4*c)/(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)) + 15*e^(-6*d*x - 6*c)/(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)) + 1/(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))) + 4/3*a^3*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1)) - 1/(d*(3*e^(-2*d*x - 2*c) - 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) - 1))) - 4/3*b^3*(3*e^(-4*d*x - 4*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) - 4*e^(-6*d*x - 6*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) + 10*e^(-8*d*x - 8*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) - 4*e^(-10*d*x - 10*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)) + 3*e^(-12*d*x - 12*c)/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1)))","B",0
73,0,0,0,0.000000," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-6 \, a^{4} b {\left(\frac{-{\left(a - b\right)} \int \frac{1}{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a - b}\,{d x} + x}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{d x + c}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d}\right)} - 12 \, a^{2} b^{3} {\left(\frac{-{\left(a - b\right)} \int \frac{1}{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a - b}\,{d x} + x}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{d x + c}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d}\right)} + \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} - \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} + \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} - \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} + \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} - \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} - \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} + \frac{0 \, }{a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}} - \frac{{\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} - 24 \, {\left(a^{4} d e^{\left(4 \, c\right)} - 7 \, a^{3} b d e^{\left(4 \, c\right)} + 11 \, a^{2} b^{2} d e^{\left(4 \, c\right)} - 5 \, a b^{3} d e^{\left(4 \, c\right)}\right)} x e^{\left(4 \, d x\right)} - {\left(a^{4} e^{\left(8 \, c\right)} - 2 \, a^{2} b^{2} e^{\left(8 \, c\right)} + b^{4} e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(2 \, a^{4} e^{\left(6 \, c\right)} - 3 \, a^{3} b e^{\left(6 \, c\right)} - a^{2} b^{2} e^{\left(6 \, c\right)} + 3 \, a b^{3} e^{\left(6 \, c\right)} - b^{4} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - 4 \, {\left(2 \, a^{4} e^{\left(2 \, c\right)} + 7 \, a^{3} b e^{\left(2 \, c\right)} + 9 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 5 \, a b^{3} e^{\left(2 \, c\right)} + b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)} e^{\left(-4 \, d x\right)}}{64 \, {\left(a^{5} d e^{\left(4 \, c\right)} + a^{4} b d e^{\left(4 \, c\right)} - 2 \, a^{3} b^{2} d e^{\left(4 \, c\right)} - 2 \, a^{2} b^{3} d e^{\left(4 \, c\right)} + a b^{4} d e^{\left(4 \, c\right)} + b^{5} d e^{\left(4 \, c\right)}\right)}}"," ",0,"-6*a^4*b*(integrate(((a + b)*e^(4*d*x + 4*c) + 3*(a - b)*e^(2*d*x + 2*c) + 3*a + 3*b)*e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (d*x + c)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d)) - 12*a^2*b^3*(integrate(((a + b)*e^(4*d*x + 4*c) + 3*(a - b)*e^(2*d*x + 2*c) + 3*a + 3*b)*e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (d*x + c)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d)) + 10*a^4*b*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) - 20*a^3*b^2*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) + 20*a^2*b^3*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) - 4*a*b^4*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) + 8*a^4*b*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) - 4*a^3*b^2*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) - 8*a^2*b^3*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) + 4*a*b^4*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5) - 1/64*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 - 24*(a^4*d*e^(4*c) - 7*a^3*b*d*e^(4*c) + 11*a^2*b^2*d*e^(4*c) - 5*a*b^3*d*e^(4*c))*x*e^(4*d*x) - (a^4*e^(8*c) - 2*a^2*b^2*e^(8*c) + b^4*e^(8*c))*e^(8*d*x) + 4*(2*a^4*e^(6*c) - 3*a^3*b*e^(6*c) - a^2*b^2*e^(6*c) + 3*a*b^3*e^(6*c) - b^4*e^(6*c))*e^(6*d*x) - 4*(2*a^4*e^(2*c) + 7*a^3*b*e^(2*c) + 9*a^2*b^2*e^(2*c) + 5*a*b^3*e^(2*c) + b^4*e^(2*c))*e^(2*d*x))*e^(-4*d*x)/(a^5*d*e^(4*c) + a^4*b*d*e^(4*c) - 2*a^3*b^2*d*e^(4*c) - 2*a^2*b^3*d*e^(4*c) + a*b^4*d*e^(4*c) + b^5*d*e^(4*c))","F",0
74,0,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","\frac{{\left(a^{3} + a^{2} b - a b^{2} - b^{3} + {\left(a^{3} e^{\left(6 \, c\right)} - a^{2} b e^{\left(6 \, c\right)} - a b^{2} e^{\left(6 \, c\right)} + b^{3} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - 9 \, {\left(a^{3} e^{\left(4 \, c\right)} - 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} - b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - 9 \, {\left(a^{3} e^{\left(2 \, c\right)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 3 \, a b^{2} e^{\left(2 \, c\right)} + b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)} e^{\left(-3 \, d x\right)}}{24 \, {\left(a^{4} d e^{\left(3 \, c\right)} - 2 \, a^{2} b^{2} d e^{\left(3 \, c\right)} + b^{4} d e^{\left(3 \, c\right)}\right)}} - \frac{1}{8} \, \int \frac{16 \, {\left(3 \, {\left(a^{3} b e^{\left(5 \, c\right)} - a^{2} b^{2} e^{\left(5 \, c\right)} + a b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 2 \, {\left(a^{3} b e^{\left(3 \, c\right)} - a b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + 3 \, {\left(a^{3} b e^{c} + a^{2} b^{2} e^{c} + a b^{3} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5} + {\left(a^{5} e^{\left(6 \, c\right)} + a^{4} b e^{\left(6 \, c\right)} - 2 \, a^{3} b^{2} e^{\left(6 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(6 \, c\right)} + a b^{4} e^{\left(6 \, c\right)} + b^{5} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a^{5} e^{\left(4 \, c\right)} - a^{4} b e^{\left(4 \, c\right)} - 2 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 2 \, a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)} - b^{5} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)} - 2 \, a^{3} b^{2} e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} + a b^{4} e^{\left(2 \, c\right)} + b^{5} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/24*(a^3 + a^2*b - a*b^2 - b^3 + (a^3*e^(6*c) - a^2*b*e^(6*c) - a*b^2*e^(6*c) + b^3*e^(6*c))*e^(6*d*x) - 9*(a^3*e^(4*c) - 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) - b^3*e^(4*c))*e^(4*d*x) - 9*(a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 3*a*b^2*e^(2*c) + b^3*e^(2*c))*e^(2*d*x))*e^(-3*d*x)/(a^4*d*e^(3*c) - 2*a^2*b^2*d*e^(3*c) + b^4*d*e^(3*c)) - 1/8*integrate(16*(3*(a^3*b*e^(5*c) - a^2*b^2*e^(5*c) + a*b^3*e^(5*c))*e^(5*d*x) + 2*(a^3*b*e^(3*c) - a*b^3*e^(3*c))*e^(3*d*x) + 3*(a^3*b*e^c + a^2*b^2*e^c + a*b^3*e^c)*e^(d*x))/(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 + (a^5*e^(6*c) + a^4*b*e^(6*c) - 2*a^3*b^2*e^(6*c) - 2*a^2*b^3*e^(6*c) + a*b^4*e^(6*c) + b^5*e^(6*c))*e^(6*d*x) + 3*(a^5*e^(4*c) - a^4*b*e^(4*c) - 2*a^3*b^2*e^(4*c) + 2*a^2*b^3*e^(4*c) + a*b^4*e^(4*c) - b^5*e^(4*c))*e^(4*d*x) + 3*(a^5*e^(2*c) + a^4*b*e^(2*c) - 2*a^3*b^2*e^(2*c) - 2*a^2*b^3*e^(2*c) + a*b^4*e^(2*c) + b^5*e^(2*c))*e^(2*d*x)), x)","F",0
75,0,0,0,0.000000," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","4 \, a^{2} b {\left(\frac{-{\left(a - b\right)} \int \frac{1}{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a - b}\,{d x} + x}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{d x + c}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d}\right)} + 2 \, b^{3} {\left(\frac{-{\left(a - b\right)} \int \frac{1}{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a - b}\,{d x} + x}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{d x + c}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d}\right)} - \frac{0 \, }{a^{3} + a^{2} b - a b^{2} - b^{3}} + \frac{0 \, }{a^{3} + a^{2} b - a b^{2} - b^{3}} - \frac{0 \, }{a^{3} + a^{2} b - a b^{2} - b^{3}} - \frac{0 \, }{a^{3} + a^{2} b - a b^{2} - b^{3}} + \frac{0 \, }{a^{3} + a^{2} b - a b^{2} - b^{3}} - \frac{{\left(4 \, {\left(a^{2} d e^{\left(2 \, c\right)} - 3 \, a b d e^{\left(2 \, c\right)} + 2 \, b^{2} d e^{\left(2 \, c\right)}\right)} x e^{\left(2 \, d x\right)} + a^{2} + 2 \, a b + b^{2} - {\left(a^{2} e^{\left(4 \, c\right)} - b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)}\right)} e^{\left(-2 \, d x\right)}}{8 \, {\left(a^{3} d e^{\left(2 \, c\right)} + a^{2} b d e^{\left(2 \, c\right)} - a b^{2} d e^{\left(2 \, c\right)} - b^{3} d e^{\left(2 \, c\right)}\right)}}"," ",0,"4*a^2*b*(integrate(((a + b)*e^(4*d*x + 4*c) + 3*(a - b)*e^(2*d*x + 2*c) + 3*a + 3*b)*e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^4 - 2*a^2*b^2 + b^4) - (d*x + c)/((a^4 - 2*a^2*b^2 + b^4)*d)) + 2*b^3*(integrate(((a + b)*e^(4*d*x + 4*c) + 3*(a - b)*e^(2*d*x + 2*c) + 3*a + 3*b)*e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^4 - 2*a^2*b^2 + b^4) - (d*x + c)/((a^4 - 2*a^2*b^2 + b^4)*d)) - 8*a^2*b*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 + a^2*b - a*b^2 - b^3) + 8*a*b^2*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 + a^2*b - a*b^2 - b^3) - 2*b^3*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 + a^2*b - a*b^2 - b^3) - 4*a^2*b*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 + a^2*b - a*b^2 - b^3) + 4*b^3*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 + a^2*b - a*b^2 - b^3) - 1/8*(4*(a^2*d*e^(2*c) - 3*a*b*d*e^(2*c) + 2*b^2*d*e^(2*c))*x*e^(2*d*x) + a^2 + 2*a*b + b^2 - (a^2*e^(4*c) - b^2*e^(4*c))*e^(4*d*x))*e^(-2*d*x)/(a^3*d*e^(2*c) + a^2*b*d*e^(2*c) - a*b^2*d*e^(2*c) - b^3*d*e^(2*c))","F",0
76,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","\frac{{\left({\left(a e^{\left(2 \, c\right)} - b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a + b\right)} e^{\left(-d x\right)}}{2 \, {\left(a^{2} d e^{c} - b^{2} d e^{c}\right)}} + \frac{1}{2} \, \int \frac{4 \, {\left({\left(2 \, a b e^{\left(5 \, c\right)} - b^{2} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(2 \, a b e^{c} + b^{2} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{3} - a^{2} b - a b^{2} + b^{3} + {\left(a^{3} e^{\left(6 \, c\right)} + a^{2} b e^{\left(6 \, c\right)} - a b^{2} e^{\left(6 \, c\right)} - b^{3} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a^{3} e^{\left(4 \, c\right)} - a^{2} b e^{\left(4 \, c\right)} - a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/2*((a*e^(2*c) - b*e^(2*c))*e^(2*d*x) + a + b)*e^(-d*x)/(a^2*d*e^c - b^2*d*e^c) + 1/2*integrate(4*((2*a*b*e^(5*c) - b^2*e^(5*c))*e^(5*d*x) + (2*a*b*e^c + b^2*e^c)*e^(d*x))/(a^3 - a^2*b - a*b^2 + b^3 + (a^3*e^(6*c) + a^2*b*e^(6*c) - a*b^2*e^(6*c) - b^3*e^(6*c))*e^(6*d*x) + 3*(a^3*e^(4*c) - a^2*b*e^(4*c) - a*b^2*e^(4*c) + b^3*e^(4*c))*e^(4*d*x) + 3*(a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))*e^(2*d*x)), x)","F",0
77,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-\frac{\log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{a d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a d} - 2 \, \int \frac{b e^{\left(5 \, d x + 5 \, c\right)} - 2 \, b e^{\left(3 \, d x + 3 \, c\right)} + b e^{\left(d x + c\right)}}{a^{2} - a b + {\left(a^{2} e^{\left(6 \, c\right)} + a b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a^{2} e^{\left(4 \, c\right)} - a b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a^{2} e^{\left(2 \, c\right)} + a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-log((e^(d*x + c) + 1)*e^(-c))/(a*d) + log((e^(d*x + c) - 1)*e^(-c))/(a*d) - 2*integrate((b*e^(5*d*x + 5*c) - 2*b*e^(3*d*x + 3*c) + b*e^(d*x + c))/(a^2 - a*b + (a^2*e^(6*c) + a*b*e^(6*c))*e^(6*d*x) + 3*(a^2*e^(4*c) - a*b*e^(4*c))*e^(4*d*x) + 3*(a^2*e^(2*c) + a*b*e^(2*c))*e^(2*d*x)), x)","F",0
78,0,0,0,0.000000," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-\frac{2}{a d e^{\left(2 \, d x + 2 \, c\right)} - a d} - 4 \, \int \frac{b e^{\left(4 \, d x + 4 \, c\right)} - b e^{\left(2 \, d x + 2 \, c\right)}}{a^{2} - a b + {\left(a^{2} e^{\left(6 \, c\right)} + a b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a^{2} e^{\left(4 \, c\right)} - a b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a^{2} e^{\left(2 \, c\right)} + a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-2/(a*d*e^(2*d*x + 2*c) - a*d) - 4*integrate((b*e^(4*d*x + 4*c) - b*e^(2*d*x + 2*c))/(a^2 - a*b + (a^2*e^(6*c) + a*b*e^(6*c))*e^(6*d*x) + 3*(a^2*e^(4*c) - a*b*e^(4*c))*e^(4*d*x) + 3*(a^2*e^(2*c) + a*b*e^(2*c))*e^(2*d*x)), x)","F",0
79,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","-8 \, b \int \frac{e^{\left(3 \, d x + 3 \, c\right)}}{a^{2} - a b + {\left(a^{2} e^{\left(6 \, c\right)} + a b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a^{2} e^{\left(4 \, c\right)} - a b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a^{2} e^{\left(2 \, c\right)} + a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x} - \frac{e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}}{a d e^{\left(4 \, d x + 4 \, c\right)} - 2 \, a d e^{\left(2 \, d x + 2 \, c\right)} + a d} + \frac{\log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, a d} - \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, a d}"," ",0,"-8*b*integrate(e^(3*d*x + 3*c)/(a^2 - a*b + (a^2*e^(6*c) + a*b*e^(6*c))*e^(6*d*x) + 3*(a^2*e^(4*c) - a*b*e^(4*c))*e^(4*d*x) + 3*(a^2*e^(2*c) + a*b*e^(2*c))*e^(2*d*x)), x) - (e^(3*d*x + 3*c) + e^(d*x + c))/(a*d*e^(4*d*x + 4*c) - 2*a*d*e^(2*d*x + 2*c) + a*d) + 1/2*log((e^(d*x + c) + 1)*e^(-c))/(a*d) - 1/2*log((e^(d*x + c) - 1)*e^(-c))/(a*d)","F",0
80,0,0,0,0.000000," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^3),x, algorithm=""maxima"")","2 \, a b {\left(\frac{-{\left(a - b\right)} \int \frac{1}{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a - b}\,{d x} + x}{a^{3} - a^{2} b} - \frac{d x + c}{{\left(a^{3} - a^{2} b\right)} d}\right)} - 2 \, b^{2} {\left(\frac{-{\left(a - b\right)} \int \frac{1}{{\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(a e^{\left(4 \, c\right)} - b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a - b}\,{d x} + x}{a^{3} - a^{2} b} - \frac{d x + c}{{\left(a^{3} - a^{2} b\right)} d}\right)} + \frac{0 \, }{a} + \frac{0 \, }{a^{2}} - \frac{0 \, }{a} - \frac{0 \, }{a^{2}} + \frac{2 \, {\left(3 \, b d x e^{\left(6 \, d x + 6 \, c\right)} - 9 \, b d x e^{\left(4 \, d x + 4 \, c\right)} - 3 \, b d x + 3 \, {\left(3 \, b d x e^{\left(2 \, c\right)} - 2 \, a e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + 2 \, a\right)}}{3 \, {\left(a^{2} d e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} d e^{\left(2 \, d x + 2 \, c\right)} - a^{2} d\right)}} - \frac{b \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{a^{2} d} - \frac{b \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a^{2} d}"," ",0,"2*a*b*(integrate(((a + b)*e^(4*d*x + 4*c) + 3*(a - b)*e^(2*d*x + 2*c) + 3*a + 3*b)*e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 - a^2*b) - (d*x + c)/((a^3 - a^2*b)*d)) - 2*b^2*(integrate(((a + b)*e^(4*d*x + 4*c) + 3*(a - b)*e^(2*d*x + 2*c) + 3*a + 3*b)*e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/(a^3 - a^2*b) - (d*x + c)/((a^3 - a^2*b)*d)) + 2*b*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/a + 2*b^2*integrate(e^(4*d*x + 4*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/a^2 - 8*b*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/a - 4*b^2*integrate(e^(2*d*x + 2*c)/((a + b)*e^(6*d*x + 6*c) + 3*(a - b)*e^(4*d*x + 4*c) + 3*(a + b)*e^(2*d*x + 2*c) + a - b), x)/a^2 + 2/3*(3*b*d*x*e^(6*d*x + 6*c) - 9*b*d*x*e^(4*d*x + 4*c) - 3*b*d*x + 3*(3*b*d*x*e^(2*c) - 2*a*e^(2*c))*e^(2*d*x) + 2*a)/(a^2*d*e^(6*d*x + 6*c) - 3*a^2*d*e^(4*d*x + 4*c) + 3*a^2*d*e^(2*d*x + 2*c) - a^2*d) - b*log((e^(d*x + c) + 1)*e^(-c))/(a^2*d) - b*log((e^(d*x + c) - 1)*e^(-c))/(a^2*d)","F",0
81,1,104,0,0.348615," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{64} \, a {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} + \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} - \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} - \frac{1}{64} \, b {\left(\frac{8 \, {\left(d x + c\right)}}{d} - \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} + \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)}"," ",0,"1/64*a*(24*x + e^(4*d*x + 4*c)/d + 8*e^(2*d*x + 2*c)/d - 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) - 1/64*b*(8*(d*x + c)/d - e^(4*d*x + 4*c)/d + e^(-4*d*x - 4*c)/d)","A",0
82,1,83,0,0.344139," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{b {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{3}}{24 \, d} + \frac{1}{24} \, a {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} + \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} - \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"1/24*b*(e^(d*x + c) - e^(-d*x - c))^3/d + 1/24*a*(e^(3*d*x + 3*c)/d + 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d - e^(-3*d*x - 3*c)/d)","B",0
83,1,69,0,0.322256," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(4 \, x + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{8} \, b {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)}"," ",0,"1/8*a*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) - 1/8*b*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d)","B",0
84,1,55,0,0.440104," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{4 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(d x + c\right)}}{d} - \frac{e^{\left(-d x - c\right)}}{d}\right)} + \frac{a \sinh\left(d x + c\right)}{d}"," ",0,"1/2*b*(4*arctan(e^(-d*x - c))/d + e^(d*x + c)/d - e^(-d*x - c)/d) + a*sinh(d*x + c)/d","B",0
85,1,80,0,0.425869," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a \arctan\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"-b*(arctan(e^(-d*x - c))/d + (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a*arctan(sinh(d*x + c))/d","B",0
86,1,34,0,0.344050," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \tanh\left(d x + c\right)^{3}}{3 \, d} + \frac{2 \, a}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"1/3*b*tanh(d*x + c)^3/d + 2*a/(d*(e^(-2*d*x - 2*c) + 1))","A",0
87,1,181,0,0.438390," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{1}{4} \, b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - 7 \, e^{\left(-3 \, d x - 3 \, c\right)} + 7 \, e^{\left(-5 \, d x - 5 \, c\right)} - e^{\left(-7 \, d x - 7 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} - a {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)}"," ",0,"-1/4*b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - 7*e^(-3*d*x - 3*c) + 7*e^(-5*d*x - 5*c) - e^(-7*d*x - 7*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) - a*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1)))","B",0
88,1,371,0,0.347064," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{4}{15} \, b {\left(\frac{5 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{5 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{15 \, e^{\left(-6 \, d x - 6 \, c\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)}} + \frac{1}{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{4}{3} \, a {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} + \frac{1}{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)}"," ",0,"4/15*b*(5*e^(-2*d*x - 2*c)/(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)) - 5*e^(-4*d*x - 4*c)/(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)) + 15*e^(-6*d*x - 6*c)/(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)) + 1/(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))) + 4/3*a*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)))","B",0
89,1,171,0,0.360681," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{64} \, a^{2} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} + \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} - \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{64} \, b^{2} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} - \frac{1}{32} \, a b {\left(\frac{8 \, {\left(d x + c\right)}}{d} - \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} + \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)}"," ",0,"1/64*a^2*(24*x + e^(4*d*x + 4*c)/d + 8*e^(2*d*x + 2*c)/d - 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/64*b^2*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) - 1/32*a*b*(8*(d*x + c)/d - e^(4*d*x + 4*c)/d + e^(-4*d*x - 4*c)/d)","B",0
90,1,161,0,0.501514," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{a b {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{3}}{12 \, d} - \frac{1}{24} \, b^{2} {\left(\frac{{\left(15 \, e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)} e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{15 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{48 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d}\right)} + \frac{1}{24} \, a^{2} {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} + \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} - \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"1/12*a*b*(e^(d*x + c) - e^(-d*x - c))^3/d - 1/24*b^2*((15*e^(-2*d*x - 2*c) - 1)*e^(3*d*x + 3*c)/d - (15*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + 48*arctan(e^(-d*x - c))/d) + 1/24*a^2*(e^(3*d*x + 3*c)/d + 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d - e^(-3*d*x - 3*c)/d)","B",0
91,1,140,0,0.340211," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} {\left(4 \, x + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{4} \, a b {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{8} \, b^{2} {\left(\frac{12 \, {\left(d x + c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{17 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)}\right)}}\right)}"," ",0,"1/8*a^2*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) - 1/4*a*b*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/8*b^2*(12*(d*x + c)/d + e^(-2*d*x - 2*c)/d - (17*e^(-2*d*x - 2*c) + 1)/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c))))","B",0
92,1,152,0,0.445991," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} {\left(\frac{6 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)}}{d} + \frac{4 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + a b {\left(\frac{4 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(d x + c\right)}}{d} - \frac{e^{\left(-d x - c\right)}}{d}\right)} + \frac{a^{2} \sinh\left(d x + c\right)}{d}"," ",0,"1/2*b^2*(6*arctan(e^(-d*x - c))/d - e^(-d*x - c)/d + (4*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + 1)/(d*(e^(-d*x - c) + 2*e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + a*b*(4*arctan(e^(-d*x - c))/d + e^(d*x + c)/d - e^(-d*x - c)/d) + a^2*sinh(d*x + c)/d","B",0
93,1,199,0,0.460505," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, b^{2} {\left(\frac{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{5 \, e^{\left(-d x - c\right)} - 3 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)} - 5 \, e^{\left(-7 \, d x - 7 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} - 2 \, a b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a^{2} \arctan\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"-1/4*b^2*(3*arctan(e^(-d*x - c))/d + (5*e^(-d*x - c) - 3*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c) - 5*e^(-7*d*x - 7*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) - 2*a*b*(arctan(e^(-d*x - c))/d + (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a^2*arctan(sinh(d*x + c))/d","B",0
94,1,53,0,0.329496," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{b^{2} \tanh\left(d x + c\right)^{5}}{5 \, d} + \frac{2 \, a b \tanh\left(d x + c\right)^{3}}{3 \, d} + \frac{2 \, a^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"1/5*b^2*tanh(d*x + c)^5/d + 2/3*a*b*tanh(d*x + c)^3/d + 2*a^2/(d*(e^(-2*d*x - 2*c) + 1))","A",0
95,1,345,0,0.426128," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{1}{24} \, b^{2} {\left(\frac{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{3 \, e^{\left(-d x - c\right)} - 47 \, e^{\left(-3 \, d x - 3 \, c\right)} + 78 \, e^{\left(-5 \, d x - 5 \, c\right)} - 78 \, e^{\left(-7 \, d x - 7 \, c\right)} + 47 \, e^{\left(-9 \, d x - 9 \, c\right)} - 3 \, e^{\left(-11 \, d x - 11 \, c\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} + 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} + 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} - \frac{1}{2} \, a b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - 7 \, e^{\left(-3 \, d x - 3 \, c\right)} + 7 \, e^{\left(-5 \, d x - 5 \, c\right)} - e^{\left(-7 \, d x - 7 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} - a^{2} {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)}"," ",0,"-1/24*b^2*(3*arctan(e^(-d*x - c))/d - (3*e^(-d*x - c) - 47*e^(-3*d*x - 3*c) + 78*e^(-5*d*x - 5*c) - 78*e^(-7*d*x - 7*c) + 47*e^(-9*d*x - 9*c) - 3*e^(-11*d*x - 11*c))/(d*(6*e^(-2*d*x - 2*c) + 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) + 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c) + 1))) - 1/2*a*b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - 7*e^(-3*d*x - 3*c) + 7*e^(-5*d*x - 5*c) - e^(-7*d*x - 7*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) - a^2*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1)))","B",0
96,1,928,0,0.341814," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{4}{35} \, b^{2} {\left(\frac{7 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{14 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{70 \, e^{\left(-6 \, d x - 6 \, c\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)}} - \frac{35 \, e^{\left(-8 \, d x - 8 \, c\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)}} + \frac{35 \, e^{\left(-10 \, d x - 10 \, c\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)}} + \frac{1}{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{8}{15} \, a b {\left(\frac{5 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{5 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{15 \, e^{\left(-6 \, d x - 6 \, c\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)}} + \frac{1}{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{4}{3} \, a^{2} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} + \frac{1}{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)}"," ",0,"4/35*b^2*(7*e^(-2*d*x - 2*c)/(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)) - 14*e^(-4*d*x - 4*c)/(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)) + 70*e^(-6*d*x - 6*c)/(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)) - 35*e^(-8*d*x - 8*c)/(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)) + 35*e^(-10*d*x - 10*c)/(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)) + 1/(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))) + 8/15*a*b*(5*e^(-2*d*x - 2*c)/(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)) - 5*e^(-4*d*x - 4*c)/(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)) + 15*e^(-6*d*x - 6*c)/(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)) + 1/(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))) + 4/3*a^2*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)))","B",0
97,1,267,0,0.328859," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{64} \, a^{3} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} + \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} - \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{3}{64} \, a b^{2} {\left(24 \, x + \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} - \frac{8 \, e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{8 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)} + \frac{1}{64} \, b^{3} {\left(\frac{120 \, {\left(d x + c\right)}}{d} + \frac{16 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)}}{d} - \frac{15 \, e^{\left(-2 \, d x - 2 \, c\right)} + 144 \, e^{\left(-4 \, d x - 4 \, c\right)} - 1}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}\right)} - \frac{3}{64} \, a^{2} b {\left(\frac{8 \, {\left(d x + c\right)}}{d} - \frac{e^{\left(4 \, d x + 4 \, c\right)}}{d} + \frac{e^{\left(-4 \, d x - 4 \, c\right)}}{d}\right)}"," ",0,"1/64*a^3*(24*x + e^(4*d*x + 4*c)/d + 8*e^(2*d*x + 2*c)/d - 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 3/64*a*b^2*(24*x + e^(4*d*x + 4*c)/d - 8*e^(2*d*x + 2*c)/d + 8*e^(-2*d*x - 2*c)/d - e^(-4*d*x - 4*c)/d) + 1/64*b^3*(120*(d*x + c)/d + (16*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c))/d - (15*e^(-2*d*x - 2*c) + 144*e^(-4*d*x - 4*c) - 1)/(d*(e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c)))) - 3/64*a^2*b*(8*(d*x + c)/d - e^(4*d*x + 4*c)/d + e^(-4*d*x - 4*c)/d)","B",0
98,1,284,0,0.430583," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{a^{2} b {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{3}}{8 \, d} - \frac{1}{8} \, a b^{2} {\left(\frac{{\left(15 \, e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)} e^{\left(3 \, d x + 3 \, c\right)}}{d} - \frac{15 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} + \frac{48 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d}\right)} + \frac{1}{24} \, b^{3} {\left(\frac{27 \, e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d} - \frac{120 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{25 \, e^{\left(-2 \, d x - 2 \, c\right)} + 77 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} - 1}{d {\left(e^{\left(-3 \, d x - 3 \, c\right)} + 2 \, e^{\left(-5 \, d x - 5 \, c\right)} + e^{\left(-7 \, d x - 7 \, c\right)}\right)}}\right)} + \frac{1}{24} \, a^{3} {\left(\frac{e^{\left(3 \, d x + 3 \, c\right)}}{d} + \frac{9 \, e^{\left(d x + c\right)}}{d} - \frac{9 \, e^{\left(-d x - c\right)}}{d} - \frac{e^{\left(-3 \, d x - 3 \, c\right)}}{d}\right)}"," ",0,"1/8*a^2*b*(e^(d*x + c) - e^(-d*x - c))^3/d - 1/8*a*b^2*((15*e^(-2*d*x - 2*c) - 1)*e^(3*d*x + 3*c)/d - (15*e^(-d*x - c) - e^(-3*d*x - 3*c))/d + 48*arctan(e^(-d*x - c))/d) + 1/24*b^3*((27*e^(-d*x - c) - e^(-3*d*x - 3*c))/d - 120*arctan(e^(-d*x - c))/d - (25*e^(-2*d*x - 2*c) + 77*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) - 1)/(d*(e^(-3*d*x - 3*c) + 2*e^(-5*d*x - 5*c) + e^(-7*d*x - 7*c)))) + 1/24*a^3*(e^(3*d*x + 3*c)/d + 9*e^(d*x + c)/d - 9*e^(-d*x - c)/d - e^(-3*d*x - 3*c)/d)","B",0
99,1,256,0,0.409902," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a^{3} {\left(4 \, x + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{3}{8} \, a^{2} b {\left(4 \, x - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d}\right)} - \frac{1}{24} \, b^{3} {\left(\frac{60 \, {\left(d x + c\right)}}{d} + \frac{3 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{121 \, e^{\left(-2 \, d x - 2 \, c\right)} + 201 \, e^{\left(-4 \, d x - 4 \, c\right)} + 147 \, e^{\left(-6 \, d x - 6 \, c\right)} + 3}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)}\right)}}\right)} - \frac{3}{8} \, a b^{2} {\left(\frac{12 \, {\left(d x + c\right)}}{d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{d} - \frac{17 \, e^{\left(-2 \, d x - 2 \, c\right)} + 1}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)}\right)}}\right)}"," ",0,"1/8*a^3*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) - 3/8*a^2*b*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) - 1/24*b^3*(60*(d*x + c)/d + 3*e^(-2*d*x - 2*c)/d - (121*e^(-2*d*x - 2*c) + 201*e^(-4*d*x - 4*c) + 147*e^(-6*d*x - 6*c) + 3)/(d*(e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + 3*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c)))) - 3/8*a*b^2*(12*(d*x + c)/d + e^(-2*d*x - 2*c)/d - (17*e^(-2*d*x - 2*c) + 1)/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c))))","B",0
100,1,295,0,0.698071," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{4} \, b^{3} {\left(\frac{15 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{2 \, e^{\left(-d x - c\right)}}{d} + \frac{17 \, e^{\left(-2 \, d x - 2 \, c\right)} + 13 \, e^{\left(-4 \, d x - 4 \, c\right)} + 7 \, e^{\left(-6 \, d x - 6 \, c\right)} - 7 \, e^{\left(-8 \, d x - 8 \, c\right)} + 2}{d {\left(e^{\left(-d x - c\right)} + 4 \, e^{\left(-3 \, d x - 3 \, c\right)} + 6 \, e^{\left(-5 \, d x - 5 \, c\right)} + 4 \, e^{\left(-7 \, d x - 7 \, c\right)} + e^{\left(-9 \, d x - 9 \, c\right)}\right)}}\right)} + \frac{3}{2} \, a b^{2} {\left(\frac{6 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)}}{d} + \frac{4 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + 1}{d {\left(e^{\left(-d x - c\right)} + 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + e^{\left(-5 \, d x - 5 \, c\right)}\right)}}\right)} + \frac{3}{2} \, a^{2} b {\left(\frac{4 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(d x + c\right)}}{d} - \frac{e^{\left(-d x - c\right)}}{d}\right)} + \frac{a^{3} \sinh\left(d x + c\right)}{d}"," ",0,"1/4*b^3*(15*arctan(e^(-d*x - c))/d - 2*e^(-d*x - c)/d + (17*e^(-2*d*x - 2*c) + 13*e^(-4*d*x - 4*c) + 7*e^(-6*d*x - 6*c) - 7*e^(-8*d*x - 8*c) + 2)/(d*(e^(-d*x - c) + 4*e^(-3*d*x - 3*c) + 6*e^(-5*d*x - 5*c) + 4*e^(-7*d*x - 7*c) + e^(-9*d*x - 9*c)))) + 3/2*a*b^2*(6*arctan(e^(-d*x - c))/d - e^(-d*x - c)/d + (4*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + 1)/(d*(e^(-d*x - c) + 2*e^(-3*d*x - 3*c) + e^(-5*d*x - 5*c)))) + 3/2*a^2*b*(4*arctan(e^(-d*x - c))/d + e^(d*x + c)/d - e^(-d*x - c)/d) + a^3*sinh(d*x + c)/d","B",0
101,1,362,0,0.432243," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{24} \, b^{3} {\left(\frac{15 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{33 \, e^{\left(-d x - c\right)} - 5 \, e^{\left(-3 \, d x - 3 \, c\right)} + 90 \, e^{\left(-5 \, d x - 5 \, c\right)} - 90 \, e^{\left(-7 \, d x - 7 \, c\right)} + 5 \, e^{\left(-9 \, d x - 9 \, c\right)} - 33 \, e^{\left(-11 \, d x - 11 \, c\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} + 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} + 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} - \frac{3}{4} \, a b^{2} {\left(\frac{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{5 \, e^{\left(-d x - c\right)} - 3 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)} - 5 \, e^{\left(-7 \, d x - 7 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} - 3 \, a^{2} b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a^{3} \arctan\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"-1/24*b^3*(15*arctan(e^(-d*x - c))/d + (33*e^(-d*x - c) - 5*e^(-3*d*x - 3*c) + 90*e^(-5*d*x - 5*c) - 90*e^(-7*d*x - 7*c) + 5*e^(-9*d*x - 9*c) - 33*e^(-11*d*x - 11*c))/(d*(6*e^(-2*d*x - 2*c) + 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) + 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c) + 1))) - 3/4*a*b^2*(3*arctan(e^(-d*x - c))/d + (5*e^(-d*x - c) - 3*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c) - 5*e^(-7*d*x - 7*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) - 3*a^2*b*(arctan(e^(-d*x - c))/d + (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a^3*arctan(sinh(d*x + c))/d","B",0
102,1,71,0,0.325147," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{b^{3} \tanh\left(d x + c\right)^{7}}{7 \, d} + \frac{3 \, a b^{2} \tanh\left(d x + c\right)^{5}}{5 \, d} + \frac{a^{2} b \tanh\left(d x + c\right)^{3}}{d} + \frac{2 \, a^{3}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"1/7*b^3*tanh(d*x + c)^7/d + 3/5*a*b^2*tanh(d*x + c)^5/d + a^2*b*tanh(d*x + c)^3/d + 2*a^3/(d*(e^(-2*d*x - 2*c) + 1))","A",0
103,1,553,0,0.693017," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{192} \, b^{3} {\left(\frac{15 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{15 \, e^{\left(-d x - c\right)} - 397 \, e^{\left(-3 \, d x - 3 \, c\right)} + 895 \, e^{\left(-5 \, d x - 5 \, c\right)} - 1765 \, e^{\left(-7 \, d x - 7 \, c\right)} + 1765 \, e^{\left(-9 \, d x - 9 \, c\right)} - 895 \, e^{\left(-11 \, d x - 11 \, c\right)} + 397 \, e^{\left(-13 \, d x - 13 \, c\right)} - 15 \, e^{\left(-15 \, d x - 15 \, c\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)} - \frac{1}{8} \, a b^{2} {\left(\frac{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{3 \, e^{\left(-d x - c\right)} - 47 \, e^{\left(-3 \, d x - 3 \, c\right)} + 78 \, e^{\left(-5 \, d x - 5 \, c\right)} - 78 \, e^{\left(-7 \, d x - 7 \, c\right)} + 47 \, e^{\left(-9 \, d x - 9 \, c\right)} - 3 \, e^{\left(-11 \, d x - 11 \, c\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} + 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} + 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} - \frac{3}{4} \, a^{2} b {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - 7 \, e^{\left(-3 \, d x - 3 \, c\right)} + 7 \, e^{\left(-5 \, d x - 5 \, c\right)} - e^{\left(-7 \, d x - 7 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} - a^{3} {\left(\frac{\arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{e^{\left(-d x - c\right)} - e^{\left(-3 \, d x - 3 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)}"," ",0,"-1/192*b^3*(15*arctan(e^(-d*x - c))/d - (15*e^(-d*x - c) - 397*e^(-3*d*x - 3*c) + 895*e^(-5*d*x - 5*c) - 1765*e^(-7*d*x - 7*c) + 1765*e^(-9*d*x - 9*c) - 895*e^(-11*d*x - 11*c) + 397*e^(-13*d*x - 13*c) - 15*e^(-15*d*x - 15*c))/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1))) - 1/8*a*b^2*(3*arctan(e^(-d*x - c))/d - (3*e^(-d*x - c) - 47*e^(-3*d*x - 3*c) + 78*e^(-5*d*x - 5*c) - 78*e^(-7*d*x - 7*c) + 47*e^(-9*d*x - 9*c) - 3*e^(-11*d*x - 11*c))/(d*(6*e^(-2*d*x - 2*c) + 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) + 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c) + 1))) - 3/4*a^2*b*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - 7*e^(-3*d*x - 3*c) + 7*e^(-5*d*x - 5*c) - e^(-7*d*x - 7*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) - a^3*(arctan(e^(-d*x - c))/d - (e^(-d*x - c) - e^(-3*d*x - 3*c))/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1)))","B",0
104,1,1847,0,0.349822," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{4}{63} \, b^{3} {\left(\frac{9 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{27 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{189 \, e^{\left(-6 \, d x - 6 \, c\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)}} - \frac{189 \, e^{\left(-8 \, d x - 8 \, c\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)}} + \frac{315 \, e^{\left(-10 \, d x - 10 \, c\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)}} - \frac{105 \, e^{\left(-12 \, d x - 12 \, c\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)}} + \frac{63 \, e^{\left(-14 \, d x - 14 \, c\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)}} + \frac{1}{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{12}{35} \, a b^{2} {\left(\frac{7 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{14 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{70 \, e^{\left(-6 \, d x - 6 \, c\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)}} - \frac{35 \, e^{\left(-8 \, d x - 8 \, c\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)}} + \frac{35 \, e^{\left(-10 \, d x - 10 \, c\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)}} + \frac{1}{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}{5} \, a^{2} b {\left(\frac{5 \, e^{\left(-2 \, d x - 2 \, c\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)}} - \frac{5 \, e^{\left(-4 \, d x - 4 \, c\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)}} + \frac{15 \, e^{\left(-6 \, d x - 6 \, c\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)}} + \frac{1}{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{4}{3} \, a^{3} {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, c\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)}} + \frac{1}{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)}"," ",0,"4/63*b^3*(9*e^(-2*d*x - 2*c)/(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)) - 27*e^(-4*d*x - 4*c)/(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)) + 189*e^(-6*d*x - 6*c)/(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)) - 189*e^(-8*d*x - 8*c)/(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)) + 315*e^(-10*d*x - 10*c)/(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)) - 105*e^(-12*d*x - 12*c)/(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)) + 63*e^(-14*d*x - 14*c)/(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/(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))) + 12/35*a*b^2*(7*e^(-2*d*x - 2*c)/(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)) - 14*e^(-4*d*x - 4*c)/(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)) + 70*e^(-6*d*x - 6*c)/(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)) - 35*e^(-8*d*x - 8*c)/(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)) + 35*e^(-10*d*x - 10*c)/(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)) + 1/(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))) + 4/5*a^2*b*(5*e^(-2*d*x - 2*c)/(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)) - 5*e^(-4*d*x - 4*c)/(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)) + 15*e^(-6*d*x - 6*c)/(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)) + 1/(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))) + 4/3*a^3*(3*e^(-2*d*x - 2*c)/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)) + 1/(d*(3*e^(-2*d*x - 2*c) + 3*e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c) + 1)))","B",0
105,1,514,0,0.509040," ","integrate(cosh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a b - b^{2}\right)} {\left(d x + c\right)}}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(8 \, b e^{\left(-2 \, d x - 2 \, c\right)} + a + b\right)} e^{\left(4 \, d x + 4 \, c\right)}}{64 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} - \frac{{\left(a^{2} b - 6 \, a b^{2} + 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^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{a b} d} + \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} - \frac{3 \, b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} {\left(a + b\right)} d} - \frac{8 \, b e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{3 \, {\left(d x + c\right)}}{8 \, {\left(a + b\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a + b\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a + b\right)} d}"," ",0,"-1/2*(a*b - b^2)*(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/64*(8*b*e^(-2*d*x - 2*c) + a + b)*e^(4*d*x + 4*c)/((a^2 + 2*a*b + b^2)*d) + 1/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) - 1/8*(a^2*b - 6*a*b^2 + b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt(a*b)*d) + 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) - 3/8*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) - 1/64*(8*b*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c))/((a^2 + 2*a*b + b^2)*d) + 3/8*(d*x + c)/((a + b)*d) + 1/8*e^(2*d*x + 2*c)/((a + b)*d) - 1/8*e^(-2*d*x - 2*c)/((a + b)*d)","B",0
106,0,0,0,0.000000," ","integrate(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left({\left(a e^{\left(6 \, c\right)} + b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 3 \, {\left(3 \, a e^{\left(4 \, c\right)} + 7 \, b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - 3 \, {\left(3 \, a e^{\left(2 \, c\right)} + 7 \, b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} - a - b\right)} e^{\left(-3 \, d x\right)}}{24 \, {\left(a^{2} d e^{\left(3 \, c\right)} + 2 \, a b d e^{\left(3 \, c\right)} + b^{2} d e^{\left(3 \, c\right)}\right)}} + \frac{1}{8} \, \int \frac{16 \, {\left(b^{2} e^{\left(3 \, d x + 3 \, c\right)} + b^{2} e^{\left(d x + c\right)}\right)}}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + {\left(a^{3} e^{\left(4 \, c\right)} + 3 \, a^{2} b e^{\left(4 \, c\right)} + 3 \, a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} + a^{2} b e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/24*((a*e^(6*c) + b*e^(6*c))*e^(6*d*x) + 3*(3*a*e^(4*c) + 7*b*e^(4*c))*e^(4*d*x) - 3*(3*a*e^(2*c) + 7*b*e^(2*c))*e^(2*d*x) - a - b)*e^(-3*d*x)/(a^2*d*e^(3*c) + 2*a*b*d*e^(3*c) + b^2*d*e^(3*c)) + 1/8*integrate(16*(b^2*e^(3*d*x + 3*c) + b^2*e^(d*x + c))/(a^3 + 3*a^2*b + 3*a*b^2 + b^3 + (a^3*e^(4*c) + 3*a^2*b*e^(4*c) + 3*a*b^2*e^(4*c) + b^3*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) + a^2*b*e^(2*c) - a*b^2*e^(2*c) - b^3*e^(2*c))*e^(2*d*x)), x)","F",0
107,1,316,0,0.615724," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} + \frac{{\left(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)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a b} d} - \frac{b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} {\left(a + b\right)} d} + \frac{d x + c}{2 \, {\left(a + b\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a + b\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a + b\right)} d}"," ",0,"1/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) + 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^2 + 2*a*b + b^2)*sqrt(a*b)*d) - 1/2*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) + 1/2*(d*x + c)/((a + b)*d) + 1/8*e^(2*d*x + 2*c)/((a + b)*d) - 1/8*e^(-2*d*x - 2*c)/((a + b)*d)","B",0
108,0,0,0,0.000000," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} e^{\left(-d x\right)}}{2 \, {\left(a d e^{c} + b d e^{c}\right)}} + \frac{1}{2} \, \int \frac{4 \, {\left(b e^{\left(3 \, d x + 3 \, c\right)} + b e^{\left(d x + c\right)}\right)}}{a^{2} + 2 \, a b + b^{2} + {\left(a^{2} e^{\left(4 \, c\right)} + 2 \, a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/2*(e^(2*d*x + 2*c) - 1)*e^(-d*x)/(a*d*e^c + b*d*e^c) + 1/2*integrate(4*(b*e^(3*d*x + 3*c) + b*e^(d*x + c))/(a^2 + 2*a*b + b^2 + (a^2*e^(4*c) + 2*a*b*e^(4*c) + b^2*e^(4*c))*e^(4*d*x) + 2*(a^2*e^(2*c) - b^2*e^(2*c))*e^(2*d*x)), x)","F",0
109,0,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\int \frac{\operatorname{sech}\left(d x + c\right)}{b \tanh\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(sech(d*x + c)/(b*tanh(d*x + c)^2 + a), x)","F",0
110,1,36,0,0.524589," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\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} d}"," ",0,"-arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*d)","A",0
111,0,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{2 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b d} + 8 \, \int \frac{{\left(a e^{\left(3 \, c\right)} + b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a e^{c} + b e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a b + b^{2} + {\left(a b e^{\left(4 \, c\right)} + b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a b e^{\left(2 \, c\right)} - b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-2*arctan(e^(d*x + c))/(b*d) + 8*integrate(1/4*((a*e^(3*c) + b*e^(3*c))*e^(3*d*x) + (a*e^c + b*e^c)*e^(d*x))/(a*b + b^2 + (a*b*e^(4*c) + b^2*e^(4*c))*e^(4*d*x) + 2*(a*b*e^(2*c) - b^2*e^(2*c))*e^(2*d*x)), x)","F",0
112,1,63,0,0.448626," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a + b\right)} \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} b d} - \frac{2}{{\left(b e^{\left(-2 \, d x - 2 \, c\right)} + b\right)} d}"," ",0,"-(a + b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*b*d) - 2/((b*e^(-2*d*x - 2*c) + b)*d)","A",0
113,0,0,0,0.000000," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{e^{\left(3 \, d x + 3 \, c\right)} - e^{\left(d x + c\right)}}{b d e^{\left(4 \, d x + 4 \, c\right)} + 2 \, b d e^{\left(2 \, d x + 2 \, c\right)} + b d} - \frac{{\left(2 \, a e^{c} + 3 \, b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)}}{b^{2} d} + 32 \, \int \frac{{\left(a^{2} e^{\left(3 \, c\right)} + 2 \, a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{2} e^{c} + 2 \, a b e^{c} + b^{2} e^{c}\right)} e^{\left(d x\right)}}{16 \, {\left(a b^{2} + b^{3} + {\left(a b^{2} e^{\left(4 \, c\right)} + b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a b^{2} e^{\left(2 \, c\right)} - b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-(e^(3*d*x + 3*c) - e^(d*x + c))/(b*d*e^(4*d*x + 4*c) + 2*b*d*e^(2*d*x + 2*c) + b*d) - (2*a*e^c + 3*b*e^c)*arctan(e^(d*x + c))*e^(-c)/(b^2*d) + 32*integrate(1/16*((a^2*e^(3*c) + 2*a*b*e^(3*c) + b^2*e^(3*c))*e^(3*d*x) + (a^2*e^c + 2*a*b*e^c + b^2*e^c)*e^(d*x))/(a*b^2 + b^3 + (a*b^2*e^(4*c) + b^3*e^(4*c))*e^(4*d*x) + 2*(a*b^2*e^(2*c) - b^3*e^(2*c))*e^(2*d*x)), x)","F",0
114,1,140,0,0.455950," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(6 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, a + 5 \, b\right)}}{3 \, {\left(3 \, b^{2} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, b^{2} e^{\left(-4 \, d x - 4 \, c\right)} + b^{2} e^{\left(-6 \, d x - 6 \, c\right)} + b^{2}\right)} d} - \frac{{\left(a^{2} + 2 \, 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)}{\sqrt{a b} b^{2} d}"," ",0,"-2/3*(6*(a + 2*b)*e^(-2*d*x - 2*c) + 3*(a + b)*e^(-4*d*x - 4*c) + 3*a + 5*b)/((3*b^2*e^(-2*d*x - 2*c) + 3*b^2*e^(-4*d*x - 4*c) + b^2*e^(-6*d*x - 6*c) + b^2)*d) - (a^2 + 2*a*b + b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*b^2*d)","B",0
115,0,0,0,0.000000," ","integrate(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} e^{\left(10 \, c\right)} + 2 \, a^{2} b e^{\left(10 \, c\right)} + a b^{2} e^{\left(10 \, c\right)}\right)} e^{\left(10 \, d x\right)} - {\left(11 \, a^{3} e^{\left(8 \, c\right)} + 42 \, a^{2} b e^{\left(8 \, c\right)} + 31 \, a b^{2} e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - 2 \, {\left(5 \, a^{3} e^{\left(6 \, c\right)} + 4 \, a^{2} b e^{\left(6 \, c\right)} - 49 \, a b^{2} e^{\left(6 \, c\right)} + 12 \, b^{3} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(5 \, a^{3} e^{\left(4 \, c\right)} + 4 \, a^{2} b e^{\left(4 \, c\right)} - 49 \, a b^{2} e^{\left(4 \, c\right)} + 12 \, b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + {\left(11 \, a^{3} e^{\left(2 \, c\right)} + 42 \, a^{2} b e^{\left(2 \, c\right)} + 31 \, a b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{24 \, {\left({\left(a^{5} d e^{\left(7 \, c\right)} + 4 \, a^{4} b d e^{\left(7 \, c\right)} + 6 \, a^{3} b^{2} d e^{\left(7 \, c\right)} + 4 \, a^{2} b^{3} d e^{\left(7 \, c\right)} + a b^{4} d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(a^{5} d e^{\left(5 \, c\right)} + 2 \, a^{4} b d e^{\left(5 \, c\right)} - 2 \, a^{2} b^{3} d e^{\left(5 \, c\right)} - a b^{4} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(a^{5} d e^{\left(3 \, c\right)} + 4 \, a^{4} b d e^{\left(3 \, c\right)} + 6 \, a^{3} b^{2} d e^{\left(3 \, c\right)} + 4 \, a^{2} b^{3} d e^{\left(3 \, c\right)} + a b^{4} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)}\right)}} + \frac{1}{8} \, \int \frac{8 \, {\left({\left(6 \, a b^{2} e^{\left(3 \, c\right)} + b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(6 \, a b^{2} e^{c} + b^{3} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} e^{\left(4 \, c\right)} + 4 \, a^{4} b e^{\left(4 \, c\right)} + 6 \, a^{3} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{5} e^{\left(2 \, c\right)} + 2 \, a^{4} b e^{\left(2 \, c\right)} - 2 \, a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-1/24*(a^3 + 2*a^2*b + a*b^2 - (a^3*e^(10*c) + 2*a^2*b*e^(10*c) + a*b^2*e^(10*c))*e^(10*d*x) - (11*a^3*e^(8*c) + 42*a^2*b*e^(8*c) + 31*a*b^2*e^(8*c))*e^(8*d*x) - 2*(5*a^3*e^(6*c) + 4*a^2*b*e^(6*c) - 49*a*b^2*e^(6*c) + 12*b^3*e^(6*c))*e^(6*d*x) + 2*(5*a^3*e^(4*c) + 4*a^2*b*e^(4*c) - 49*a*b^2*e^(4*c) + 12*b^3*e^(4*c))*e^(4*d*x) + (11*a^3*e^(2*c) + 42*a^2*b*e^(2*c) + 31*a*b^2*e^(2*c))*e^(2*d*x))/((a^5*d*e^(7*c) + 4*a^4*b*d*e^(7*c) + 6*a^3*b^2*d*e^(7*c) + 4*a^2*b^3*d*e^(7*c) + a*b^4*d*e^(7*c))*e^(7*d*x) + 2*(a^5*d*e^(5*c) + 2*a^4*b*d*e^(5*c) - 2*a^2*b^3*d*e^(5*c) - a*b^4*d*e^(5*c))*e^(5*d*x) + (a^5*d*e^(3*c) + 4*a^4*b*d*e^(3*c) + 6*a^3*b^2*d*e^(3*c) + 4*a^2*b^3*d*e^(3*c) + a*b^4*d*e^(3*c))*e^(3*d*x)) + 1/8*integrate(8*((6*a*b^2*e^(3*c) + b^3*e^(3*c))*e^(3*d*x) + (6*a*b^2*e^c + b^3*e^c)*e^(d*x))/(a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5*e^(4*c) + 4*a^4*b*e^(4*c) + 6*a^3*b^2*e^(4*c) + 4*a^2*b^3*e^(4*c) + a*b^4*e^(4*c))*e^(4*d*x) + 2*(a^5*e^(2*c) + 2*a^4*b*e^(2*c) - 2*a^2*b^3*e^(2*c) - a*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
116,1,840,0,0.704178," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{{\left(3 \, a^{2} b - 6 \, a b^{2} - 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} + \frac{{\left(3 \, a^{2} b - 6 \, a b^{2} - 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^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} - \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)}{4 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b} d} + \frac{a^{2} b - b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{2} b - b^{3} + {\left(a^{2} b - 6 \, a b^{2} + b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{5} + 4 \, a^{4} b + 6 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{a b + b^{2} + {\left(a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{2 \, {\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}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"1/2*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/2*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/8*(3*a^2*b - 6*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)*d) + 1/8*(3*a^2*b - 6*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sqrt(a*b)*d) - 1/4*(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) + 1/4*(a^2*b - b^3 + (a^2*b - 6*a*b^2 + b^3)*e^(2*d*x + 2*c))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*e^(4*d*x + 4*c) + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*e^(2*d*x + 2*c))*d) - 1/4*(a^2*b - b^3 + (a^2*b - 6*a*b^2 + b^3)*e^(-2*d*x - 2*c))/((a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*e^(-2*d*x - 2*c) + (a^5 + 4*a^4*b + 6*a^3*b^2 + 4*a^2*b^3 + a*b^4)*e^(-4*d*x - 4*c))*d) + 1/2*(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) + 1/2*(d*x + c)/((a^2 + 2*a*b + b^2)*d) + 1/8*e^(2*d*x + 2*c)/((a^2 + 2*a*b + b^2)*d) - 1/8*e^(-2*d*x - 2*c)/((a^2 + 2*a*b + b^2)*d)","B",0
117,0,0,0,0.000000," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{a^{2} + a b - {\left(a^{2} e^{\left(6 \, c\right)} + a b e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - {\left(a^{2} e^{\left(4 \, c\right)} - 3 \, a b e^{\left(4 \, c\right)} + 2 \, b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + {\left(a^{2} e^{\left(2 \, c\right)} - 3 \, a b e^{\left(2 \, c\right)} + 2 \, b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{2 \, {\left({\left(a^{4} d e^{\left(5 \, c\right)} + 3 \, a^{3} b d e^{\left(5 \, c\right)} + 3 \, a^{2} b^{2} d e^{\left(5 \, c\right)} + a b^{3} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 2 \, {\left(a^{4} d e^{\left(3 \, c\right)} + a^{3} b d e^{\left(3 \, c\right)} - a^{2} b^{2} d e^{\left(3 \, c\right)} - a b^{3} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{4} d e^{c} + 3 \, a^{3} b d e^{c} + 3 \, a^{2} b^{2} d e^{c} + a b^{3} d e^{c}\right)} e^{\left(d x\right)}\right)}} + \frac{1}{2} \, \int \frac{2 \, {\left({\left(4 \, a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a b e^{c} + b^{2} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + {\left(a^{4} e^{\left(4 \, c\right)} + 3 \, a^{3} b e^{\left(4 \, c\right)} + 3 \, a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} + a^{3} b e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-1/2*(a^2 + a*b - (a^2*e^(6*c) + a*b*e^(6*c))*e^(6*d*x) - (a^2*e^(4*c) - 3*a*b*e^(4*c) + 2*b^2*e^(4*c))*e^(4*d*x) + (a^2*e^(2*c) - 3*a*b*e^(2*c) + 2*b^2*e^(2*c))*e^(2*d*x))/((a^4*d*e^(5*c) + 3*a^3*b*d*e^(5*c) + 3*a^2*b^2*d*e^(5*c) + a*b^3*d*e^(5*c))*e^(5*d*x) + 2*(a^4*d*e^(3*c) + a^3*b*d*e^(3*c) - a^2*b^2*d*e^(3*c) - a*b^3*d*e^(3*c))*e^(3*d*x) + (a^4*d*e^c + 3*a^3*b*d*e^c + 3*a^2*b^2*d*e^c + a*b^3*d*e^c)*e^(d*x)) + 1/2*integrate(2*((4*a*b*e^(3*c) + b^2*e^(3*c))*e^(3*d*x) + (4*a*b*e^c + b^2*e^c)*e^(d*x))/(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + (a^4*e^(4*c) + 3*a^3*b*e^(4*c) + 3*a^2*b^2*e^(4*c) + a*b^3*e^(4*c))*e^(4*d*x) + 2*(a^4*e^(2*c) + a^3*b*e^(2*c) - a^2*b^2*e^(2*c) - a*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
118,0,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{b e^{\left(3 \, d x + 3 \, c\right)} - b e^{\left(d x + c\right)}}{a^{3} d + 2 \, a^{2} b d + a b^{2} d + {\left(a^{3} d e^{\left(4 \, c\right)} + 2 \, a^{2} b d e^{\left(4 \, c\right)} + a b^{2} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(2 \, c\right)} - a b^{2} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} + 2 \, \int \frac{{\left(2 \, a e^{\left(3 \, c\right)} + b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(2 \, a e^{c} + b e^{c}\right)} e^{\left(d x\right)}}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} + {\left(a^{3} e^{\left(4 \, c\right)} + 2 \, a^{2} b e^{\left(4 \, c\right)} + a b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} - a b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^3*d + 2*a^2*b*d + a*b^2*d + (a^3*d*e^(4*c) + 2*a^2*b*d*e^(4*c) + a*b^2*d*e^(4*c))*e^(4*d*x) + 2*(a^3*d*e^(2*c) - a*b^2*d*e^(2*c))*e^(2*d*x)) + 2*integrate(1/2*((2*a*e^(3*c) + b*e^(3*c))*e^(3*d*x) + (2*a*e^c + b*e^c)*e^(d*x))/(a^3 + 2*a^2*b + a*b^2 + (a^3*e^(4*c) + 2*a^2*b*e^(4*c) + a*b^2*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) - a*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
119,1,125,0,0.517913," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a + b}{{\left(a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{\arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} a d}"," ",0,"((a - b)*e^(-2*d*x - 2*c) + a + b)/((a^3 + 2*a^2*b + a*b^2 + 2*(a^3 - a*b^2)*e^(-2*d*x - 2*c) + (a^3 + 2*a^2*b + a*b^2)*e^(-4*d*x - 4*c))*d) - 1/2*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*d)","B",0
120,0,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a e^{\left(3 \, c\right)} + b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(a e^{c} + b e^{c}\right)} e^{\left(d x\right)}}{a^{3} d + 2 \, a^{2} b d + a b^{2} d + {\left(a^{3} d e^{\left(4 \, c\right)} + 2 \, a^{2} b d e^{\left(4 \, c\right)} + a b^{2} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(2 \, c\right)} - a b^{2} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} + 8 \, \int \frac{e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}}{8 \, {\left(a^{2} + a b + {\left(a^{2} e^{\left(4 \, c\right)} + a b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} e^{\left(2 \, c\right)} - a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"((a*e^(3*c) + b*e^(3*c))*e^(3*d*x) - (a*e^c + b*e^c)*e^(d*x))/(a^3*d + 2*a^2*b*d + a*b^2*d + (a^3*d*e^(4*c) + 2*a^2*b*d*e^(4*c) + a*b^2*d*e^(4*c))*e^(4*d*x) + 2*(a^3*d*e^(2*c) - a*b^2*d*e^(2*c))*e^(2*d*x)) + 8*integrate(1/8*(e^(3*d*x + 3*c) + e^(d*x + c))/(a^2 + a*b + (a^2*e^(4*c) + a*b*e^(4*c))*e^(4*d*x) + 2*(a^2*e^(2*c) - a*b*e^(2*c))*e^(2*d*x)), x)","F",0
121,1,127,0,0.537509," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a + b}{{\left(a^{2} b + a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{2} b + a b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{{\left(a - b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} a b d}"," ",0,"((a - b)*e^(-2*d*x - 2*c) + a + b)/((a^2*b + a*b^2 + 2*(a^2*b - a*b^2)*e^(-2*d*x - 2*c) + (a^2*b + a*b^2)*e^(-4*d*x - 4*c))*d) + 1/2*(a - b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*b*d)","A",0
122,0,0,0,0.000000," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a e^{\left(3 \, c\right)} + b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(a e^{c} + b e^{c}\right)} e^{\left(d x\right)}}{a^{2} b d + a b^{2} d + {\left(a^{2} b d e^{\left(4 \, c\right)} + a b^{2} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} b d e^{\left(2 \, c\right)} - a b^{2} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} + \frac{2 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b^{2} d} - 32 \, \int \frac{{\left(2 \, a^{2} e^{\left(3 \, c\right)} + a b e^{\left(3 \, c\right)} - b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(2 \, a^{2} e^{c} + a b e^{c} - b^{2} e^{c}\right)} e^{\left(d x\right)}}{32 \, {\left(a^{2} b^{2} + a b^{3} + {\left(a^{2} b^{2} e^{\left(4 \, c\right)} + a b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} b^{2} e^{\left(2 \, c\right)} - a b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"((a*e^(3*c) + b*e^(3*c))*e^(3*d*x) - (a*e^c + b*e^c)*e^(d*x))/(a^2*b*d + a*b^2*d + (a^2*b*d*e^(4*c) + a*b^2*d*e^(4*c))*e^(4*d*x) + 2*(a^2*b*d*e^(2*c) - a*b^2*d*e^(2*c))*e^(2*d*x)) + 2*arctan(e^(d*x + c))/(b^2*d) - 32*integrate(1/32*((2*a^2*e^(3*c) + a*b*e^(3*c) - b^2*e^(3*c))*e^(3*d*x) + (2*a^2*e^c + a*b*e^c - b^2*e^c)*e^(d*x))/(a^2*b^2 + a*b^3 + (a^2*b^2*e^(4*c) + a*b^3*e^(4*c))*e^(4*d*x) + 2*(a^2*b^2*e^(2*c) - a*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
123,1,209,0,0.603863," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} + 4 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} - a b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{{\left(a^{2} b^{2} + a b^{3} + {\left(3 \, a^{2} b^{2} - a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{2} b^{2} - a b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{2} b^{2} + a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{{\left(3 \, a^{2} + 2 \, 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 \, \sqrt{a b} a b^{2} d}"," ",0,"(3*a^2 + 4*a*b + b^2 + 2*(3*a^2 - a*b)*e^(-2*d*x - 2*c) + (3*a^2 + 2*a*b - b^2)*e^(-4*d*x - 4*c))/((a^2*b^2 + a*b^3 + (3*a^2*b^2 - a*b^3)*e^(-2*d*x - 2*c) + (3*a^2*b^2 - a*b^3)*e^(-4*d*x - 4*c) + (a^2*b^2 + a*b^3)*e^(-6*d*x - 6*c))*d) + 1/2*(3*a^2 + 2*a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*b^2*d)","B",0
124,0,0,0,0.000000," ","integrate(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{2} e^{\left(7 \, c\right)} + 3 \, a b e^{\left(7 \, c\right)} + b^{2} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(2 \, a^{2} e^{\left(5 \, c\right)} - a b e^{\left(5 \, c\right)} + b^{2} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(2 \, a^{2} e^{\left(3 \, c\right)} - a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(2 \, a^{2} e^{c} + 3 \, a b e^{c} + b^{2} e^{c}\right)} e^{\left(d x\right)}}{4 \, a^{2} b^{2} d e^{\left(6 \, d x + 6 \, c\right)} + 4 \, a^{2} b^{2} d e^{\left(2 \, d x + 2 \, c\right)} + a^{2} b^{2} d + a b^{3} d + {\left(a^{2} b^{2} d e^{\left(8 \, c\right)} + a b^{3} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 2 \, {\left(3 \, a^{2} b^{2} d e^{\left(4 \, c\right)} - a b^{3} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)}} + \frac{{\left(4 \, a e^{c} + 5 \, b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)}}{b^{3} d} - 128 \, \int \frac{{\left(4 \, a^{3} e^{\left(3 \, c\right)} + 7 \, a^{2} b e^{\left(3 \, c\right)} + 2 \, a b^{2} e^{\left(3 \, c\right)} - b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a^{3} e^{c} + 7 \, a^{2} b e^{c} + 2 \, a b^{2} e^{c} - b^{3} e^{c}\right)} e^{\left(d x\right)}}{128 \, {\left(a^{2} b^{3} + a b^{4} + {\left(a^{2} b^{3} e^{\left(4 \, c\right)} + a b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{2} b^{3} e^{\left(2 \, c\right)} - a b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"((2*a^2*e^(7*c) + 3*a*b*e^(7*c) + b^2*e^(7*c))*e^(7*d*x) + (2*a^2*e^(5*c) - a*b*e^(5*c) + b^2*e^(5*c))*e^(5*d*x) - (2*a^2*e^(3*c) - a*b*e^(3*c) + b^2*e^(3*c))*e^(3*d*x) - (2*a^2*e^c + 3*a*b*e^c + b^2*e^c)*e^(d*x))/(4*a^2*b^2*d*e^(6*d*x + 6*c) + 4*a^2*b^2*d*e^(2*d*x + 2*c) + a^2*b^2*d + a*b^3*d + (a^2*b^2*d*e^(8*c) + a*b^3*d*e^(8*c))*e^(8*d*x) + 2*(3*a^2*b^2*d*e^(4*c) - a*b^3*d*e^(4*c))*e^(4*d*x)) + (4*a*e^c + 5*b*e^c)*arctan(e^(d*x + c))*e^(-c)/(b^3*d) - 128*integrate(1/128*((4*a^3*e^(3*c) + 7*a^2*b*e^(3*c) + 2*a*b^2*e^(3*c) - b^3*e^(3*c))*e^(3*d*x) + (4*a^3*e^c + 7*a^2*b*e^c + 2*a*b^2*e^c - b^3*e^c)*e^(d*x))/(a^2*b^3 + a*b^4 + (a^2*b^3*e^(4*c) + a*b^4*e^(4*c))*e^(4*d*x) + 2*(a^2*b^3*e^(2*c) - a*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
125,1,1806,0,1.047837," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{3 \, b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{3 \, b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{3 \, {\left(5 \, a^{3} b - 15 \, a^{2} b^{2} - 5 \, a b^{3} - 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)}{32 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} + \frac{3 \, {\left(5 \, a^{3} b - 15 \, a^{2} b^{2} - 5 \, a b^{3} - 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)}{32 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} - \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)}{16 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b} d} + \frac{9 \, a^{4} b + 4 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 20 \, a b^{4} - 3 \, b^{5} + 3 \, {\left(3 \, a^{4} b - 22 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{4} b - 156 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 36 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{4} b - 86 \, a^{3} b^{2} - 84 \, a^{2} b^{3} + 38 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{9 \, a^{4} b + 4 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 20 \, a b^{4} - 3 \, b^{5} + {\left(27 \, a^{4} b - 86 \, a^{3} b^{2} - 84 \, a^{2} b^{3} + 38 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{4} b - 156 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 36 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(3 \, a^{4} b - 22 \, a^{3} b^{2} - 20 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} 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)}}{8 \, {\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}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"3/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 3/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 3/32*(5*a^3*b - 15*a^2*b^2 - 5*a*b^3 - b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) + 3/32*(5*a^3*b - 15*a^2*b^2 - 5*a*b^3 - b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) - 1/16*(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) + 1/16*(9*a^4*b + 4*a^3*b^2 - 22*a^2*b^3 - 20*a*b^4 - 3*b^5 + 3*(3*a^4*b - 22*a^3*b^2 - 20*a^2*b^3 + 6*a*b^4 + b^5)*e^(6*d*x + 6*c) + (27*a^4*b - 156*a^3*b^2 + 110*a^2*b^3 - 36*a*b^4 - 9*b^5)*e^(4*d*x + 4*c) + (27*a^4*b - 86*a^3*b^2 - 84*a^2*b^3 + 38*a*b^4 + 9*b^5)*e^(2*d*x + 2*c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*e^(8*d*x + 8*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(6*d*x + 6*c) + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*e^(4*d*x + 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(2*d*x + 2*c))*d) - 1/16*(9*a^4*b + 4*a^3*b^2 - 22*a^2*b^3 - 20*a*b^4 - 3*b^5 + (27*a^4*b - 86*a^3*b^2 - 84*a^2*b^3 + 38*a*b^4 + 9*b^5)*e^(-2*d*x - 2*c) + (27*a^4*b - 156*a^3*b^2 + 110*a^2*b^3 - 36*a*b^4 - 9*b^5)*e^(-4*d*x - 4*c) + 3*(3*a^4*b - 22*a^3*b^2 - 20*a^2*b^3 + 6*a*b^4 + b^5)*e^(-6*d*x - 6*c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(-2*d*x - 2*c) + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*e^(-4*d*x - 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*e^(-6*d*x - 6*c) + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*e^(-8*d*x - 8*c))*d) + 1/8*(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) + 1/2*(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/8*e^(2*d*x + 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/8*e^(-2*d*x - 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
126,0,0,0,0.000000," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{2 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} - 2 \, {\left(a^{4} e^{\left(10 \, c\right)} + 2 \, a^{3} b e^{\left(10 \, c\right)} + a^{2} b^{2} e^{\left(10 \, c\right)}\right)} e^{\left(10 \, d x\right)} - {\left(6 \, a^{4} e^{\left(8 \, c\right)} - 4 \, a^{3} b e^{\left(8 \, c\right)} + 2 \, a^{2} b^{2} e^{\left(8 \, c\right)} + 15 \, a b^{3} e^{\left(8 \, c\right)} + 3 \, b^{4} e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - {\left(4 \, a^{4} e^{\left(6 \, c\right)} - 8 \, a^{3} b e^{\left(6 \, c\right)} + 32 \, a^{2} b^{2} e^{\left(6 \, c\right)} - 25 \, a b^{3} e^{\left(6 \, c\right)} - 9 \, b^{4} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + {\left(4 \, a^{4} e^{\left(4 \, c\right)} - 8 \, a^{3} b e^{\left(4 \, c\right)} + 32 \, a^{2} b^{2} e^{\left(4 \, c\right)} - 25 \, a b^{3} e^{\left(4 \, c\right)} - 9 \, b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + {\left(6 \, a^{4} e^{\left(2 \, c\right)} - 4 \, a^{3} b e^{\left(2 \, c\right)} + 2 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 15 \, a b^{3} e^{\left(2 \, c\right)} + 3 \, b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{4 \, {\left({\left(a^{7} d e^{\left(9 \, c\right)} + 5 \, a^{6} b d e^{\left(9 \, c\right)} + 10 \, a^{5} b^{2} d e^{\left(9 \, c\right)} + 10 \, a^{4} b^{3} d e^{\left(9 \, c\right)} + 5 \, a^{3} b^{4} d e^{\left(9 \, c\right)} + a^{2} b^{5} d e^{\left(9 \, c\right)}\right)} e^{\left(9 \, d x\right)} + 4 \, {\left(a^{7} d e^{\left(7 \, c\right)} + 3 \, a^{6} b d e^{\left(7 \, c\right)} + 2 \, a^{5} b^{2} d e^{\left(7 \, c\right)} - 2 \, a^{4} b^{3} d e^{\left(7 \, c\right)} - 3 \, a^{3} b^{4} d e^{\left(7 \, c\right)} - a^{2} b^{5} d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(3 \, a^{7} d e^{\left(5 \, c\right)} + 7 \, a^{6} b d e^{\left(5 \, c\right)} + 6 \, a^{5} b^{2} d e^{\left(5 \, c\right)} + 6 \, a^{4} b^{3} d e^{\left(5 \, c\right)} + 7 \, a^{3} b^{4} d e^{\left(5 \, c\right)} + 3 \, a^{2} b^{5} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 4 \, {\left(a^{7} d e^{\left(3 \, c\right)} + 3 \, a^{6} b d e^{\left(3 \, c\right)} + 2 \, a^{5} b^{2} d e^{\left(3 \, c\right)} - 2 \, a^{4} b^{3} d e^{\left(3 \, c\right)} - 3 \, a^{3} b^{4} d e^{\left(3 \, c\right)} - a^{2} b^{5} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{7} d e^{c} + 5 \, a^{6} b d e^{c} + 10 \, a^{5} b^{2} d e^{c} + 10 \, a^{4} b^{3} d e^{c} + 5 \, a^{3} b^{4} d e^{c} + a^{2} b^{5} d e^{c}\right)} e^{\left(d x\right)}\right)}} + \frac{1}{2} \, \int \frac{3 \, {\left({\left(8 \, a^{2} b e^{\left(3 \, c\right)} + 4 \, a b^{2} e^{\left(3 \, c\right)} + b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(8 \, a^{2} b e^{c} + 4 \, a b^{2} e^{c} + b^{3} e^{c}\right)} e^{\left(d x\right)}\right)}}{2 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} e^{\left(4 \, c\right)} + 4 \, a^{5} b e^{\left(4 \, c\right)} + 6 \, a^{4} b^{2} e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{6} e^{\left(2 \, c\right)} + 2 \, a^{5} b e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-1/4*(2*a^4 + 4*a^3*b + 2*a^2*b^2 - 2*(a^4*e^(10*c) + 2*a^3*b*e^(10*c) + a^2*b^2*e^(10*c))*e^(10*d*x) - (6*a^4*e^(8*c) - 4*a^3*b*e^(8*c) + 2*a^2*b^2*e^(8*c) + 15*a*b^3*e^(8*c) + 3*b^4*e^(8*c))*e^(8*d*x) - (4*a^4*e^(6*c) - 8*a^3*b*e^(6*c) + 32*a^2*b^2*e^(6*c) - 25*a*b^3*e^(6*c) - 9*b^4*e^(6*c))*e^(6*d*x) + (4*a^4*e^(4*c) - 8*a^3*b*e^(4*c) + 32*a^2*b^2*e^(4*c) - 25*a*b^3*e^(4*c) - 9*b^4*e^(4*c))*e^(4*d*x) + (6*a^4*e^(2*c) - 4*a^3*b*e^(2*c) + 2*a^2*b^2*e^(2*c) + 15*a*b^3*e^(2*c) + 3*b^4*e^(2*c))*e^(2*d*x))/((a^7*d*e^(9*c) + 5*a^6*b*d*e^(9*c) + 10*a^5*b^2*d*e^(9*c) + 10*a^4*b^3*d*e^(9*c) + 5*a^3*b^4*d*e^(9*c) + a^2*b^5*d*e^(9*c))*e^(9*d*x) + 4*(a^7*d*e^(7*c) + 3*a^6*b*d*e^(7*c) + 2*a^5*b^2*d*e^(7*c) - 2*a^4*b^3*d*e^(7*c) - 3*a^3*b^4*d*e^(7*c) - a^2*b^5*d*e^(7*c))*e^(7*d*x) + 2*(3*a^7*d*e^(5*c) + 7*a^6*b*d*e^(5*c) + 6*a^5*b^2*d*e^(5*c) + 6*a^4*b^3*d*e^(5*c) + 7*a^3*b^4*d*e^(5*c) + 3*a^2*b^5*d*e^(5*c))*e^(5*d*x) + 4*(a^7*d*e^(3*c) + 3*a^6*b*d*e^(3*c) + 2*a^5*b^2*d*e^(3*c) - 2*a^4*b^3*d*e^(3*c) - 3*a^3*b^4*d*e^(3*c) - a^2*b^5*d*e^(3*c))*e^(3*d*x) + (a^7*d*e^c + 5*a^6*b*d*e^c + 10*a^5*b^2*d*e^c + 10*a^4*b^3*d*e^c + 5*a^3*b^4*d*e^c + a^2*b^5*d*e^c)*e^(d*x)) + 1/2*integrate(3/2*((8*a^2*b*e^(3*c) + 4*a*b^2*e^(3*c) + b^3*e^(3*c))*e^(3*d*x) + (8*a^2*b*e^c + 4*a*b^2*e^c + b^3*e^c)*e^(d*x))/(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + (a^6*e^(4*c) + 4*a^5*b*e^(4*c) + 6*a^4*b^2*e^(4*c) + 4*a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))*e^(4*d*x) + 2*(a^6*e^(2*c) + 2*a^5*b*e^(2*c) - 2*a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
127,0,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(8 \, a^{2} b e^{\left(7 \, c\right)} + 11 \, a b^{2} e^{\left(7 \, c\right)} + 3 \, b^{3} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(8 \, a^{2} b e^{\left(5 \, c\right)} - 13 \, a b^{2} e^{\left(5 \, c\right)} - 9 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(8 \, a^{2} b e^{\left(3 \, c\right)} - 13 \, a b^{2} e^{\left(3 \, c\right)} - 9 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(8 \, a^{2} b e^{c} + 11 \, a b^{2} e^{c} + 3 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{6} d + 4 \, a^{5} b d + 6 \, a^{4} b^{2} d + 4 \, a^{3} b^{3} d + a^{2} b^{4} d + {\left(a^{6} d e^{\left(8 \, c\right)} + 4 \, a^{5} b d e^{\left(8 \, c\right)} + 6 \, a^{4} b^{2} d e^{\left(8 \, c\right)} + 4 \, a^{3} b^{3} d e^{\left(8 \, c\right)} + a^{2} b^{4} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{6} d e^{\left(6 \, c\right)} + 2 \, a^{5} b d e^{\left(6 \, c\right)} - 2 \, a^{3} b^{3} d e^{\left(6 \, c\right)} - a^{2} b^{4} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{6} d e^{\left(4 \, c\right)} + 4 \, a^{5} b d e^{\left(4 \, c\right)} + 2 \, a^{4} b^{2} d e^{\left(4 \, c\right)} + 4 \, a^{3} b^{3} d e^{\left(4 \, c\right)} + 3 \, a^{2} b^{4} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{6} d e^{\left(2 \, c\right)} + 2 \, a^{5} b d e^{\left(2 \, c\right)} - 2 \, a^{3} b^{3} d e^{\left(2 \, c\right)} - a^{2} b^{4} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} + 2 \, \int \frac{{\left(8 \, a^{2} e^{\left(3 \, c\right)} + 8 \, a b e^{\left(3 \, c\right)} + 3 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(8 \, a^{2} e^{c} + 8 \, a b e^{c} + 3 \, b^{2} e^{c}\right)} e^{\left(d x\right)}}{8 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} e^{\left(4 \, c\right)} + 3 \, a^{4} b e^{\left(4 \, c\right)} + 3 \, a^{3} b^{2} e^{\left(4 \, c\right)} + a^{2} b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{5} e^{\left(2 \, c\right)} + a^{4} b e^{\left(2 \, c\right)} - a^{3} b^{2} e^{\left(2 \, c\right)} - a^{2} b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*((8*a^2*b*e^(7*c) + 11*a*b^2*e^(7*c) + 3*b^3*e^(7*c))*e^(7*d*x) + (8*a^2*b*e^(5*c) - 13*a*b^2*e^(5*c) - 9*b^3*e^(5*c))*e^(5*d*x) - (8*a^2*b*e^(3*c) - 13*a*b^2*e^(3*c) - 9*b^3*e^(3*c))*e^(3*d*x) - (8*a^2*b*e^c + 11*a*b^2*e^c + 3*b^3*e^c)*e^(d*x))/(a^6*d + 4*a^5*b*d + 6*a^4*b^2*d + 4*a^3*b^3*d + a^2*b^4*d + (a^6*d*e^(8*c) + 4*a^5*b*d*e^(8*c) + 6*a^4*b^2*d*e^(8*c) + 4*a^3*b^3*d*e^(8*c) + a^2*b^4*d*e^(8*c))*e^(8*d*x) + 4*(a^6*d*e^(6*c) + 2*a^5*b*d*e^(6*c) - 2*a^3*b^3*d*e^(6*c) - a^2*b^4*d*e^(6*c))*e^(6*d*x) + 2*(3*a^6*d*e^(4*c) + 4*a^5*b*d*e^(4*c) + 2*a^4*b^2*d*e^(4*c) + 4*a^3*b^3*d*e^(4*c) + 3*a^2*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^6*d*e^(2*c) + 2*a^5*b*d*e^(2*c) - 2*a^3*b^3*d*e^(2*c) - a^2*b^4*d*e^(2*c))*e^(2*d*x)) + 2*integrate(1/8*((8*a^2*e^(3*c) + 8*a*b*e^(3*c) + 3*b^2*e^(3*c))*e^(3*d*x) + (8*a^2*e^c + 8*a*b*e^c + 3*b^2*e^c)*e^(d*x))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5*e^(4*c) + 3*a^4*b*e^(4*c) + 3*a^3*b^2*e^(4*c) + a^2*b^3*e^(4*c))*e^(4*d*x) + 2*(a^5*e^(2*c) + a^4*b*e^(2*c) - a^3*b^2*e^(2*c) - a^2*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
128,1,366,0,0.631952," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{5 \, a^{3} + 13 \, a^{2} b + 11 \, a b^{2} + 3 \, b^{3} + {\left(15 \, a^{3} + 13 \, a^{2} b - 11 \, a b^{2} - 9 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(15 \, a^{3} - a^{2} b + 9 \, a b^{2} + 9 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(5 \, a^{3} - a^{2} b - 9 \, a b^{2} - 3 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + 4 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} + 4 \, a^{5} b + 2 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 3 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{3 \, \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} d}"," ",0,"1/4*(5*a^3 + 13*a^2*b + 11*a*b^2 + 3*b^3 + (15*a^3 + 13*a^2*b - 11*a*b^2 - 9*b^3)*e^(-2*d*x - 2*c) + (15*a^3 - a^2*b + 9*a*b^2 + 9*b^3)*e^(-4*d*x - 4*c) + (5*a^3 - a^2*b - 9*a*b^2 - 3*b^3)*e^(-6*d*x - 6*c))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + 4*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^6 + 4*a^5*b + 2*a^4*b^2 + 4*a^3*b^3 + 3*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*e^(-6*d*x - 6*c) + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*e^(-8*d*x - 8*c))*d) - 3/8*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d)","B",0
129,0,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(4 \, a^{2} e^{\left(7 \, c\right)} + 7 \, a b e^{\left(7 \, c\right)} + 3 \, b^{2} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(4 \, a^{2} e^{\left(5 \, c\right)} - a b e^{\left(5 \, c\right)} - 9 \, b^{2} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(4 \, a^{2} e^{\left(3 \, c\right)} - a b e^{\left(3 \, c\right)} - 9 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(4 \, a^{2} e^{c} + 7 \, a b e^{c} + 3 \, b^{2} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{5} d + 3 \, a^{4} b d + 3 \, a^{3} b^{2} d + a^{2} b^{3} d + {\left(a^{5} d e^{\left(8 \, c\right)} + 3 \, a^{4} b d e^{\left(8 \, c\right)} + 3 \, a^{3} b^{2} d e^{\left(8 \, c\right)} + a^{2} b^{3} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(6 \, c\right)} + a^{4} b d e^{\left(6 \, c\right)} - a^{3} b^{2} d e^{\left(6 \, c\right)} - a^{2} b^{3} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{5} d e^{\left(4 \, c\right)} + a^{4} b d e^{\left(4 \, c\right)} + a^{3} b^{2} d e^{\left(4 \, c\right)} + 3 \, a^{2} b^{3} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(2 \, c\right)} + a^{4} b d e^{\left(2 \, c\right)} - a^{3} b^{2} d e^{\left(2 \, c\right)} - a^{2} b^{3} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} + 8 \, \int \frac{{\left(4 \, a e^{\left(3 \, c\right)} + 3 \, b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a e^{c} + 3 \, b e^{c}\right)} e^{\left(d x\right)}}{32 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} e^{\left(4 \, c\right)} + 2 \, a^{3} b e^{\left(4 \, c\right)} + a^{2} b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} - a^{2} b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*((4*a^2*e^(7*c) + 7*a*b*e^(7*c) + 3*b^2*e^(7*c))*e^(7*d*x) + (4*a^2*e^(5*c) - a*b*e^(5*c) - 9*b^2*e^(5*c))*e^(5*d*x) - (4*a^2*e^(3*c) - a*b*e^(3*c) - 9*b^2*e^(3*c))*e^(3*d*x) - (4*a^2*e^c + 7*a*b*e^c + 3*b^2*e^c)*e^(d*x))/(a^5*d + 3*a^4*b*d + 3*a^3*b^2*d + a^2*b^3*d + (a^5*d*e^(8*c) + 3*a^4*b*d*e^(8*c) + 3*a^3*b^2*d*e^(8*c) + a^2*b^3*d*e^(8*c))*e^(8*d*x) + 4*(a^5*d*e^(6*c) + a^4*b*d*e^(6*c) - a^3*b^2*d*e^(6*c) - a^2*b^3*d*e^(6*c))*e^(6*d*x) + 2*(3*a^5*d*e^(4*c) + a^4*b*d*e^(4*c) + a^3*b^2*d*e^(4*c) + 3*a^2*b^3*d*e^(4*c))*e^(4*d*x) + 4*(a^5*d*e^(2*c) + a^4*b*d*e^(2*c) - a^3*b^2*d*e^(2*c) - a^2*b^3*d*e^(2*c))*e^(2*d*x)) + 8*integrate(1/32*((4*a*e^(3*c) + 3*b*e^(3*c))*e^(3*d*x) + (4*a*e^c + 3*b*e^c)*e^(d*x))/(a^4 + 2*a^3*b + a^2*b^2 + (a^4*e^(4*c) + 2*a^3*b*e^(4*c) + a^2*b^2*e^(4*c))*e^(4*d*x) + 2*(a^4*e^(2*c) - a^2*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
130,1,360,0,0.697080," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{a^{3} + 5 \, a^{2} b + 7 \, a b^{2} + 3 \, b^{3} + {\left(3 \, a^{3} + 13 \, a^{2} b + a b^{2} - 9 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{3} + 7 \, a^{2} b - 3 \, a b^{2} + 9 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4} + 4 \, {\left(a^{5} b + a^{4} b^{2} - a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3} + 3 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} b + a^{4} b^{2} - a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{{\left(a - 3 \, b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b d}"," ",0,"1/4*(a^3 + 5*a^2*b + 7*a*b^2 + 3*b^3 + (3*a^3 + 13*a^2*b + a*b^2 - 9*b^3)*e^(-2*d*x - 2*c) + (3*a^3 + 7*a^2*b - 3*a*b^2 + 9*b^3)*e^(-4*d*x - 4*c) + (a^3 - a^2*b - 5*a*b^2 - 3*b^3)*e^(-6*d*x - 6*c))/((a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4 + 4*(a^5*b + a^4*b^2 - a^3*b^3 - a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^5*b + a^4*b^2 + a^3*b^3 + 3*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^5*b + a^4*b^2 - a^3*b^3 - a^2*b^4)*e^(-6*d*x - 6*c) + (a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*e^(-8*d*x - 8*c))*d) + 1/8*(a - 3*b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b*d)","B",0
131,0,0,0,0.000000," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(a e^{\left(7 \, c\right)} + b e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(11 \, a e^{\left(5 \, c\right)} - 9 \, b e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(11 \, a e^{\left(3 \, c\right)} - 9 \, b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - 3 \, {\left(a e^{c} + b e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{4} d + 2 \, a^{3} b d + a^{2} b^{2} d + {\left(a^{4} d e^{\left(8 \, c\right)} + 2 \, a^{3} b d e^{\left(8 \, c\right)} + a^{2} b^{2} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{4} d e^{\left(6 \, c\right)} - a^{2} b^{2} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{4} d e^{\left(4 \, c\right)} - 2 \, a^{3} b d e^{\left(4 \, c\right)} + 3 \, a^{2} b^{2} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{4} d e^{\left(2 \, c\right)} - a^{2} b^{2} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} + 32 \, \int \frac{3 \, {\left(e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}\right)}}{128 \, {\left(a^{3} + a^{2} b + {\left(a^{3} e^{\left(4 \, c\right)} + a^{2} b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} - a^{2} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*(3*(a*e^(7*c) + b*e^(7*c))*e^(7*d*x) + (11*a*e^(5*c) - 9*b*e^(5*c))*e^(5*d*x) - (11*a*e^(3*c) - 9*b*e^(3*c))*e^(3*d*x) - 3*(a*e^c + b*e^c)*e^(d*x))/(a^4*d + 2*a^3*b*d + a^2*b^2*d + (a^4*d*e^(8*c) + 2*a^3*b*d*e^(8*c) + a^2*b^2*d*e^(8*c))*e^(8*d*x) + 4*(a^4*d*e^(6*c) - a^2*b^2*d*e^(6*c))*e^(6*d*x) + 2*(3*a^4*d*e^(4*c) - 2*a^3*b*d*e^(4*c) + 3*a^2*b^2*d*e^(4*c))*e^(4*d*x) + 4*(a^4*d*e^(2*c) - a^2*b^2*d*e^(2*c))*e^(2*d*x)) + 32*integrate(3/128*(e^(3*d*x + 3*c) + e^(d*x + c))/(a^3 + a^2*b + (a^3*e^(4*c) + a^2*b*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) - a^2*b*e^(2*c))*e^(2*d*x)), x)","F",0
132,1,332,0,0.677302," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{3 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 3 \, b^{3} + {\left(9 \, a^{3} - 13 \, a^{2} b - 13 \, a b^{2} + 9 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(3 \, a^{3} - 5 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{3} + a^{2} b + a b^{2} + 3 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{4} b^{2} - 2 \, a^{3} b^{3} + 3 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{{\left(3 \, a^{2} - 2 \, a b + 3 \, 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)}{8 \, \sqrt{a b} a^{2} b^{2} d}"," ",0,"-1/4*(3*a^3 + 3*a^2*b - 3*a*b^2 - 3*b^3 + (9*a^3 - 13*a^2*b - 13*a*b^2 + 9*b^3)*e^(-2*d*x - 2*c) + 3*(3*a^3 - 5*a^2*b + 5*a*b^2 - 3*b^3)*e^(-4*d*x - 4*c) + (3*a^3 + a^2*b + a*b^2 + 3*b^3)*e^(-6*d*x - 6*c))/((a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + 4*(a^4*b^2 - a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^4*b^2 - 2*a^3*b^3 + 3*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^4*b^2 - a^2*b^4)*e^(-6*d*x - 6*c) + (a^4*b^2 + 2*a^3*b^3 + a^2*b^4)*e^(-8*d*x - 8*c))*d) - 1/8*(3*a^2 - 2*a*b + 3*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2*d)","B",0
133,0,0,0,0.000000," ","integrate(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, a^{3} e^{\left(7 \, c\right)} + 5 \, a^{2} b e^{\left(7 \, c\right)} - 2 \, a b^{2} e^{\left(7 \, c\right)} - 3 \, b^{3} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(4 \, a^{3} e^{\left(5 \, c\right)} - 19 \, a^{2} b e^{\left(5 \, c\right)} - 14 \, a b^{2} e^{\left(5 \, c\right)} + 9 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(4 \, a^{3} e^{\left(3 \, c\right)} - 19 \, a^{2} b e^{\left(3 \, c\right)} - 14 \, a b^{2} e^{\left(3 \, c\right)} + 9 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(4 \, a^{3} e^{c} + 5 \, a^{2} b e^{c} - 2 \, a b^{2} e^{c} - 3 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{4} b^{2} d + 2 \, a^{3} b^{3} d + a^{2} b^{4} d + {\left(a^{4} b^{2} d e^{\left(8 \, c\right)} + 2 \, a^{3} b^{3} d e^{\left(8 \, c\right)} + a^{2} b^{4} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{4} b^{2} d e^{\left(6 \, c\right)} - a^{2} b^{4} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{4} b^{2} d e^{\left(4 \, c\right)} - 2 \, a^{3} b^{3} d e^{\left(4 \, c\right)} + 3 \, a^{2} b^{4} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{4} b^{2} d e^{\left(2 \, c\right)} - a^{2} b^{4} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} - \frac{2 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b^{3} d} + 128 \, \int \frac{{\left(8 \, a^{3} e^{\left(3 \, c\right)} + 4 \, a^{2} b e^{\left(3 \, c\right)} - a b^{2} e^{\left(3 \, c\right)} + 3 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(8 \, a^{3} e^{c} + 4 \, a^{2} b e^{c} - a b^{2} e^{c} + 3 \, b^{3} e^{c}\right)} e^{\left(d x\right)}}{512 \, {\left(a^{3} b^{3} + a^{2} b^{4} + {\left(a^{3} b^{3} e^{\left(4 \, c\right)} + a^{2} b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} b^{3} e^{\left(2 \, c\right)} - a^{2} b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-1/4*((4*a^3*e^(7*c) + 5*a^2*b*e^(7*c) - 2*a*b^2*e^(7*c) - 3*b^3*e^(7*c))*e^(7*d*x) + (4*a^3*e^(5*c) - 19*a^2*b*e^(5*c) - 14*a*b^2*e^(5*c) + 9*b^3*e^(5*c))*e^(5*d*x) - (4*a^3*e^(3*c) - 19*a^2*b*e^(3*c) - 14*a*b^2*e^(3*c) + 9*b^3*e^(3*c))*e^(3*d*x) - (4*a^3*e^c + 5*a^2*b*e^c - 2*a*b^2*e^c - 3*b^3*e^c)*e^(d*x))/(a^4*b^2*d + 2*a^3*b^3*d + a^2*b^4*d + (a^4*b^2*d*e^(8*c) + 2*a^3*b^3*d*e^(8*c) + a^2*b^4*d*e^(8*c))*e^(8*d*x) + 4*(a^4*b^2*d*e^(6*c) - a^2*b^4*d*e^(6*c))*e^(6*d*x) + 2*(3*a^4*b^2*d*e^(4*c) - 2*a^3*b^3*d*e^(4*c) + 3*a^2*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^4*b^2*d*e^(2*c) - a^2*b^4*d*e^(2*c))*e^(2*d*x)) - 2*arctan(e^(d*x + c))/(b^3*d) + 128*integrate(1/512*((8*a^3*e^(3*c) + 4*a^2*b*e^(3*c) - a*b^2*e^(3*c) + 3*b^3*e^(3*c))*e^(3*d*x) + (8*a^3*e^c + 4*a^2*b*e^c - a*b^2*e^c + 3*b^3*e^c)*e^(d*x))/(a^3*b^3 + a^2*b^4 + (a^3*b^3*e^(4*c) + a^2*b^4*e^(4*c))*e^(4*d*x) + 2*(a^3*b^3*e^(2*c) - a^2*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
134,1,199,0,0.327628," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{15} \, b {\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{1}{3} \, a {\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)}"," ",0,"1/15*b*(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))) + 1/3*a*(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)))","B",0
135,1,168,0,0.405318," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + a {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)}"," ",0,"b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 4*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) + a*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1)))","B",0
136,1,105,0,0.325667," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{3} \, b {\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)} + a {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)}"," ",0,"1/3*b*(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))) + a*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1)))","B",0
137,1,76,0,0.406001," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a \log\left(\cosh\left(d x + c\right)\right)}{d}"," ",0,"b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a*log(cosh(d*x + c))/d","B",0
138,1,31,0,0.301065," ","integrate(a+b*tanh(d*x+c)^2,x, algorithm=""maxima"")","b {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} + a x"," ",0,"b*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + a*x","A",0
139,1,35,0,0.311524," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}{d} + \frac{a \log\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"b*log(e^(d*x + c) + e^(-d*x - c))/d + a*log(sinh(d*x + c))/d","A",0
140,1,31,0,0.322579," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","a {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + b x"," ",0,"a*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + b*x","A",0
141,1,106,0,0.320410," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","a {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} + \frac{b \log\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}{d}"," ",0,"a*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) + b*log(e^(d*x + c) - e^(-d*x - c))/d","B",0
142,1,105,0,0.329036," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\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)} + b {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)}"," ",0,"1/3*a*(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))) + b*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1)))","B",0
143,1,206,0,0.336705," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","a {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} - 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)}"," ",0,"a*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 4*(e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) - 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) - 1))) + b*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1)))","B",0
144,1,369,0,0.343632," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{105} \, b^{2} {\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}{15} \, a b {\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{1}{3} \, a^{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)}"," ",0,"1/105*b^2*(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))) + 2/15*a*b*(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))) + 1/3*a^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)))","B",0
145,1,333,0,0.429298," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} {\left(3 \, x + \frac{3 \, c}{d} + \frac{3 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, {\left(9 \, e^{\left(-2 \, d x - 2 \, c\right)} + 18 \, e^{\left(-4 \, d x - 4 \, c\right)} + 34 \, e^{\left(-6 \, d x - 6 \, c\right)} + 18 \, e^{\left(-8 \, d x - 8 \, c\right)} + 9 \, e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} + 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} + 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} + 2 \, a b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + a^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)}"," ",0,"1/3*b^2*(3*x + 3*c/d + 3*log(e^(-2*d*x - 2*c) + 1)/d + 2*(9*e^(-2*d*x - 2*c) + 18*e^(-4*d*x - 4*c) + 34*e^(-6*d*x - 6*c) + 18*e^(-8*d*x - 8*c) + 9*e^(-10*d*x - 10*c))/(d*(6*e^(-2*d*x - 2*c) + 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) + 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c) + 1))) + 2*a*b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 4*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) + a^2*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1)))","B",0
146,1,231,0,0.338121," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{15} \, b^{2} {\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{2}{3} \, a b {\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)} + a^{2} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)}"," ",0,"1/15*b^2*(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))) + 2/3*a*b*(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))) + a^2*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1)))","B",0
147,1,186,0,0.420343," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","b^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + 2 \, a b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a^{2} \log\left(\cosh\left(d x + c\right)\right)}{d}"," ",0,"b^2*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 4*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) + 2*a*b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a^2*log(cosh(d*x + c))/d","B",0
148,1,114,0,0.326690," ","integrate((a+b*tanh(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
149,1,104,0,0.422272," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","b^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{2 \, a b \log\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}{d} + \frac{a^{2} \log\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"b^2*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 2*a*b*log(e^(d*x + c) + e^(-d*x - c))/d + a^2*log(sinh(d*x + c))/d","B",0
150,1,64,0,0.346716," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","b^{2} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} + a^{2} {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + 2 \, a b x"," ",0,"b^2*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + a^2*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + 2*a*b*x","A",0
151,1,134,0,0.329782," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} + \frac{b^{2} \log\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}{d} + \frac{2 \, a b \log\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}{d}"," ",0,"a^2*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) + b^2*log(e^(d*x + c) + e^(-d*x - c))/d + 2*a*b*log(e^(d*x + c) - e^(-d*x - c))/d","B",0
152,1,114,0,0.331870," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{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)} + b^{2} x"," ",0,"1/3*a^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))) + b^2*x","B",0
153,1,236,0,0.335353," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} - 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + 2 \, a b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} + \frac{b^{2} \log\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}{d}"," ",0,"a^2*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 4*(e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) - 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) - 1))) + 2*a*b*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) + b^2*log(e^(d*x + c) - e^(-d*x - c))/d","B",0
154,1,231,0,0.351323," ","integrate(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{15} \, a^{2} {\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{2}{3} \, a b {\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)} + b^{2} {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)}"," ",0,"1/15*a^2*(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))) + 2/3*a*b*(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))) + b^2*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1)))","B",0
155,1,390,0,0.354481," ","integrate(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(3 \, x + \frac{3 \, c}{d} + \frac{3 \, \log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{3 \, \log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(9 \, e^{\left(-2 \, d x - 2 \, c\right)} - 18 \, e^{\left(-4 \, d x - 4 \, c\right)} + 34 \, e^{\left(-6 \, d x - 6 \, c\right)} - 18 \, e^{\left(-8 \, d x - 8 \, c\right)} + 9 \, e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} - 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} - e^{\left(-12 \, d x - 12 \, c\right)} - 1\right)}}\right)} + 2 \, a b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} - 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + b^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)}"," ",0,"1/3*a^2*(3*x + 3*c/d + 3*log(e^(-d*x - c) + 1)/d + 3*log(e^(-d*x - c) - 1)/d + 2*(9*e^(-2*d*x - 2*c) - 18*e^(-4*d*x - 4*c) + 34*e^(-6*d*x - 6*c) - 18*e^(-8*d*x - 8*c) + 9*e^(-10*d*x - 10*c))/(d*(6*e^(-2*d*x - 2*c) - 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) - 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) - e^(-12*d*x - 12*c) - 1))) + 2*a*b*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 4*(e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) - 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) - 1))) + b^2*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1)))","B",0
156,1,583,0,0.367506," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{315} \, b^{3} {\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}{35} \, a b^{2} {\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{1}{5} \, a^{2} b {\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{1}{3} \, a^{3} {\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)}"," ",0,"1/315*b^3*(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))) + 1/35*a*b^2*(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))) + 1/5*a^2*b*(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))) + 1/3*a^3*(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)))","B",0
157,1,540,0,0.454298," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","a b^{2} {\left(3 \, x + \frac{3 \, c}{d} + \frac{3 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, {\left(9 \, e^{\left(-2 \, d x - 2 \, c\right)} + 18 \, e^{\left(-4 \, d x - 4 \, c\right)} + 34 \, e^{\left(-6 \, d x - 6 \, c\right)} + 18 \, e^{\left(-8 \, d x - 8 \, c\right)} + 9 \, e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} + 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} + 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} + \frac{1}{3} \, b^{3} {\left(3 \, x + \frac{3 \, c}{d} + \frac{3 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{8 \, {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} + 9 \, e^{\left(-4 \, d x - 4 \, c\right)} + 25 \, e^{\left(-6 \, d x - 6 \, c\right)} + 26 \, e^{\left(-8 \, d x - 8 \, c\right)} + 25 \, e^{\left(-10 \, d x - 10 \, c\right)} + 9 \, e^{\left(-12 \, d x - 12 \, c\right)} + 3 \, e^{\left(-14 \, d x - 14 \, c\right)}\right)}}{d {\left(8 \, e^{\left(-2 \, d x - 2 \, c\right)} + 28 \, e^{\left(-4 \, d x - 4 \, c\right)} + 56 \, e^{\left(-6 \, d x - 6 \, c\right)} + 70 \, e^{\left(-8 \, d x - 8 \, c\right)} + 56 \, e^{\left(-10 \, d x - 10 \, c\right)} + 28 \, e^{\left(-12 \, d x - 12 \, c\right)} + 8 \, e^{\left(-14 \, d x - 14 \, c\right)} + e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)} + 3 \, a^{2} b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + a^{3} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)}"," ",0,"a*b^2*(3*x + 3*c/d + 3*log(e^(-2*d*x - 2*c) + 1)/d + 2*(9*e^(-2*d*x - 2*c) + 18*e^(-4*d*x - 4*c) + 34*e^(-6*d*x - 6*c) + 18*e^(-8*d*x - 8*c) + 9*e^(-10*d*x - 10*c))/(d*(6*e^(-2*d*x - 2*c) + 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) + 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c) + 1))) + 1/3*b^3*(3*x + 3*c/d + 3*log(e^(-2*d*x - 2*c) + 1)/d + 8*(3*e^(-2*d*x - 2*c) + 9*e^(-4*d*x - 4*c) + 25*e^(-6*d*x - 6*c) + 26*e^(-8*d*x - 8*c) + 25*e^(-10*d*x - 10*c) + 9*e^(-12*d*x - 12*c) + 3*e^(-14*d*x - 14*c))/(d*(8*e^(-2*d*x - 2*c) + 28*e^(-4*d*x - 4*c) + 56*e^(-6*d*x - 6*c) + 70*e^(-8*d*x - 8*c) + 56*e^(-10*d*x - 10*c) + 28*e^(-12*d*x - 12*c) + 8*e^(-14*d*x - 14*c) + e^(-16*d*x - 16*c) + 1))) + 3*a^2*b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 4*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) + a^3*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1)))","B",0
158,1,400,0,0.346899," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{105} \, b^{3} {\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{1}{5} \, a b^{2} {\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^{2} b {\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)} + a^{3} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)}"," ",0,"1/105*b^3*(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))) + 1/5*a*b^2*(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^2*b*(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))) + a^3*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1)))","B",0
159,1,351,0,0.440824," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} {\left(3 \, x + \frac{3 \, c}{d} + \frac{3 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, {\left(9 \, e^{\left(-2 \, d x - 2 \, c\right)} + 18 \, e^{\left(-4 \, d x - 4 \, c\right)} + 34 \, e^{\left(-6 \, d x - 6 \, c\right)} + 18 \, e^{\left(-8 \, d x - 8 \, c\right)} + 9 \, e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} + 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} + 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} + 3 \, a b^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + 3 \, a^{2} b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{a^{3} \log\left(\cosh\left(d x + c\right)\right)}{d}"," ",0,"1/3*b^3*(3*x + 3*c/d + 3*log(e^(-2*d*x - 2*c) + 1)/d + 2*(9*e^(-2*d*x - 2*c) + 18*e^(-4*d*x - 4*c) + 34*e^(-6*d*x - 6*c) + 18*e^(-8*d*x - 8*c) + 9*e^(-10*d*x - 10*c))/(d*(6*e^(-2*d*x - 2*c) + 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) + 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) + e^(-12*d*x - 12*c) + 1))) + 3*a*b^2*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 4*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) + 3*a^2*b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a^3*log(cosh(d*x + c))/d","B",0
160,1,239,0,0.348358," ","integrate((a+b*tanh(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
161,1,214,0,0.437374," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","b^{3} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + 3 \, a b^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{3 \, a^{2} b \log\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}{d} + \frac{a^{3} \log\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"b^3*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 4*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) + 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + 1))) + 3*a*b^2*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 3*a^2*b*log(e^(d*x + c) + e^(-d*x - c))/d + a^3*log(sinh(d*x + c))/d","B",0
162,1,147,0,0.341350," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} {\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 b^{2} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} + a^{3} {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + 3 \, a^{2} b x"," ",0,"1/3*b^3*(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*b^2*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + a^3*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + 3*a^2*b*x","B",0
163,1,203,0,0.438366," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} + b^{3} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + \frac{3 \, a b^{2} \log\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}{d} + \frac{3 \, a^{2} b \log\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}{d}"," ",0,"a^3*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) + b^3*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + 3*a*b^2*log(e^(d*x + c) + e^(-d*x - c))/d + 3*a^2*b*log(e^(d*x + c) - e^(-d*x - c))/d","B",0
164,1,147,0,0.340313," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} {\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)} + b^{3} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, 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)} + 3 \, a b^{2} x"," ",0,"1/3*a^3*(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))) + b^3*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + 3*a^2*b*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + 3*a*b^2*x","B",0
165,1,264,0,0.350398," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} - 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + 3 \, a^{2} b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} + \frac{b^{3} \log\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}{d} + \frac{3 \, a b^{2} \log\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}{d}"," ",0,"a^3*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 4*(e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) - 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) - 1))) + 3*a^2*b*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) + b^3*log(e^(d*x + c) + e^(-d*x - c))/d + 3*a*b^2*log(e^(d*x + c) - e^(-d*x - c))/d","B",0
166,1,239,0,0.348619," ","integrate(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{15} \, a^{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^{2} b {\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 b^{2} {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + b^{3} x"," ",0,"1/15*a^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^2*b*(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*b^2*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + b^3*x","B",0
167,1,420,0,0.354727," ","integrate(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} {\left(3 \, x + \frac{3 \, c}{d} + \frac{3 \, \log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{3 \, \log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, {\left(9 \, e^{\left(-2 \, d x - 2 \, c\right)} - 18 \, e^{\left(-4 \, d x - 4 \, c\right)} + 34 \, e^{\left(-6 \, d x - 6 \, c\right)} - 18 \, e^{\left(-8 \, d x - 8 \, c\right)} + 9 \, e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{d {\left(6 \, e^{\left(-2 \, d x - 2 \, c\right)} - 15 \, e^{\left(-4 \, d x - 4 \, c\right)} + 20 \, e^{\left(-6 \, d x - 6 \, c\right)} - 15 \, e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} - e^{\left(-12 \, d x - 12 \, c\right)} - 1\right)}}\right)} + 3 \, a^{2} b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{4 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} - 6 \, e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + 3 \, a b^{2} {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}\right)} + \frac{b^{3} \log\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}{d}"," ",0,"1/3*a^3*(3*x + 3*c/d + 3*log(e^(-d*x - c) + 1)/d + 3*log(e^(-d*x - c) - 1)/d + 2*(9*e^(-2*d*x - 2*c) - 18*e^(-4*d*x - 4*c) + 34*e^(-6*d*x - 6*c) - 18*e^(-8*d*x - 8*c) + 9*e^(-10*d*x - 10*c))/(d*(6*e^(-2*d*x - 2*c) - 15*e^(-4*d*x - 4*c) + 20*e^(-6*d*x - 6*c) - 15*e^(-8*d*x - 8*c) + 6*e^(-10*d*x - 10*c) - e^(-12*d*x - 12*c) - 1))) + 3*a^2*b*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 4*(e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) + e^(-6*d*x - 6*c))/(d*(4*e^(-2*d*x - 2*c) - 6*e^(-4*d*x - 4*c) + 4*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) - 1))) + 3*a*b^2*(x + c/d + log(e^(-d*x - c) + 1)/d + log(e^(-d*x - c) - 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - e^(-4*d*x - 4*c) - 1))) + b^3*log(e^(d*x + c) - e^(-d*x - c))/d","B",0
168,1,410,0,0.352502," ","integrate((a+b*tanh(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
169,1,624,0,0.356874," ","integrate((a+b*tanh(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
170,1,133,0,0.428399," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{a^{2} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a b^{2} + b^{3}\right)} d} + \frac{d x + c}{{\left(a + b\right)} d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(2 \, b e^{\left(-2 \, d x - 2 \, c\right)} + b e^{\left(-4 \, d x - 4 \, c\right)} + b\right)} d} - \frac{{\left(a - b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{b^{2} d}"," ",0,"1/2*a^2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a*b^2 + b^3)*d) + (d*x + c)/((a + b)*d) + 2*e^(-2*d*x - 2*c)/((2*b*e^(-2*d*x - 2*c) + b*e^(-4*d*x - 4*c) + b)*d) - (a - b)*log(e^(-2*d*x - 2*c) + 1)/(b^2*d)","B",0
171,1,509,0,0.603368," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{8 \, {\left(a b + b^{2}\right)} d} + \frac{{\left(a - b\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{8 \, {\left(a b + b^{2}\right)} d} + \frac{{\left(a^{2} - 6 \, 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)}{16 \, {\left(a b + b^{2}\right)} \sqrt{a b} d} + \frac{{\left(a - b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{4 \, \sqrt{a b} b d} - \frac{{\left(a^{2} - 6 \, 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)}{16 \, {\left(a b + b^{2}\right)} \sqrt{a b} d} - \frac{3 \, {\left(a + b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} b d} - \frac{{\left(a - b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{4 \, \sqrt{a b} b d} - \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, b d} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, b d} + \frac{3 \, \log\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)}{4 \, b d} - \frac{3 \, \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{4 \, b d} + \frac{5}{8 \, {\left(b e^{\left(2 \, d x + 2 \, c\right)} + b\right)} d} - \frac{11}{8 \, {\left(b e^{\left(-2 \, d x - 2 \, c\right)} + b\right)} d}"," ",0,"-1/8*(a - b)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a*b + b^2)*d) + 1/8*(a - b)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a*b + b^2)*d) + 1/16*(a^2 - 6*a*b + b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a*b + b^2)*sqrt(a*b)*d) + 1/4*(a - b)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*b*d) - 1/16*(a^2 - 6*a*b + b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a*b + b^2)*sqrt(a*b)*d) - 3/8*(a + b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*b*d) - 1/4*(a - b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*b*d) - 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/(b*d) + 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/(b*d) + 3/4*log(e^(2*d*x + 2*c) + 1)/(b*d) - 3/4*log(e^(-2*d*x - 2*c) + 1)/(b*d) + 5/8/((b*e^(2*d*x + 2*c) + b)*d) - 11/8/((b*e^(-2*d*x - 2*c) + b)*d)","B",0
172,1,82,0,0.408966," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{a \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a b + b^{2}\right)} d} + \frac{d x + c}{{\left(a + b\right)} d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{b d}"," ",0,"-1/2*a*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a*b + b^2)*d) + (d*x + c)/((a + b)*d) + log(e^(-2*d*x - 2*c) + 1)/(b*d)","A",0
173,1,215,0,0.450659," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a - b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{4 \, \sqrt{a b} {\left(a + b\right)} d} + \frac{\arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} d} + \frac{{\left(a - b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{4 \, \sqrt{a b} {\left(a + b\right)} d} + \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a + b\right)} d} - \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a + b\right)} d}"," ",0,"-1/4*(a - b)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) + 1/2*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*d) + 1/4*(a - b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*(a + b)*d) + 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a + b)*d) - 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a + b)*d)","B",0
174,1,58,0,0.326923," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{d x + c}{{\left(a + b\right)} d} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a + b\right)} d}"," ",0,"(d*x + c)/((a + b)*d) + 1/2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a + b)*d)","A",0
175,1,57,0,0.421914," ","integrate(1/(a+b*tanh(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
176,1,101,0,0.328546," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{2} + a b\right)} d} + \frac{d x + c}{{\left(a + b\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{a d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{a d}"," ",0,"-1/2*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + a*b)*d) + (d*x + c)/((a + b)*d) + log(e^(-d*x - c) + 1)/(a*d) + log(e^(-d*x - c) - 1)/(a*d)","A",0
177,1,329,0,0.474921," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + a b\right)} d} + \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + a b\right)} d} + \frac{{\left(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)}{4 \, {\left(a^{2} + a b\right)} \sqrt{a b} d} - \frac{{\left(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)}{4 \, {\left(a^{2} + a b\right)} \sqrt{a b} d} + \frac{b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{2 \, \sqrt{a b} a d} + \frac{\log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, a d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, a d} - \frac{1}{2 \, {\left(a e^{\left(2 \, d x + 2 \, c\right)} - a\right)} d} + \frac{3}{2 \, {\left(a e^{\left(-2 \, d x - 2 \, c\right)} - a\right)} d}"," ",0,"-1/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + a*b)*d) + 1/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + a*b)*d) + 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^2 + a*b)*sqrt(a*b)*d) - 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^2 + a*b)*sqrt(a*b)*d) + 1/2*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*d) + 1/2*log(e^(2*d*x + 2*c) - 1)/(a*d) - 1/2*log(e^(-2*d*x - 2*c) - 1)/(a*d) - 1/2/((a*e^(2*d*x + 2*c) - a)*d) + 3/2/((a*e^(-2*d*x - 2*c) - a)*d)","B",0
178,1,159,0,0.330677," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","\frac{b^{2} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + a^{2} b\right)} d} + \frac{d x + c}{{\left(a + b\right)} d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(2 \, a e^{\left(-2 \, d x - 2 \, c\right)} - a e^{\left(-4 \, d x - 4 \, c\right)} - a\right)} d} + \frac{{\left(a - b\right)} \log\left(e^{\left(-d x - c\right)} + 1\right)}{a^{2} d} + \frac{{\left(a - b\right)} \log\left(e^{\left(-d x - c\right)} - 1\right)}{a^{2} d}"," ",0,"1/2*b^2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + a^2*b)*d) + (d*x + c)/((a + b)*d) + 2*e^(-2*d*x - 2*c)/((2*a*e^(-2*d*x - 2*c) - a*e^(-4*d*x - 4*c) - a)*d) + (a - b)*log(e^(-d*x - c) + 1)/(a^2*d) + (a - b)*log(e^(-d*x - c) - 1)/(a^2*d)","A",0
179,1,1038,0,0.613225," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a b - b^{2}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{8 \, {\left(a^{3} + a^{2} b\right)} d} + \frac{{\left(a b - b^{2}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{8 \, {\left(a^{3} + a^{2} b\right)} d} + \frac{{\left(a^{2} b - 6 \, a b^{2} + 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)}{16 \, {\left(a^{3} + a^{2} b\right)} \sqrt{a b} d} - \frac{{\left(a^{2} b - 6 \, a b^{2} + 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)}{16 \, {\left(a^{3} + a^{2} b\right)} \sqrt{a b} d} - \frac{3 \, {\left(12 \, a - b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 6 \, {\left(9 \, a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 22 \, a - 3 \, b}{24 \, {\left(a^{2} e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - a^{2}\right)} d} - \frac{3 \, {\left(4 \, a - b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 6 \, {\left(2 \, a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a - 3 \, b}{6 \, {\left(a^{2} e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} e^{\left(2 \, d x + 2 \, c\right)} - a^{2}\right)} d} - \frac{6 \, {\left(9 \, a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, {\left(12 \, a - b\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 22 \, a + 3 \, b}{24 \, {\left(3 \, a^{2} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, a^{2} e^{\left(-4 \, d x - 4 \, c\right)} + a^{2} e^{\left(-6 \, d x - 6 \, c\right)} - a^{2}\right)} d} - \frac{6 \, {\left(2 \, a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, {\left(4 \, a - b\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, a + 3 \, b}{6 \, {\left(3 \, a^{2} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, a^{2} e^{\left(-4 \, d x - 4 \, c\right)} + a^{2} e^{\left(-6 \, d x - 6 \, c\right)} - a^{2}\right)} d} + \frac{6 \, {\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, b e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, a - 3 \, b}{4 \, {\left(3 \, a^{2} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, a^{2} e^{\left(-4 \, d x - 4 \, c\right)} + a^{2} e^{\left(-6 \, d x - 6 \, c\right)} - a^{2}\right)} d} + \frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, a^{2} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, a^{2} d} + \frac{{\left(2 \, a - b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{4 \, a^{2} d} - \frac{b \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, a^{2} d} - \frac{{\left(2 \, a - b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{4 \, a^{2} d} + \frac{b \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, a^{2} d} - \frac{{\left(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)}{4 \, \sqrt{a b} a^{2} d} - \frac{3 \, {\left(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)}{8 \, \sqrt{a b} a^{2} d} + \frac{{\left(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)}{4 \, \sqrt{a b} a^{2} d}"," ",0,"-1/8*(a*b - b^2)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + a^2*b)*d) + 1/8*(a*b - b^2)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + a^2*b)*d) + 1/16*(a^2*b - 6*a*b^2 + b^3)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3 + a^2*b)*sqrt(a*b)*d) - 1/16*(a^2*b - 6*a*b^2 + b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^3 + a^2*b)*sqrt(a*b)*d) - 1/24*(3*(12*a - b)*e^(4*d*x + 4*c) - 6*(9*a - b)*e^(2*d*x + 2*c) + 22*a - 3*b)/((a^2*e^(6*d*x + 6*c) - 3*a^2*e^(4*d*x + 4*c) + 3*a^2*e^(2*d*x + 2*c) - a^2)*d) - 1/6*(3*(4*a - b)*e^(4*d*x + 4*c) - 6*(2*a - b)*e^(2*d*x + 2*c) + 4*a - 3*b)/((a^2*e^(6*d*x + 6*c) - 3*a^2*e^(4*d*x + 4*c) + 3*a^2*e^(2*d*x + 2*c) - a^2)*d) - 1/24*(6*(9*a - b)*e^(-2*d*x - 2*c) - 3*(12*a - b)*e^(-4*d*x - 4*c) - 22*a + 3*b)/((3*a^2*e^(-2*d*x - 2*c) - 3*a^2*e^(-4*d*x - 4*c) + a^2*e^(-6*d*x - 6*c) - a^2)*d) - 1/6*(6*(2*a - b)*e^(-2*d*x - 2*c) - 3*(4*a - b)*e^(-4*d*x - 4*c) - 4*a + 3*b)/((3*a^2*e^(-2*d*x - 2*c) - 3*a^2*e^(-4*d*x - 4*c) + a^2*e^(-6*d*x - 6*c) - a^2)*d) + 1/4*(6*(a + b)*e^(-2*d*x - 2*c) - 3*b*e^(-4*d*x - 4*c) - 2*a - 3*b)/((3*a^2*e^(-2*d*x - 2*c) - 3*a^2*e^(-4*d*x - 4*c) + a^2*e^(-6*d*x - 6*c) - a^2)*d) + 1/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/(a^2*d) - 1/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/(a^2*d) + 1/4*(2*a - b)*log(e^(2*d*x + 2*c) - 1)/(a^2*d) - 1/2*b*log(e^(2*d*x + 2*c) - 1)/(a^2*d) - 1/4*(2*a - b)*log(e^(-2*d*x - 2*c) - 1)/(a^2*d) + 1/2*b*log(e^(-2*d*x - 2*c) - 1)/(a^2*d) - 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d) - 3/8*(a*b + b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d) + 1/4*(a*b - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d)","B",0
180,1,217,0,0.438302," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{{\left(a^{2} + 2 \, a b\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d} + \frac{d x + c}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{b^{2} d}"," ",0,"-2*a^2*e^(-2*d*x - 2*c)/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*e^(-2*d*x - 2*c) + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*e^(-4*d*x - 4*c))*d) - 1/2*(a^2 + 2*a*b)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2*b^2 + 2*a*b^3 + b^4)*d) + (d*x + c)/((a^2 + 2*a*b + b^2)*d) + log(e^(-2*d*x - 2*c) + 1)/(b^2*d)","B",0
181,1,1010,0,0.792351," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} + 9 \, a^{2} b - 9 \, a b^{2} - 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)}{32 \, {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} + \frac{{\left(a^{3} + 9 \, a^{2} b - 9 \, a b^{2} - 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)}{32 \, {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} \sqrt{a b} d} - \frac{a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3} + {\left(a^{3} - 15 \, a^{2} b + 15 \, a b^{2} - b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4} + {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3} + {\left(a^{3} - 15 \, a^{2} b + 15 \, a b^{2} - b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{16 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4} + 2 \, {\left(a^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} b + 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} + a b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{a^{2} - b^{2} + {\left(a^{2} - 6 \, a b + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3} + {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{3} b - a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{2} - b^{2} + {\left(a^{2} - 6 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3} + 2 \, {\left(a^{3} b - a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} b + 2 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{3 \, {\left({\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a + b\right)}}{8 \, {\left(a^{2} b + a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{2} b + a b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(a + b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} a b d} + \frac{{\left(a + b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{8 \, \sqrt{a b} a b d} + \frac{3 \, {\left(a - b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{16 \, \sqrt{a b} a b d}"," ",0,"-1/32*(a^3 + 9*a^2*b - 9*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^3*b + 2*a^2*b^2 + a*b^3)*sqrt(a*b)*d) + 1/32*(a^3 + 9*a^2*b - 9*a*b^2 - b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^3*b + 2*a^2*b^2 + a*b^3)*sqrt(a*b)*d) - 1/16*(a^3 - 5*a^2*b - 5*a*b^2 + b^3 + (a^3 - 15*a^2*b + 15*a*b^2 - b^3)*e^(2*d*x + 2*c))/((a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4 + (a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*e^(4*d*x + 4*c) + 2*(a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*e^(2*d*x + 2*c))*d) + 1/16*(a^3 - 5*a^2*b - 5*a*b^2 + b^3 + (a^3 - 15*a^2*b + 15*a*b^2 - b^3)*e^(-2*d*x - 2*c))/((a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4 + 2*(a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*e^(-2*d*x - 2*c) + (a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*e^(-4*d*x - 4*c))*d) - 1/4*(a^2 - b^2 + (a^2 - 6*a*b + b^2)*e^(2*d*x + 2*c))/((a^3*b + 2*a^2*b^2 + a*b^3 + (a^3*b + 2*a^2*b^2 + a*b^3)*e^(4*d*x + 4*c) + 2*(a^3*b - a*b^3)*e^(2*d*x + 2*c))*d) + 1/4*(a^2 - b^2 + (a^2 - 6*a*b + b^2)*e^(-2*d*x - 2*c))/((a^3*b + 2*a^2*b^2 + a*b^3 + 2*(a^3*b - a*b^3)*e^(-2*d*x - 2*c) + (a^3*b + 2*a^2*b^2 + a*b^3)*e^(-4*d*x - 4*c))*d) + 3/8*((a - b)*e^(-2*d*x - 2*c) + a + b)/((a^2*b + a*b^2 + 2*(a^2*b - a*b^2)*e^(-2*d*x - 2*c) + (a^2*b + a*b^2)*e^(-4*d*x - 4*c))*d) + 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/8*(a + b)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*b*d) + 1/8*(a + b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*b*d) + 3/16*(a - b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*b*d)","B",0
182,1,170,0,0.341129," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, a e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 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} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"2*a*e^(-2*d*x - 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*e^(-2*d*x - 2*c) + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-4*d*x - 4*c))*d) + (d*x + c)/((a^2 + 2*a*b + b^2)*d) + 1/2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d)","B",0
183,1,614,0,0.605314," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} - 4 \, 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)}{8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b} d} + \frac{{\left(a^{2} - 4 \, 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)}{8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b} d} + \frac{a^{2} - b^{2} + {\left(a^{2} - 6 \, a b + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{2} - b^{2} + {\left(a^{2} - 6 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\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{{\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a + b}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{\arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{4 \, \sqrt{a b} a d}"," ",0,"-1/8*(a^2 - 4*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) + 1/8*(a^2 - 4*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) + 1/4*(a^2 - b^2 + (a^2 - 6*a*b + b^2)*e^(2*d*x + 2*c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*e^(4*d*x + 4*c) + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*e^(2*d*x + 2*c))*d) - 1/4*(a^2 - b^2 + (a^2 - 6*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) - 1/2*((a - b)*e^(-2*d*x - 2*c) + a + b)/((a^3 + 2*a^2*b + a*b^2 + 2*(a^3 - a*b^2)*e^(-2*d*x - 2*c) + (a^3 + 2*a^2*b + a*b^2)*e^(-4*d*x - 4*c))*d) + 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^2 + 2*a*b + b^2)*d) - 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d) + 1/4*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a*d)","B",0
184,1,170,0,0.342405," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{2 \, b e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 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} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"-2*b*e^(-2*d*x - 2*c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*e^(-2*d*x - 2*c) + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*e^(-4*d*x - 4*c))*d) + (d*x + c)/((a^2 + 2*a*b + b^2)*d) + 1/2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^2 + 2*a*b + b^2)*d)","B",0
185,1,206,0,0.460986," ","integrate(1/(a+b*tanh(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
186,1,235,0,0.334700," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} 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{{\left(2 \, a b + b^{2}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d} + \frac{d x + c}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{a^{2} d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{a^{2} d}"," ",0,"2*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) - 1/2*(2*a*b + b^2)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^4 + 2*a^3*b + a^2*b^2)*d) + (d*x + c)/((a^2 + 2*a*b + b^2)*d) + log(e^(-d*x - c) + 1)/(a^2*d) + log(e^(-d*x - c) - 1)/(a^2*d)","B",0
187,1,976,0,0.636787," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, a b + b^{2}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d} + \frac{{\left(2 \, a b + b^{2}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d} + \frac{{\left(3 \, a^{2} b - 4 \, 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^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{a b} d} - \frac{{\left(3 \, a^{2} b - 4 \, 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^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{a b} d} + \frac{2 \, a^{3} + 5 \, a^{2} b + 6 \, a b^{2} + 3 \, b^{3} + {\left(2 \, a^{3} + 7 \, a^{2} b + 3 \, b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} - {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{2 \, a^{3} + 5 \, a^{2} b + 6 \, a b^{2} + 3 \, b^{3} + 2 \, {\left(2 \, a^{3} + 2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a^{3} + 7 \, a^{2} b + 3 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} - \frac{2 \, a^{2} + 5 \, a b + 3 \, b^{2} + 2 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{3 \, b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{4 \, \sqrt{a b} a^{2} d} + \frac{\log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, a^{2} d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, a^{2} d}"," ",0,"-1/4*(2*a*b + b^2)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^4 + 2*a^3*b + a^2*b^2)*d) + 1/4*(2*a*b + b^2)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^4 + 2*a^3*b + a^2*b^2)*d) + 1/8*(3*a^2*b - 4*a*b^2 - 3*b^3)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt(a*b)*d) - 1/8*(3*a^2*b - 4*a*b^2 - 3*b^3)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt(a*b)*d) + 1/4*(2*a^3 + 5*a^2*b + 6*a*b^2 + 3*b^3 + (2*a^3 + 7*a^2*b + 3*b^3)*e^(4*d*x + 4*c) + 2*(2*a^3 + 2*a^2*b + a*b^2 - 3*b^3)*e^(2*d*x + 2*c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 - (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*e^(6*d*x + 6*c) - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*e^(4*d*x + 4*c) + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*e^(2*d*x + 2*c))*d) - 1/4*(2*a^3 + 5*a^2*b + 6*a*b^2 + 3*b^3 + 2*(2*a^3 + 2*a^2*b + a*b^2 - 3*b^3)*e^(-2*d*x - 2*c) + (2*a^3 + 7*a^2*b + 3*b^3)*e^(-4*d*x - 4*c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*e^(-2*d*x - 2*c) - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*e^(-4*d*x - 4*c) - (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*e^(-6*d*x - 6*c))*d) - 1/2*(2*a^2 + 5*a*b + 3*b^2 + 2*(2*a^2 - 3*b^2)*e^(-2*d*x - 2*c) + (2*a^2 + 3*a*b + 3*b^2)*e^(-4*d*x - 4*c))/((a^4 + 2*a^3*b + a^2*b^2 + (a^4 - 2*a^3*b - 3*a^2*b^2)*e^(-2*d*x - 2*c) - (a^4 - 2*a^3*b - 3*a^2*b^2)*e^(-4*d*x - 4*c) - (a^4 + 2*a^3*b + a^2*b^2)*e^(-6*d*x - 6*c))*d) + 3/4*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d) + 1/2*log(e^(2*d*x + 2*c) - 1)/(a^2*d) - 1/2*log(e^(-2*d*x - 2*c) - 1)/(a^2*d)","B",0
188,1,402,0,0.346310," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a b^{2} + 2 \, b^{3}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d} + \frac{d x + c}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - 2 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} - 4 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{{\left(a - 2 \, b\right)} \log\left(e^{\left(-d x - c\right)} + 1\right)}{a^{3} d} + \frac{{\left(a - 2 \, b\right)} \log\left(e^{\left(-d x - c\right)} - 1\right)}{a^{3} d}"," ",0,"1/2*(3*a*b^2 + 2*b^3)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^5 + 2*a^4*b + a^3*b^2)*d) + (d*x + c)/((a^2 + 2*a*b + b^2)*d) - 2*((a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*e^(-2*d*x - 2*c) + 2*(a^3 + a^2*b - a*b^2 - 2*b^3)*e^(-4*d*x - 4*c) + (a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3)*e^(-6*d*x - 6*c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 - 4*(a^4*b + 2*a^3*b^2 + a^2*b^3)*e^(-2*d*x - 2*c) - 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*e^(-4*d*x - 4*c) - 4*(a^4*b + 2*a^3*b^2 + a^2*b^3)*e^(-6*d*x - 6*c) + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*e^(-8*d*x - 8*c))*d) + (a - 2*b)*log(e^(-d*x - c) + 1)/(a^3*d) + (a - 2*b)*log(e^(-d*x - c) - 1)/(a^3*d)","B",0
189,1,2345,0,1.083925," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} b - a b^{2} - b^{3}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d} + \frac{{\left(a^{2} b - a b^{2} - b^{3}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d} + \frac{{\left(3 \, a^{3} b - 29 \, a^{2} b^{2} - 11 \, 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)}{32 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{a b} d} - \frac{{\left(3 \, a^{3} b - 29 \, a^{2} b^{2} - 11 \, 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)}{32 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{a b} d} + \frac{44 \, a^{4} + 117 \, a^{3} b + 111 \, a^{2} b^{2} + 23 \, a b^{3} - 15 \, b^{4} + 3 \, {\left(24 \, a^{4} + 69 \, a^{3} b + 45 \, a^{2} b^{2} + 27 \, a b^{3} - 5 \, b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 6 \, {\left(6 \, a^{4} - 31 \, a^{3} b - 50 \, a^{2} b^{2} - 51 \, a b^{3} + 10 \, b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(50 \, a^{4} - 78 \, a^{3} b - 225 \, a^{2} b^{2} - 196 \, a b^{3} + 45 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(10 \, a^{4} + 115 \, a^{3} b + 182 \, a^{2} b^{2} + 95 \, a b^{3} - 30 \, b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{48 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3} - {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{44 \, a^{4} + 117 \, a^{3} b + 111 \, a^{2} b^{2} + 23 \, a b^{3} - 15 \, b^{4} - 2 \, {\left(10 \, a^{4} + 115 \, a^{3} b + 182 \, a^{2} b^{2} + 95 \, a b^{3} - 30 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(50 \, a^{4} - 78 \, a^{3} b - 225 \, a^{2} b^{2} - 196 \, a b^{3} + 45 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 6 \, {\left(6 \, a^{4} - 31 \, a^{3} b - 50 \, a^{2} b^{2} - 51 \, a b^{3} + 10 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(24 \, a^{4} + 69 \, a^{3} b + 45 \, a^{2} b^{2} + 27 \, a b^{3} - 5 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{48 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{8 \, a^{3} + 7 \, a^{2} b - 16 \, a b^{2} - 15 \, b^{3} + 3 \, {\left(8 \, a^{3} + 11 \, a^{2} b + 6 \, a b^{2} - 5 \, b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 6 \, {\left(4 \, a^{3} - 7 \, a^{2} b - 13 \, a b^{2} + 10 \, b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(8 \, a^{3} - 44 \, a^{2} b - 43 \, a b^{2} + 45 \, b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(4 \, a^{3} + 27 \, a^{2} b + 5 \, a b^{2} - 30 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{12 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} - {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(a^{5} + 6 \, a^{4} b + 5 \, a^{3} b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(a^{5} - 4 \, a^{4} b - 5 \, a^{3} b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(a^{5} - 4 \, a^{4} b - 5 \, a^{3} b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(a^{5} + 6 \, a^{4} b + 5 \, a^{3} b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{8 \, a^{3} + 7 \, a^{2} b - 16 \, a b^{2} - 15 \, b^{3} - 2 \, {\left(4 \, a^{3} + 27 \, a^{2} b + 5 \, a b^{2} - 30 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(8 \, a^{3} - 44 \, a^{2} b - 43 \, a b^{2} + 45 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 6 \, {\left(4 \, a^{3} - 7 \, a^{2} b - 13 \, a b^{2} + 10 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(8 \, a^{3} + 11 \, a^{2} b + 6 \, a b^{2} - 5 \, b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{12 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} - {\left(a^{5} + 6 \, a^{4} b + 5 \, a^{3} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{5} - 4 \, a^{4} b - 5 \, a^{3} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{5} - 4 \, a^{4} b - 5 \, a^{3} b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} + 6 \, a^{4} b + 5 \, a^{3} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{4 \, a^{2} + 19 \, a b + 15 \, b^{2} - 2 \, {\left(2 \, a^{2} + 13 \, a b + 30 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(3 \, a b + 5 \, b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{8 \, {\left(a^{4} + a^{3} b - {\left(a^{4} + 5 \, a^{3} b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{4} + 5 \, a^{3} b\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{4} + a^{3} b\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{2 \, a^{3} d} - \frac{b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, a^{3} d} + \frac{{\left(a - b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, a^{3} d} - \frac{b \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{a^{3} d} - \frac{{\left(a - b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, a^{3} d} + \frac{b \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{a^{3} d} - \frac{{\left(3 \, a b - 5 \, 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)}{8 \, \sqrt{a b} a^{3} d} - \frac{3 \, {\left(3 \, a b + 5 \, 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)}{16 \, \sqrt{a b} a^{3} d} + \frac{{\left(3 \, a b - 5 \, 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)}{8 \, \sqrt{a b} a^{3} d}"," ",0,"-1/4*(a^2*b - a*b^2 - b^3)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^5 + 2*a^4*b + a^3*b^2)*d) + 1/4*(a^2*b - a*b^2 - b^3)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^5 + 2*a^4*b + a^3*b^2)*d) + 1/32*(3*a^3*b - 29*a^2*b^2 - 11*a*b^3 + 5*b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt(a*b)*d) - 1/32*(3*a^3*b - 29*a^2*b^2 - 11*a*b^3 + 5*b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt(a*b)*d) + 1/48*(44*a^4 + 117*a^3*b + 111*a^2*b^2 + 23*a*b^3 - 15*b^4 + 3*(24*a^4 + 69*a^3*b + 45*a^2*b^2 + 27*a*b^3 - 5*b^4)*e^(8*d*x + 8*c) + 6*(6*a^4 - 31*a^3*b - 50*a^2*b^2 - 51*a*b^3 + 10*b^4)*e^(6*d*x + 6*c) - 2*(50*a^4 - 78*a^3*b - 225*a^2*b^2 - 196*a*b^3 + 45*b^4)*e^(4*d*x + 4*c) - 2*(10*a^4 + 115*a^3*b + 182*a^2*b^2 + 95*a*b^3 - 30*b^4)*e^(2*d*x + 2*c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3 - (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*e^(10*d*x + 10*c) + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*e^(8*d*x + 8*c) + 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*e^(6*d*x + 6*c) - 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*e^(4*d*x + 4*c) - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*e^(2*d*x + 2*c))*d) - 1/48*(44*a^4 + 117*a^3*b + 111*a^2*b^2 + 23*a*b^3 - 15*b^4 - 2*(10*a^4 + 115*a^3*b + 182*a^2*b^2 + 95*a*b^3 - 30*b^4)*e^(-2*d*x - 2*c) - 2*(50*a^4 - 78*a^3*b - 225*a^2*b^2 - 196*a*b^3 + 45*b^4)*e^(-4*d*x - 4*c) + 6*(6*a^4 - 31*a^3*b - 50*a^2*b^2 - 51*a*b^3 + 10*b^4)*e^(-6*d*x - 6*c) + 3*(24*a^4 + 69*a^3*b + 45*a^2*b^2 + 27*a*b^3 - 5*b^4)*e^(-8*d*x - 8*c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*e^(-2*d*x - 2*c) - 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*e^(-4*d*x - 4*c) + 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*e^(-6*d*x - 6*c) + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*e^(-8*d*x - 8*c) - (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*e^(-10*d*x - 10*c))*d) + 1/12*(8*a^3 + 7*a^2*b - 16*a*b^2 - 15*b^3 + 3*(8*a^3 + 11*a^2*b + 6*a*b^2 - 5*b^3)*e^(8*d*x + 8*c) + 6*(4*a^3 - 7*a^2*b - 13*a*b^2 + 10*b^3)*e^(6*d*x + 6*c) - 2*(8*a^3 - 44*a^2*b - 43*a*b^2 + 45*b^3)*e^(4*d*x + 4*c) - 2*(4*a^3 + 27*a^2*b + 5*a*b^2 - 30*b^3)*e^(2*d*x + 2*c))/((a^5 + 2*a^4*b + a^3*b^2 - (a^5 + 2*a^4*b + a^3*b^2)*e^(10*d*x + 10*c) + (a^5 + 6*a^4*b + 5*a^3*b^2)*e^(8*d*x + 8*c) + 2*(a^5 - 4*a^4*b - 5*a^3*b^2)*e^(6*d*x + 6*c) - 2*(a^5 - 4*a^4*b - 5*a^3*b^2)*e^(4*d*x + 4*c) - (a^5 + 6*a^4*b + 5*a^3*b^2)*e^(2*d*x + 2*c))*d) - 1/12*(8*a^3 + 7*a^2*b - 16*a*b^2 - 15*b^3 - 2*(4*a^3 + 27*a^2*b + 5*a*b^2 - 30*b^3)*e^(-2*d*x - 2*c) - 2*(8*a^3 - 44*a^2*b - 43*a*b^2 + 45*b^3)*e^(-4*d*x - 4*c) + 6*(4*a^3 - 7*a^2*b - 13*a*b^2 + 10*b^3)*e^(-6*d*x - 6*c) + 3*(8*a^3 + 11*a^2*b + 6*a*b^2 - 5*b^3)*e^(-8*d*x - 8*c))/((a^5 + 2*a^4*b + a^3*b^2 - (a^5 + 6*a^4*b + 5*a^3*b^2)*e^(-2*d*x - 2*c) - 2*(a^5 - 4*a^4*b - 5*a^3*b^2)*e^(-4*d*x - 4*c) + 2*(a^5 - 4*a^4*b - 5*a^3*b^2)*e^(-6*d*x - 6*c) + (a^5 + 6*a^4*b + 5*a^3*b^2)*e^(-8*d*x - 8*c) - (a^5 + 2*a^4*b + a^3*b^2)*e^(-10*d*x - 10*c))*d) + 1/8*(4*a^2 + 19*a*b + 15*b^2 - 2*(2*a^2 + 13*a*b + 30*b^2)*e^(-2*d*x - 2*c) - 2*(10*a^2 - 2*a*b - 45*b^2)*e^(-4*d*x - 4*c) - 6*(2*a^2 + a*b + 10*b^2)*e^(-6*d*x - 6*c) + 3*(3*a*b + 5*b^2)*e^(-8*d*x - 8*c))/((a^4 + a^3*b - (a^4 + 5*a^3*b)*e^(-2*d*x - 2*c) - 2*(a^4 - 5*a^3*b)*e^(-4*d*x - 4*c) + 2*(a^4 - 5*a^3*b)*e^(-6*d*x - 6*c) + (a^4 + 5*a^3*b)*e^(-8*d*x - 8*c) - (a^4 + a^3*b)*e^(-10*d*x - 10*c))*d) + 1/2*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/(a^3*d) - 1/2*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/(a^3*d) + 1/2*(a - b)*log(e^(2*d*x + 2*c) - 1)/(a^3*d) - b*log(e^(2*d*x + 2*c) - 1)/(a^3*d) - 1/2*(a - b)*log(e^(-2*d*x - 2*c) - 1)/(a^3*d) + b*log(e^(-2*d*x - 2*c) - 1)/(a^3*d) - 1/8*(3*a*b - 5*b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3*d) - 3/16*(3*a*b + 5*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3*d) + 1/8*(3*a*b - 5*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3*d)","B",0
190,1,3354,0,1.890912," ","integrate(tanh(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{5} + 25 \, a^{4} b + 150 \, a^{3} b^{2} - 150 \, a^{2} b^{3} - 25 \, a b^{4} - 3 \, b^{5}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{512 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5}\right)} \sqrt{a b} d} + \frac{{\left(3 \, a^{5} + 25 \, a^{4} b + 150 \, a^{3} b^{2} - 150 \, a^{2} b^{3} - 25 \, a b^{4} - 3 \, b^{5}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{512 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5}\right)} \sqrt{a b} d} - \frac{3 \, a^{6} + 30 \, a^{5} b - 99 \, a^{4} b^{2} - 252 \, a^{3} b^{3} - 99 \, a^{2} b^{4} + 30 \, a b^{5} + 3 \, b^{6} + {\left(3 \, a^{6} + 28 \, a^{5} b - 465 \, a^{4} b^{2} + 465 \, a^{2} b^{4} - 28 \, a b^{5} - 3 \, b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(9 \, a^{6} + 66 \, a^{5} b - 905 \, a^{4} b^{2} + 1148 \, a^{3} b^{3} - 905 \, a^{2} b^{4} + 66 \, a b^{5} + 9 \, b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(9 \, a^{6} + 68 \, a^{5} b - 659 \, a^{4} b^{2} + 659 \, a^{2} b^{4} - 68 \, a b^{5} - 9 \, b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{256 \, {\left(a^{7} b^{2} + 5 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 5 \, a^{3} b^{6} + a^{2} b^{7} + {\left(a^{7} b^{2} + 5 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 5 \, a^{3} b^{6} + a^{2} b^{7}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{7} b^{2} + 3 \, a^{6} b^{3} + 2 \, a^{5} b^{4} - 2 \, a^{4} b^{5} - 3 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{7} b^{2} + 3 \, a^{6} b^{3} + 2 \, a^{5} b^{4} - 2 \, a^{4} b^{5} - 3 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{3 \, a^{6} + 30 \, a^{5} b - 99 \, a^{4} b^{2} - 252 \, a^{3} b^{3} - 99 \, a^{2} b^{4} + 30 \, a b^{5} + 3 \, b^{6} + {\left(9 \, a^{6} + 68 \, a^{5} b - 659 \, a^{4} b^{2} + 659 \, a^{2} b^{4} - 68 \, a b^{5} - 9 \, b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(9 \, a^{6} + 66 \, a^{5} b - 905 \, a^{4} b^{2} + 1148 \, a^{3} b^{3} - 905 \, a^{2} b^{4} + 66 \, a b^{5} + 9 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{6} + 28 \, a^{5} b - 465 \, a^{4} b^{2} + 465 \, a^{2} b^{4} - 28 \, a b^{5} - 3 \, b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{256 \, {\left(a^{7} b^{2} + 5 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 5 \, a^{3} b^{6} + a^{2} b^{7} + 4 \, {\left(a^{7} b^{2} + 3 \, a^{6} b^{3} + 2 \, a^{5} b^{4} - 2 \, a^{4} b^{5} - 3 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} b^{2} + 7 \, a^{6} b^{3} + 6 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + 7 \, a^{3} b^{6} + 3 \, a^{2} b^{7}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} b^{2} + 3 \, a^{6} b^{3} + 2 \, a^{5} b^{4} - 2 \, a^{4} b^{5} - 3 \, a^{3} b^{6} - a^{2} b^{7}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} b^{2} + 5 \, a^{6} b^{3} + 10 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 5 \, a^{3} b^{6} + a^{2} b^{7}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{3 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 14 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 17 \, a b^{4} - 3 \, b^{5} + {\left(3 \, a^{5} + 15 \, a^{4} b - 98 \, a^{3} b^{2} - 98 \, a^{2} b^{3} + 15 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(9 \, a^{5} + 27 \, a^{4} b - 110 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 27 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(9 \, a^{5} + 29 \, a^{4} b - 86 \, a^{3} b^{2} - 86 \, a^{2} b^{3} + 29 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{128 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6} + {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + 2 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{3 \, {\left(3 \, a^{5} + 17 \, a^{4} b + 14 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 17 \, a b^{4} - 3 \, b^{5} + {\left(9 \, a^{5} + 29 \, a^{4} b - 86 \, a^{3} b^{2} - 86 \, a^{2} b^{3} + 29 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(9 \, a^{5} + 27 \, a^{4} b - 110 \, a^{3} b^{2} + 110 \, a^{2} b^{3} - 27 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{5} + 15 \, a^{4} b - 98 \, a^{3} b^{2} - 98 \, a^{2} b^{3} + 15 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{128 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6} + 4 \, {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + 2 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 4 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{15 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(9 \, a^{4} + 46 \, a^{2} b^{2} + 9 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(9 \, a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{256 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{5} b^{2} + a^{4} b^{3} - a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{5} b^{2} + a^{4} b^{3} - a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{15 \, {\left(3 \, a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4} + {\left(9 \, a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(9 \, a^{4} + 46 \, a^{2} b^{2} + 9 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{256 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5} + 4 \, {\left(a^{5} b^{2} + a^{4} b^{3} - a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} b^{2} + a^{4} b^{3} - a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} + a^{2} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{5 \, {\left(3 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 3 \, b^{3} + {\left(9 \, a^{3} - 13 \, a^{2} b - 13 \, a b^{2} + 9 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(3 \, a^{3} - 5 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{3} + a^{2} b + a b^{2} + 3 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{64 \, {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{4} b^{2} - 2 \, a^{3} b^{3} + 3 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{4} b^{2} + 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{9 \, {\left(a^{2} + 2 \, 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)}{256 \, \sqrt{a b} a^{2} b^{2} d} - \frac{45 \, {\left(a^{2} - 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)}{512 \, \sqrt{a b} a^{2} b^{2} d} + \frac{5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, 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)}{128 \, \sqrt{a b} a^{2} b^{2} d} + \frac{9 \, {\left(a^{2} + 2 \, 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)}{256 \, \sqrt{a b} a^{2} b^{2} d} + \frac{45 \, {\left(a^{2} - 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)}{512 \, \sqrt{a b} a^{2} b^{2} d}"," ",0,"-1/512*(3*a^5 + 25*a^4*b + 150*a^3*b^2 - 150*a^2*b^3 - 25*a*b^4 - 3*b^5)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5)*sqrt(a*b)*d) + 1/512*(3*a^5 + 25*a^4*b + 150*a^3*b^2 - 150*a^2*b^3 - 25*a*b^4 - 3*b^5)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5)*sqrt(a*b)*d) - 1/256*(3*a^6 + 30*a^5*b - 99*a^4*b^2 - 252*a^3*b^3 - 99*a^2*b^4 + 30*a*b^5 + 3*b^6 + (3*a^6 + 28*a^5*b - 465*a^4*b^2 + 465*a^2*b^4 - 28*a*b^5 - 3*b^6)*e^(6*d*x + 6*c) + (9*a^6 + 66*a^5*b - 905*a^4*b^2 + 1148*a^3*b^3 - 905*a^2*b^4 + 66*a*b^5 + 9*b^6)*e^(4*d*x + 4*c) + (9*a^6 + 68*a^5*b - 659*a^4*b^2 + 659*a^2*b^4 - 68*a*b^5 - 9*b^6)*e^(2*d*x + 2*c))/((a^7*b^2 + 5*a^6*b^3 + 10*a^5*b^4 + 10*a^4*b^5 + 5*a^3*b^6 + a^2*b^7 + (a^7*b^2 + 5*a^6*b^3 + 10*a^5*b^4 + 10*a^4*b^5 + 5*a^3*b^6 + a^2*b^7)*e^(8*d*x + 8*c) + 4*(a^7*b^2 + 3*a^6*b^3 + 2*a^5*b^4 - 2*a^4*b^5 - 3*a^3*b^6 - a^2*b^7)*e^(6*d*x + 6*c) + 2*(3*a^7*b^2 + 7*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 + 7*a^3*b^6 + 3*a^2*b^7)*e^(4*d*x + 4*c) + 4*(a^7*b^2 + 3*a^6*b^3 + 2*a^5*b^4 - 2*a^4*b^5 - 3*a^3*b^6 - a^2*b^7)*e^(2*d*x + 2*c))*d) + 1/256*(3*a^6 + 30*a^5*b - 99*a^4*b^2 - 252*a^3*b^3 - 99*a^2*b^4 + 30*a*b^5 + 3*b^6 + (9*a^6 + 68*a^5*b - 659*a^4*b^2 + 659*a^2*b^4 - 68*a*b^5 - 9*b^6)*e^(-2*d*x - 2*c) + (9*a^6 + 66*a^5*b - 905*a^4*b^2 + 1148*a^3*b^3 - 905*a^2*b^4 + 66*a*b^5 + 9*b^6)*e^(-4*d*x - 4*c) + (3*a^6 + 28*a^5*b - 465*a^4*b^2 + 465*a^2*b^4 - 28*a*b^5 - 3*b^6)*e^(-6*d*x - 6*c))/((a^7*b^2 + 5*a^6*b^3 + 10*a^5*b^4 + 10*a^4*b^5 + 5*a^3*b^6 + a^2*b^7 + 4*(a^7*b^2 + 3*a^6*b^3 + 2*a^5*b^4 - 2*a^4*b^5 - 3*a^3*b^6 - a^2*b^7)*e^(-2*d*x - 2*c) + 2*(3*a^7*b^2 + 7*a^6*b^3 + 6*a^5*b^4 + 6*a^4*b^5 + 7*a^3*b^6 + 3*a^2*b^7)*e^(-4*d*x - 4*c) + 4*(a^7*b^2 + 3*a^6*b^3 + 2*a^5*b^4 - 2*a^4*b^5 - 3*a^3*b^6 - a^2*b^7)*e^(-6*d*x - 6*c) + (a^7*b^2 + 5*a^6*b^3 + 10*a^5*b^4 + 10*a^4*b^5 + 5*a^3*b^6 + a^2*b^7)*e^(-8*d*x - 8*c))*d) - 3/128*(3*a^5 + 17*a^4*b + 14*a^3*b^2 - 14*a^2*b^3 - 17*a*b^4 - 3*b^5 + (3*a^5 + 15*a^4*b - 98*a^3*b^2 - 98*a^2*b^3 + 15*a*b^4 + 3*b^5)*e^(6*d*x + 6*c) + (9*a^5 + 27*a^4*b - 110*a^3*b^2 + 110*a^2*b^3 - 27*a*b^4 - 9*b^5)*e^(4*d*x + 4*c) + (9*a^5 + 29*a^4*b - 86*a^3*b^2 - 86*a^2*b^3 + 29*a*b^4 + 9*b^5)*e^(2*d*x + 2*c))/((a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6 + (a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6)*e^(8*d*x + 8*c) + 4*(a^6*b^2 + 2*a^5*b^3 - 2*a^3*b^5 - a^2*b^6)*e^(6*d*x + 6*c) + 2*(3*a^6*b^2 + 4*a^5*b^3 + 2*a^4*b^4 + 4*a^3*b^5 + 3*a^2*b^6)*e^(4*d*x + 4*c) + 4*(a^6*b^2 + 2*a^5*b^3 - 2*a^3*b^5 - a^2*b^6)*e^(2*d*x + 2*c))*d) + 3/128*(3*a^5 + 17*a^4*b + 14*a^3*b^2 - 14*a^2*b^3 - 17*a*b^4 - 3*b^5 + (9*a^5 + 29*a^4*b - 86*a^3*b^2 - 86*a^2*b^3 + 29*a*b^4 + 9*b^5)*e^(-2*d*x - 2*c) + (9*a^5 + 27*a^4*b - 110*a^3*b^2 + 110*a^2*b^3 - 27*a*b^4 - 9*b^5)*e^(-4*d*x - 4*c) + (3*a^5 + 15*a^4*b - 98*a^3*b^2 - 98*a^2*b^3 + 15*a*b^4 + 3*b^5)*e^(-6*d*x - 6*c))/((a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6 + 4*(a^6*b^2 + 2*a^5*b^3 - 2*a^3*b^5 - a^2*b^6)*e^(-2*d*x - 2*c) + 2*(3*a^6*b^2 + 4*a^5*b^3 + 2*a^4*b^4 + 4*a^3*b^5 + 3*a^2*b^6)*e^(-4*d*x - 4*c) + 4*(a^6*b^2 + 2*a^5*b^3 - 2*a^3*b^5 - a^2*b^6)*e^(-6*d*x - 6*c) + (a^6*b^2 + 4*a^5*b^3 + 6*a^4*b^4 + 4*a^3*b^5 + a^2*b^6)*e^(-8*d*x - 8*c))*d) - 15/256*(3*a^4 + 8*a^3*b + 10*a^2*b^2 + 8*a*b^3 + 3*b^4 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*e^(6*d*x + 6*c) + (9*a^4 + 46*a^2*b^2 + 9*b^4)*e^(4*d*x + 4*c) + (9*a^4 + 2*a^3*b - 2*a*b^3 - 9*b^4)*e^(2*d*x + 2*c))/((a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5 + (a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5)*e^(8*d*x + 8*c) + 4*(a^5*b^2 + a^4*b^3 - a^3*b^4 - a^2*b^5)*e^(6*d*x + 6*c) + 2*(3*a^5*b^2 + a^4*b^3 + a^3*b^4 + 3*a^2*b^5)*e^(4*d*x + 4*c) + 4*(a^5*b^2 + a^4*b^3 - a^3*b^4 - a^2*b^5)*e^(2*d*x + 2*c))*d) + 15/256*(3*a^4 + 8*a^3*b + 10*a^2*b^2 + 8*a*b^3 + 3*b^4 + (9*a^4 + 2*a^3*b - 2*a*b^3 - 9*b^4)*e^(-2*d*x - 2*c) + (9*a^4 + 46*a^2*b^2 + 9*b^4)*e^(-4*d*x - 4*c) + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*e^(-6*d*x - 6*c))/((a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5 + 4*(a^5*b^2 + a^4*b^3 - a^3*b^4 - a^2*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^5*b^2 + a^4*b^3 + a^3*b^4 + 3*a^2*b^5)*e^(-4*d*x - 4*c) + 4*(a^5*b^2 + a^4*b^3 - a^3*b^4 - a^2*b^5)*e^(-6*d*x - 6*c) + (a^5*b^2 + 3*a^4*b^3 + 3*a^3*b^4 + a^2*b^5)*e^(-8*d*x - 8*c))*d) + 5/64*(3*a^3 + 3*a^2*b - 3*a*b^2 - 3*b^3 + (9*a^3 - 13*a^2*b - 13*a*b^2 + 9*b^3)*e^(-2*d*x - 2*c) + 3*(3*a^3 - 5*a^2*b + 5*a*b^2 - 3*b^3)*e^(-4*d*x - 4*c) + (3*a^3 + a^2*b + a*b^2 + 3*b^3)*e^(-6*d*x - 6*c))/((a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + 4*(a^4*b^2 - a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^4*b^2 - 2*a^3*b^3 + 3*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^4*b^2 - a^2*b^4)*e^(-6*d*x - 6*c) + (a^4*b^2 + 2*a^3*b^3 + a^2*b^4)*e^(-8*d*x - 8*c))*d) + 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 9/256*(a^2 + 2*a*b + b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2*d) - 45/512*(a^2 - b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2*d) + 5/128*(3*a^2 - 2*a*b + 3*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2*d) + 9/256*(a^2 + 2*a*b + b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2*d) + 45/512*(a^2 - b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b^2*d)","B",0
191,1,376,0,0.363010," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{d x + c}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{4 \, {\left({\left(a^{2} + a b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{2} - 2 \, a b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{2} + a b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 4*((a^2 + a*b)*e^(-2*d*x - 2*c) + (a^2 - 2*a*b)*e^(-4*d*x - 4*c) + (a^2 + a*b)*e^(-6*d*x - 6*c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*e^(-2*d*x - 2*c) + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*e^(-4*d*x - 4*c) + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*e^(-6*d*x - 6*c) + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*e^(-8*d*x - 8*c))*d) + 1/2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
192,1,2432,0,1.345095," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(a^{4} + 24 \, a^{3} b - 54 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, 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)}{128 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} + \frac{{\left(a^{4} + 24 \, a^{3} b - 54 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, 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)}{128 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} \sqrt{a b} d} - \frac{a^{5} - 33 \, a^{4} b - 54 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 21 \, a b^{4} + 3 \, b^{5} + {\left(a^{5} - 71 \, a^{4} b + 98 \, a^{3} b^{2} + 154 \, a^{2} b^{3} - 19 \, a b^{4} - 3 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(3 \, a^{5} - 171 \, a^{4} b + 310 \, a^{3} b^{2} - 254 \, a^{2} b^{3} + 39 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(3 \, a^{5} - 133 \, a^{4} b + 86 \, a^{3} b^{2} + 190 \, a^{2} b^{3} - 41 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{64 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{5} - 33 \, a^{4} b - 54 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 21 \, a b^{4} + 3 \, b^{5} + {\left(3 \, a^{5} - 133 \, a^{4} b + 86 \, a^{3} b^{2} + 190 \, a^{2} b^{3} - 41 \, a b^{4} - 9 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{5} - 171 \, a^{4} b + 310 \, a^{3} b^{2} - 254 \, a^{2} b^{3} + 39 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{5} - 71 \, a^{4} b + 98 \, a^{3} b^{2} + 154 \, a^{2} b^{3} - 19 \, a b^{4} - 3 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{64 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{a^{4} - 4 \, a^{3} b - 14 \, a^{2} b^{2} - 12 \, a b^{3} - 3 \, b^{4} + {\left(a^{4} - 26 \, a^{3} b - 20 \, a^{2} b^{2} + 10 \, a b^{3} + 3 \, b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(3 \, a^{4} - 52 \, a^{3} b + 6 \, a^{2} b^{2} - 12 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(3 \, a^{4} - 30 \, a^{3} b - 28 \, a^{2} b^{2} + 14 \, a b^{3} + 9 \, b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5} + {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{6} b + 4 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{4} - 4 \, a^{3} b - 14 \, a^{2} b^{2} - 12 \, a b^{3} - 3 \, b^{4} + {\left(3 \, a^{4} - 30 \, a^{3} b - 28 \, a^{2} b^{2} + 14 \, a b^{3} + 9 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{4} - 52 \, a^{3} b + 6 \, a^{2} b^{2} - 12 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{4} - 26 \, a^{3} b - 20 \, a^{2} b^{2} + 10 \, a b^{3} + 3 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5} + 4 \, {\left(a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} b + 4 \, a^{5} b^{2} + 2 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - a^{2} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} b + 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{3 \, {\left(a^{3} + 5 \, a^{2} b + 7 \, a b^{2} + 3 \, b^{3} + {\left(3 \, a^{3} + 13 \, a^{2} b + a b^{2} - 9 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{3} + 7 \, a^{2} b - 3 \, a b^{2} + 9 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{32 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4} + 4 \, {\left(a^{5} b + a^{4} b^{2} - a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3} + 3 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} b + a^{4} b^{2} - a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} b + 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} + a^{2} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{{\left(a + 3 \, b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{32 \, \sqrt{a b} a^{2} b d} + \frac{{\left(a + 3 \, b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{32 \, \sqrt{a b} a^{2} b d} + \frac{3 \, {\left(a - 3 \, b\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{64 \, \sqrt{a b} a^{2} b d}"," ",0,"-1/128*(a^4 + 24*a^3*b - 54*a^2*b^2 - 16*a*b^3 - 3*b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) + 1/128*(a^4 + 24*a^3*b - 54*a^2*b^2 - 16*a*b^3 - 3*b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*sqrt(a*b)*d) - 1/64*(a^5 - 33*a^4*b - 54*a^3*b^2 - 2*a^2*b^3 + 21*a*b^4 + 3*b^5 + (a^5 - 71*a^4*b + 98*a^3*b^2 + 154*a^2*b^3 - 19*a*b^4 - 3*b^5)*e^(6*d*x + 6*c) + (3*a^5 - 171*a^4*b + 310*a^3*b^2 - 254*a^2*b^3 + 39*a*b^4 + 9*b^5)*e^(4*d*x + 4*c) + (3*a^5 - 133*a^4*b + 86*a^3*b^2 + 190*a^2*b^3 - 41*a*b^4 - 9*b^5)*e^(2*d*x + 2*c))/((a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6 + (a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*e^(8*d*x + 8*c) + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*e^(6*d*x + 6*c) + 2*(3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*e^(4*d*x + 4*c) + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*e^(2*d*x + 2*c))*d) + 1/64*(a^5 - 33*a^4*b - 54*a^3*b^2 - 2*a^2*b^3 + 21*a*b^4 + 3*b^5 + (3*a^5 - 133*a^4*b + 86*a^3*b^2 + 190*a^2*b^3 - 41*a*b^4 - 9*b^5)*e^(-2*d*x - 2*c) + (3*a^5 - 171*a^4*b + 310*a^3*b^2 - 254*a^2*b^3 + 39*a*b^4 + 9*b^5)*e^(-4*d*x - 4*c) + (a^5 - 71*a^4*b + 98*a^3*b^2 + 154*a^2*b^3 - 19*a*b^4 - 3*b^5)*e^(-6*d*x - 6*c))/((a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6 + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*e^(-2*d*x - 2*c) + 2*(3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*e^(-4*d*x - 4*c) + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*e^(-6*d*x - 6*c) + (a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*e^(-8*d*x - 8*c))*d) - 1/16*(a^4 - 4*a^3*b - 14*a^2*b^2 - 12*a*b^3 - 3*b^4 + (a^4 - 26*a^3*b - 20*a^2*b^2 + 10*a*b^3 + 3*b^4)*e^(6*d*x + 6*c) + (3*a^4 - 52*a^3*b + 6*a^2*b^2 - 12*a*b^3 - 9*b^4)*e^(4*d*x + 4*c) + (3*a^4 - 30*a^3*b - 28*a^2*b^2 + 14*a*b^3 + 9*b^4)*e^(2*d*x + 2*c))/((a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5 + (a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5)*e^(8*d*x + 8*c) + 4*(a^6*b + 2*a^5*b^2 - 2*a^3*b^4 - a^2*b^5)*e^(6*d*x + 6*c) + 2*(3*a^6*b + 4*a^5*b^2 + 2*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5)*e^(4*d*x + 4*c) + 4*(a^6*b + 2*a^5*b^2 - 2*a^3*b^4 - a^2*b^5)*e^(2*d*x + 2*c))*d) + 1/16*(a^4 - 4*a^3*b - 14*a^2*b^2 - 12*a*b^3 - 3*b^4 + (3*a^4 - 30*a^3*b - 28*a^2*b^2 + 14*a*b^3 + 9*b^4)*e^(-2*d*x - 2*c) + (3*a^4 - 52*a^3*b + 6*a^2*b^2 - 12*a*b^3 - 9*b^4)*e^(-4*d*x - 4*c) + (a^4 - 26*a^3*b - 20*a^2*b^2 + 10*a*b^3 + 3*b^4)*e^(-6*d*x - 6*c))/((a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5 + 4*(a^6*b + 2*a^5*b^2 - 2*a^3*b^4 - a^2*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^6*b + 4*a^5*b^2 + 2*a^4*b^3 + 4*a^3*b^4 + 3*a^2*b^5)*e^(-4*d*x - 4*c) + 4*(a^6*b + 2*a^5*b^2 - 2*a^3*b^4 - a^2*b^5)*e^(-6*d*x - 6*c) + (a^6*b + 4*a^5*b^2 + 6*a^4*b^3 + 4*a^3*b^4 + a^2*b^5)*e^(-8*d*x - 8*c))*d) + 3/32*(a^3 + 5*a^2*b + 7*a*b^2 + 3*b^3 + (3*a^3 + 13*a^2*b + a*b^2 - 9*b^3)*e^(-2*d*x - 2*c) + (3*a^3 + 7*a^2*b - 3*a*b^2 + 9*b^3)*e^(-4*d*x - 4*c) + (a^3 - a^2*b - 5*a*b^2 - 3*b^3)*e^(-6*d*x - 6*c))/((a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4 + 4*(a^5*b + a^4*b^2 - a^3*b^3 - a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^5*b + a^4*b^2 + a^3*b^3 + 3*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^5*b + a^4*b^2 - a^3*b^3 - a^2*b^4)*e^(-6*d*x - 6*c) + (a^5*b + 3*a^4*b^2 + 3*a^3*b^3 + a^2*b^4)*e^(-8*d*x - 8*c))*d) + 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/32*(a + 3*b)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b*d) + 1/32*(a + 3*b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b*d) + 3/64*(a - 3*b)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*b*d)","B",0
193,1,384,0,0.366747," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{d x + c}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{2 \, {\left({\left(a^{2} - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{2} - a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{2} - b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 2*((a^2 - b^2)*e^(-2*d*x - 2*c) + 2*(a^2 - a*b + b^2)*e^(-4*d*x - 4*c) + (a^2 - b^2)*e^(-6*d*x - 6*c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*e^(-2*d*x - 2*c) + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*e^(-4*d*x - 4*c) + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*e^(-6*d*x - 6*c) + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*e^(-8*d*x - 8*c))*d) + 1/2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
194,1,1472,0,0.900555," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{3} - 21 \, a^{2} b - 11 \, 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)}{32 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b} d} + \frac{{\left(3 \, a^{3} - 21 \, a^{2} b - 11 \, 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)}{32 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{a b} d} + \frac{5 \, a^{4} - 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4} + {\left(5 \, a^{4} - 46 \, a^{3} b - 40 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(15 \, a^{4} - 104 \, a^{3} b + 58 \, a^{2} b^{2} - 24 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(15 \, a^{4} - 58 \, a^{3} b - 56 \, a^{2} b^{2} + 26 \, a b^{3} + 9 \, b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\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} + {\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)} + 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)} + 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(2 \, d x + 2 \, c\right)}\right)} d} - \frac{5 \, a^{4} - 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4} + {\left(15 \, a^{4} - 58 \, a^{3} b - 56 \, a^{2} b^{2} + 26 \, a b^{3} + 9 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(15 \, a^{4} - 104 \, a^{3} b + 58 \, a^{2} b^{2} - 24 \, a b^{3} - 9 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(5 \, a^{4} - 46 \, a^{3} b - 40 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\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{5 \, a^{3} + 13 \, a^{2} b + 11 \, a b^{2} + 3 \, b^{3} + {\left(15 \, a^{3} + 13 \, a^{2} b - 11 \, a b^{2} - 9 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(15 \, a^{3} - a^{2} b + 9 \, a b^{2} + 9 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(5 \, a^{3} - a^{2} b - 9 \, a b^{2} - 3 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{8 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4} + 4 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} + 4 \, a^{5} b + 2 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 3 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{3 \, \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{2} d}"," ",0,"-1/32*(3*a^3 - 21*a^2*b - 11*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) + 1/32*(3*a^3 - 21*a^2*b - 11*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) + 1/16*(5*a^4 - 18*a^2*b^2 - 16*a*b^3 - 3*b^4 + (5*a^4 - 46*a^3*b - 40*a^2*b^2 + 14*a*b^3 + 3*b^4)*e^(6*d*x + 6*c) + (15*a^4 - 104*a^3*b + 58*a^2*b^2 - 24*a*b^3 - 9*b^4)*e^(4*d*x + 4*c) + (15*a^4 - 58*a^3*b - 56*a^2*b^2 + 26*a*b^3 + 9*b^4)*e^(2*d*x + 2*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 + (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) + 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) + 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^(2*d*x + 2*c))*d) - 1/16*(5*a^4 - 18*a^2*b^2 - 16*a*b^3 - 3*b^4 + (15*a^4 - 58*a^3*b - 56*a^2*b^2 + 26*a*b^3 + 9*b^4)*e^(-2*d*x - 2*c) + (15*a^4 - 104*a^3*b + 58*a^2*b^2 - 24*a*b^3 - 9*b^4)*e^(-4*d*x - 4*c) + (5*a^4 - 46*a^3*b - 40*a^2*b^2 + 14*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) - 1/8*(5*a^3 + 13*a^2*b + 11*a*b^2 + 3*b^3 + (15*a^3 + 13*a^2*b - 11*a*b^2 - 9*b^3)*e^(-2*d*x - 2*c) + (15*a^3 - a^2*b + 9*a*b^2 + 9*b^3)*e^(-4*d*x - 4*c) + (5*a^3 - a^2*b - 9*a*b^2 - 3*b^3)*e^(-6*d*x - 6*c))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4 + 4*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^6 + 4*a^5*b + 2*a^4*b^2 + 4*a^3*b^3 + 3*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*e^(-6*d*x - 6*c) + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*e^(-8*d*x - 8*c))*d) + 1/4*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/4*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 3/16*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^2*d)","B",0
195,1,378,0,0.369890," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{d x + c}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{4 \, {\left({\left(a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a b - b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a b + b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"(d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 4*((a*b + b^2)*e^(-2*d*x - 2*c) + (2*a*b - b^2)*e^(-4*d*x - 4*c) + (a*b + b^2)*e^(-6*d*x - 6*c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*e^(-2*d*x - 2*c) + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*e^(-4*d*x - 4*c) + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*e^(-6*d*x - 6*c) + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*e^(-8*d*x - 8*c))*d) + 1/2*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
196,1,507,0,0.566230," ","integrate(1/(a+b*tanh(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
197,1,498,0,0.397006," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d} + \frac{d x + c}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{2 \, {\left({\left(3 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\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} + 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{\log\left(e^{\left(-d x - c\right)} + 1\right)}{a^{3} d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{a^{3} d}"," ",0,"-1/2*(3*a^2*b + 3*a*b^2 + b^3)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d) + (d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 2*((3*a^2*b^2 + 4*a*b^3 + b^4)*e^(-2*d*x - 2*c) + 2*(3*a^2*b^2 - a*b^3 - b^4)*e^(-4*d*x - 4*c) + (3*a^2*b^2 + 4*a*b^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) + log(e^(-d*x - c) + 1)/(a^3*d) + log(e^(-d*x - c) - 1)/(a^3*d)","B",0
198,1,1944,0,0.942352," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d} + \frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d} + \frac{{\left(15 \, a^{3} b - 25 \, a^{2} b^{2} - 39 \, a b^{3} - 15 \, 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)}{32 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{a b} d} - \frac{{\left(15 \, a^{3} b - 25 \, a^{2} b^{2} - 39 \, a b^{3} - 15 \, 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)}{32 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{a b} d} + \frac{8 \, a^{5} + 31 \, a^{4} b + 72 \, a^{3} b^{2} + 98 \, a^{2} b^{3} + 64 \, a b^{4} + 15 \, b^{5} + {\left(8 \, a^{5} + 49 \, a^{4} b + 18 \, a^{3} b^{2} + 38 \, a b^{4} + 15 \, b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(16 \, a^{5} + 57 \, a^{4} b - 9 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 39 \, a b^{4} - 30 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 83 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 53 \, a b^{4} + 45 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(16 \, a^{5} + 39 \, a^{4} b + 73 \, a^{3} b^{2} + 15 \, a^{2} b^{3} - 65 \, a b^{4} - 30 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} - {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} e^{\left(10 \, d x + 10 \, c\right)} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{8 \, a^{5} + 31 \, a^{4} b + 72 \, a^{3} b^{2} + 98 \, a^{2} b^{3} + 64 \, a b^{4} + 15 \, b^{5} + 2 \, {\left(16 \, a^{5} + 39 \, a^{4} b + 73 \, a^{3} b^{2} + 15 \, a^{2} b^{3} - 65 \, a b^{4} - 30 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 83 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 53 \, a b^{4} + 45 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(16 \, a^{5} + 57 \, a^{4} b - 9 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 39 \, a b^{4} - 30 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(8 \, a^{5} + 49 \, a^{4} b + 18 \, a^{3} b^{2} + 38 \, a b^{4} + 15 \, b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{16 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} - \frac{8 \, a^{4} + 41 \, a^{3} b + 73 \, a^{2} b^{2} + 55 \, a b^{3} + 15 \, b^{4} + 2 \, {\left(16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{15 \, b \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{16 \, \sqrt{a b} a^{3} d} + \frac{\log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, a^{3} d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, a^{3} d}"," ",0,"-1/4*(3*a^2*b + 3*a*b^2 + b^3)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d) + 1/4*(3*a^2*b + 3*a*b^2 + b^3)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d) + 1/32*(15*a^3*b - 25*a^2*b^2 - 39*a*b^3 - 15*b^4)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt(a*b)*d) - 1/32*(15*a^3*b - 25*a^2*b^2 - 39*a*b^3 - 15*b^4)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt(a*b)*d) + 1/16*(8*a^5 + 31*a^4*b + 72*a^3*b^2 + 98*a^2*b^3 + 64*a*b^4 + 15*b^5 + (8*a^5 + 49*a^4*b + 18*a^3*b^2 + 38*a*b^4 + 15*b^5)*e^(8*d*x + 8*c) + 2*(16*a^5 + 57*a^4*b - 9*a^3*b^2 + 37*a^2*b^3 - 39*a*b^4 - 30*b^5)*e^(6*d*x + 6*c) + 2*(24*a^5 + 56*a^4*b + 83*a^3*b^2 - 37*a^2*b^3 + 53*a*b^4 + 45*b^5)*e^(4*d*x + 4*c) + 2*(16*a^5 + 39*a^4*b + 73*a^3*b^2 + 15*a^2*b^3 - 65*a*b^4 - 30*b^5)*e^(2*d*x + 2*c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 - (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*e^(10*d*x + 10*c) - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*e^(8*d*x + 8*c) - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*e^(6*d*x + 6*c) + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*e^(4*d*x + 4*c) + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*e^(2*d*x + 2*c))*d) - 1/16*(8*a^5 + 31*a^4*b + 72*a^3*b^2 + 98*a^2*b^3 + 64*a*b^4 + 15*b^5 + 2*(16*a^5 + 39*a^4*b + 73*a^3*b^2 + 15*a^2*b^3 - 65*a*b^4 - 30*b^5)*e^(-2*d*x - 2*c) + 2*(24*a^5 + 56*a^4*b + 83*a^3*b^2 - 37*a^2*b^3 + 53*a*b^4 + 45*b^5)*e^(-4*d*x - 4*c) + 2*(16*a^5 + 57*a^4*b - 9*a^3*b^2 + 37*a^2*b^3 - 39*a*b^4 - 30*b^5)*e^(-6*d*x - 6*c) + (8*a^5 + 49*a^4*b + 18*a^3*b^2 + 38*a*b^4 + 15*b^5)*e^(-8*d*x - 8*c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*e^(-2*d*x - 2*c) + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*e^(-4*d*x - 4*c) - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*e^(-6*d*x - 6*c) - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*e^(-8*d*x - 8*c) - (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*e^(-10*d*x - 10*c))*d) - 1/8*(8*a^4 + 41*a^3*b + 73*a^2*b^2 + 55*a*b^3 + 15*b^4 + 2*(16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4)*e^(-2*d*x - 2*c) + 2*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*e^(-4*d*x - 4*c) + 2*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*e^(-6*d*x - 6*c) + (8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*e^(-8*d*x - 8*c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*e^(-2*d*x - 2*c) + 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*e^(-4*d*x - 4*c) - 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*e^(-6*d*x - 6*c) - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*e^(-8*d*x - 8*c) - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*e^(-10*d*x - 10*c))*d) + 15/16*b*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^3*d) + 1/2*log(e^(2*d*x + 2*c) - 1)/(a^3*d) - 1/2*log(e^(-2*d*x - 2*c) - 1)/(a^3*d)","B",0
199,1,770,0,0.421291," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(6 \, a^{2} b^{2} + 8 \, a b^{3} + 3 \, b^{4}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{2 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d} + \frac{d x + c}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{2 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 11 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(2 \, a^{5} + 6 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - 13 \, a b^{4} - 6 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 15 \, a b^{4} + 9 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 2 \, {\left(2 \, a^{5} + 6 \, a^{4} b + 4 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - 13 \, a b^{4} - 6 \, b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 11 \, a b^{4} + 3 \, b^{5}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{{\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5} + 2 \, {\left(a^{8} + a^{7} b - 6 \, a^{6} b^{2} - 14 \, a^{5} b^{3} - 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{8} + 5 \, a^{7} b - 6 \, a^{6} b^{2} - 38 \, a^{5} b^{3} - 43 \, a^{4} b^{4} - 15 \, a^{3} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(a^{8} + 5 \, a^{7} b - 6 \, a^{6} b^{2} - 38 \, a^{5} b^{3} - 43 \, a^{4} b^{4} - 15 \, a^{3} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 2 \, {\left(a^{8} + a^{7} b - 6 \, a^{6} b^{2} - 14 \, a^{5} b^{3} - 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} e^{\left(-12 \, d x - 12 \, c\right)}\right)} d} + \frac{{\left(a - 3 \, b\right)} \log\left(e^{\left(-d x - c\right)} + 1\right)}{a^{4} d} + \frac{{\left(a - 3 \, b\right)} \log\left(e^{\left(-d x - c\right)} - 1\right)}{a^{4} d}"," ",0,"1/2*(6*a^2*b^2 + 8*a*b^3 + 3*b^4)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d) + (d*x + c)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 2*((a^5 + 5*a^4*b + 10*a^3*b^2 + 14*a^2*b^3 + 11*a*b^4 + 3*b^5)*e^(-2*d*x - 2*c) + 2*(2*a^5 + 6*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 - 13*a*b^4 - 6*b^5)*e^(-4*d*x - 4*c) + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 2*a^2*b^3 + 15*a*b^4 + 9*b^5)*e^(-6*d*x - 6*c) + 2*(2*a^5 + 6*a^4*b + 4*a^3*b^2 - 4*a^2*b^3 - 13*a*b^4 - 6*b^5)*e^(-8*d*x - 8*c) + (a^5 + 5*a^4*b + 10*a^3*b^2 + 14*a^2*b^3 + 11*a*b^4 + 3*b^5)*e^(-10*d*x - 10*c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5 + 2*(a^8 + a^7*b - 6*a^6*b^2 - 14*a^5*b^3 - 11*a^4*b^4 - 3*a^3*b^5)*e^(-2*d*x - 2*c) - (a^8 + 5*a^7*b - 6*a^6*b^2 - 38*a^5*b^3 - 43*a^4*b^4 - 15*a^3*b^5)*e^(-4*d*x - 4*c) - 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*e^(-6*d*x - 6*c) - (a^8 + 5*a^7*b - 6*a^6*b^2 - 38*a^5*b^3 - 43*a^4*b^4 - 15*a^3*b^5)*e^(-8*d*x - 8*c) + 2*(a^8 + a^7*b - 6*a^6*b^2 - 14*a^5*b^3 - 11*a^4*b^4 - 3*a^3*b^5)*e^(-10*d*x - 10*c) + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*e^(-12*d*x - 12*c))*d) + (a - 3*b)*log(e^(-d*x - c) + 1)/(a^4*d) + (a - 3*b)*log(e^(-d*x - c) - 1)/(a^4*d)","B",0
200,1,4285,0,2.671389," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{3} b - 3 \, a^{2} b^{2} - 7 \, a b^{3} - 3 \, b^{4}\right)} \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d} + \frac{{\left(3 \, a^{3} b - 3 \, a^{2} b^{2} - 7 \, a b^{3} - 3 \, b^{4}\right)} \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} d} + \frac{{\left(15 \, a^{4} b - 200 \, a^{3} b^{2} - 186 \, a^{2} b^{3} + 35 \, b^{5}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{128 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{a b} d} - \frac{{\left(15 \, a^{4} b - 200 \, a^{3} b^{2} - 186 \, a^{2} b^{3} + 35 \, b^{5}\right)} \arctan\left(\frac{{\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a - b}{2 \, \sqrt{a b}}\right)}{128 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{a b} d} + \frac{176 \, a^{6} + 781 \, a^{5} b + 1571 \, a^{4} b^{2} + 1538 \, a^{3} b^{3} + 502 \, a^{2} b^{4} - 175 \, a b^{5} - 105 \, b^{6} + 3 \, {\left(96 \, a^{6} + 465 \, a^{5} b + 665 \, a^{4} b^{2} + 706 \, a^{3} b^{3} + 506 \, a^{2} b^{4} + 61 \, a b^{5} - 35 \, b^{6}\right)} e^{\left(12 \, d x + 12 \, c\right)} + 6 \, {\left(120 \, a^{6} + 192 \, a^{5} b - 315 \, a^{4} b^{2} - 728 \, a^{3} b^{3} - 1070 \, a^{2} b^{4} - 240 \, a b^{5} + 105 \, b^{6}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(176 \, a^{6} - 281 \, a^{5} b + 3509 \, a^{4} b^{2} + 3950 \, a^{3} b^{3} + 12226 \, a^{2} b^{4} + 3755 \, a b^{5} - 1575 \, b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} - 4 \, {\left(184 \, a^{6} + 48 \, a^{5} b + 473 \, a^{4} b^{2} + 970 \, a^{3} b^{3} + 3684 \, a^{2} b^{4} + 1070 \, a b^{5} - 525 \, b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(384 \, a^{6} + 1127 \, a^{5} b - 861 \, a^{4} b^{2} - 7146 \, a^{3} b^{3} - 11386 \, a^{2} b^{4} - 1965 \, a b^{5} + 1575 \, b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(136 \, a^{6} - 96 \, a^{5} b - 1309 \, a^{4} b^{2} - 2996 \, a^{3} b^{3} - 2238 \, a^{2} b^{4} - 4 \, a b^{5} + 315 \, b^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{192 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5} - {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} e^{\left(14 \, d x + 14 \, c\right)} - {\left(a^{9} - 3 \, a^{8} b - 22 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 27 \, a^{5} b^{4} - 7 \, a^{4} b^{5}\right)} e^{\left(12 \, d x + 12 \, c\right)} + {\left(3 \, a^{9} + 7 \, a^{8} b - 18 \, a^{7} b^{2} - 66 \, a^{6} b^{3} - 65 \, a^{5} b^{4} - 21 \, a^{4} b^{5}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(3 \, a^{9} - a^{8} b + 14 \, a^{7} b^{2} + 78 \, a^{6} b^{3} + 95 \, a^{5} b^{4} + 35 \, a^{4} b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} - {\left(3 \, a^{9} - a^{8} b + 14 \, a^{7} b^{2} + 78 \, a^{6} b^{3} + 95 \, a^{5} b^{4} + 35 \, a^{4} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(3 \, a^{9} + 7 \, a^{8} b - 18 \, a^{7} b^{2} - 66 \, a^{6} b^{3} - 65 \, a^{5} b^{4} - 21 \, a^{4} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{9} - 3 \, a^{8} b - 22 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 27 \, a^{5} b^{4} - 7 \, a^{4} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{176 \, a^{6} + 781 \, a^{5} b + 1571 \, a^{4} b^{2} + 1538 \, a^{3} b^{3} + 502 \, a^{2} b^{4} - 175 \, a b^{5} - 105 \, b^{6} + 2 \, {\left(136 \, a^{6} - 96 \, a^{5} b - 1309 \, a^{4} b^{2} - 2996 \, a^{3} b^{3} - 2238 \, a^{2} b^{4} - 4 \, a b^{5} + 315 \, b^{6}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(384 \, a^{6} + 1127 \, a^{5} b - 861 \, a^{4} b^{2} - 7146 \, a^{3} b^{3} - 11386 \, a^{2} b^{4} - 1965 \, a b^{5} + 1575 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(184 \, a^{6} + 48 \, a^{5} b + 473 \, a^{4} b^{2} + 970 \, a^{3} b^{3} + 3684 \, a^{2} b^{4} + 1070 \, a b^{5} - 525 \, b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(176 \, a^{6} - 281 \, a^{5} b + 3509 \, a^{4} b^{2} + 3950 \, a^{3} b^{3} + 12226 \, a^{2} b^{4} + 3755 \, a b^{5} - 1575 \, b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, {\left(120 \, a^{6} + 192 \, a^{5} b - 315 \, a^{4} b^{2} - 728 \, a^{3} b^{3} - 1070 \, a^{2} b^{4} - 240 \, a b^{5} + 105 \, b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + 3 \, {\left(96 \, a^{6} + 465 \, a^{5} b + 665 \, a^{4} b^{2} + 706 \, a^{3} b^{3} + 506 \, a^{2} b^{4} + 61 \, a b^{5} - 35 \, b^{6}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{192 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5} + {\left(a^{9} - 3 \, a^{8} b - 22 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 27 \, a^{5} b^{4} - 7 \, a^{4} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{9} + 7 \, a^{8} b - 18 \, a^{7} b^{2} - 66 \, a^{6} b^{3} - 65 \, a^{5} b^{4} - 21 \, a^{4} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{9} - a^{8} b + 14 \, a^{7} b^{2} + 78 \, a^{6} b^{3} + 95 \, a^{5} b^{4} + 35 \, a^{4} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{9} - a^{8} b + 14 \, a^{7} b^{2} + 78 \, a^{6} b^{3} + 95 \, a^{5} b^{4} + 35 \, a^{4} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{9} + 7 \, a^{8} b - 18 \, a^{7} b^{2} - 66 \, a^{6} b^{3} - 65 \, a^{5} b^{4} - 21 \, a^{4} b^{5}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{9} - 3 \, a^{8} b - 22 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 27 \, a^{5} b^{4} - 7 \, a^{4} b^{5}\right)} e^{\left(-12 \, d x - 12 \, c\right)} - {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} e^{\left(-14 \, d x - 14 \, c\right)}\right)} d} + \frac{32 \, a^{5} + 83 \, a^{4} b - 60 \, a^{3} b^{2} - 346 \, a^{2} b^{3} - 340 \, a b^{4} - 105 \, b^{5} + 3 \, {\left(32 \, a^{5} + 95 \, a^{4} b + 154 \, a^{3} b^{2} + 84 \, a^{2} b^{3} - 42 \, a b^{4} - 35 \, b^{5}\right)} e^{\left(12 \, d x + 12 \, c\right)} + 6 \, {\left(48 \, a^{5} + 40 \, a^{4} b - 117 \, a^{3} b^{2} - 201 \, a^{2} b^{3} + 45 \, a b^{4} + 105 \, b^{5}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(224 \, a^{5} + 281 \, a^{4} b + 384 \, a^{3} b^{2} + 2318 \, a^{2} b^{3} - 160 \, a b^{4} - 1575 \, b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} - 4 \, {\left(16 \, a^{5} - 136 \, a^{4} b - 9 \, a^{3} b^{2} + 697 \, a^{2} b^{3} - 115 \, a b^{4} - 525 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(96 \, a^{5} + 137 \, a^{4} b - 1262 \, a^{3} b^{2} - 1840 \, a^{2} b^{3} + 1230 \, a b^{4} + 1575 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(16 \, a^{5} - 136 \, a^{4} b - 435 \, a^{3} b^{2} - 35 \, a^{2} b^{3} + 563 \, a b^{4} + 315 \, b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{48 \, {\left(a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4} - {\left(a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4}\right)} e^{\left(14 \, d x + 14 \, c\right)} - {\left(a^{8} - 4 \, a^{7} b - 18 \, a^{6} b^{2} - 20 \, a^{5} b^{3} - 7 \, a^{4} b^{4}\right)} e^{\left(12 \, d x + 12 \, c\right)} + {\left(3 \, a^{8} + 4 \, a^{7} b - 22 \, a^{6} b^{2} - 44 \, a^{5} b^{3} - 21 \, a^{4} b^{4}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(3 \, a^{8} - 4 \, a^{7} b + 18 \, a^{6} b^{2} + 60 \, a^{5} b^{3} + 35 \, a^{4} b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} - {\left(3 \, a^{8} - 4 \, a^{7} b + 18 \, a^{6} b^{2} + 60 \, a^{5} b^{3} + 35 \, a^{4} b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(3 \, a^{8} + 4 \, a^{7} b - 22 \, a^{6} b^{2} - 44 \, a^{5} b^{3} - 21 \, a^{4} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{8} - 4 \, a^{7} b - 18 \, a^{6} b^{2} - 20 \, a^{5} b^{3} - 7 \, a^{4} b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{32 \, a^{5} + 83 \, a^{4} b - 60 \, a^{3} b^{2} - 346 \, a^{2} b^{3} - 340 \, a b^{4} - 105 \, b^{5} + 2 \, {\left(16 \, a^{5} - 136 \, a^{4} b - 435 \, a^{3} b^{2} - 35 \, a^{2} b^{3} + 563 \, a b^{4} + 315 \, b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(96 \, a^{5} + 137 \, a^{4} b - 1262 \, a^{3} b^{2} - 1840 \, a^{2} b^{3} + 1230 \, a b^{4} + 1575 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(16 \, a^{5} - 136 \, a^{4} b - 9 \, a^{3} b^{2} + 697 \, a^{2} b^{3} - 115 \, a b^{4} - 525 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(224 \, a^{5} + 281 \, a^{4} b + 384 \, a^{3} b^{2} + 2318 \, a^{2} b^{3} - 160 \, a b^{4} - 1575 \, b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, {\left(48 \, a^{5} + 40 \, a^{4} b - 117 \, a^{3} b^{2} - 201 \, a^{2} b^{3} + 45 \, a b^{4} + 105 \, b^{5}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + 3 \, {\left(32 \, a^{5} + 95 \, a^{4} b + 154 \, a^{3} b^{2} + 84 \, a^{2} b^{3} - 42 \, a b^{4} - 35 \, b^{5}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{48 \, {\left(a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4} + {\left(a^{8} - 4 \, a^{7} b - 18 \, a^{6} b^{2} - 20 \, a^{5} b^{3} - 7 \, a^{4} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{8} + 4 \, a^{7} b - 22 \, a^{6} b^{2} - 44 \, a^{5} b^{3} - 21 \, a^{4} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{8} - 4 \, a^{7} b + 18 \, a^{6} b^{2} + 60 \, a^{5} b^{3} + 35 \, a^{4} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{8} - 4 \, a^{7} b + 18 \, a^{6} b^{2} + 60 \, a^{5} b^{3} + 35 \, a^{4} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{8} + 4 \, a^{7} b - 22 \, a^{6} b^{2} - 44 \, a^{5} b^{3} - 21 \, a^{4} b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{8} - 4 \, a^{7} b - 18 \, a^{6} b^{2} - 20 \, a^{5} b^{3} - 7 \, a^{4} b^{4}\right)} e^{\left(-12 \, d x - 12 \, c\right)} - {\left(a^{8} + 4 \, a^{7} b + 6 \, a^{6} b^{2} + 4 \, a^{5} b^{3} + a^{4} b^{4}\right)} e^{\left(-14 \, d x - 14 \, c\right)}\right)} d} + \frac{16 \, a^{4} + 147 \, a^{3} b + 351 \, a^{2} b^{2} + 325 \, a b^{3} + 105 \, b^{4} + 2 \, {\left(8 \, a^{4} + 32 \, a^{3} b - 251 \, a^{2} b^{2} - 590 \, a b^{3} - 315 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(96 \, a^{4} + 313 \, a^{3} b + 19 \, a^{2} b^{2} - 1725 \, a b^{3} - 1575 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(56 \, a^{4} + 80 \, a^{3} b - 65 \, a^{2} b^{2} + 400 \, a b^{3} + 525 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(176 \, a^{4} + 135 \, a^{3} b + 15 \, a^{2} b^{2} - 1375 \, a b^{3} - 1575 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - 6 \, {\left(8 \, a^{4} + 45 \, a^{2} b^{2} + 150 \, a b^{3} + 105 \, b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + 15 \, {\left(3 \, a^{3} b + 13 \, a^{2} b^{2} + 17 \, a b^{3} + 7 \, b^{4}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{32 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3} + {\left(a^{7} - 5 \, a^{6} b - 13 \, a^{5} b^{2} - 7 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{7} + a^{6} b - 23 \, a^{5} b^{2} - 21 \, a^{4} b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{7} - 7 \, a^{6} b + 25 \, a^{5} b^{2} + 35 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{7} - 7 \, a^{6} b + 25 \, a^{5} b^{2} + 35 \, a^{4} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{7} + a^{6} b - 23 \, a^{5} b^{2} - 21 \, a^{4} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{7} - 5 \, a^{6} b - 13 \, a^{5} b^{2} - 7 \, a^{4} b^{3}\right)} e^{\left(-12 \, d x - 12 \, c\right)} - {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} e^{\left(-14 \, d x - 14 \, c\right)}\right)} d} + \frac{3 \, b \log\left({\left(a + b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a - b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a + b\right)}{4 \, a^{4} d} - \frac{3 \, b \log\left(2 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a + b\right)} e^{\left(-4 \, d x - 4 \, c\right)} + a + b\right)}{4 \, a^{4} d} + \frac{{\left(2 \, a - 3 \, b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{4 \, a^{4} d} - \frac{3 \, b \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, a^{4} d} - \frac{{\left(2 \, a - 3 \, b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{4 \, a^{4} d} + \frac{3 \, b \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, a^{4} d} - \frac{5 \, {\left(3 \, a b - 7 \, 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)}{32 \, \sqrt{a b} a^{4} d} - \frac{15 \, {\left(3 \, a b + 7 \, 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)}{64 \, \sqrt{a b} a^{4} d} + \frac{5 \, {\left(3 \, a b - 7 \, 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)}{32 \, \sqrt{a b} a^{4} d}"," ",0,"-1/8*(3*a^3*b - 3*a^2*b^2 - 7*a*b^3 - 3*b^4)*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d) + 1/8*(3*a^3*b - 3*a^2*b^2 - 7*a*b^3 - 3*b^4)*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*d) + 1/128*(15*a^4*b - 200*a^3*b^2 - 186*a^2*b^3 + 35*b^5)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt(a*b)*d) - 1/128*(15*a^4*b - 200*a^3*b^2 - 186*a^2*b^3 + 35*b^5)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt(a*b)*d) + 1/192*(176*a^6 + 781*a^5*b + 1571*a^4*b^2 + 1538*a^3*b^3 + 502*a^2*b^4 - 175*a*b^5 - 105*b^6 + 3*(96*a^6 + 465*a^5*b + 665*a^4*b^2 + 706*a^3*b^3 + 506*a^2*b^4 + 61*a*b^5 - 35*b^6)*e^(12*d*x + 12*c) + 6*(120*a^6 + 192*a^5*b - 315*a^4*b^2 - 728*a^3*b^3 - 1070*a^2*b^4 - 240*a*b^5 + 105*b^6)*e^(10*d*x + 10*c) + (176*a^6 - 281*a^5*b + 3509*a^4*b^2 + 3950*a^3*b^3 + 12226*a^2*b^4 + 3755*a*b^5 - 1575*b^6)*e^(8*d*x + 8*c) - 4*(184*a^6 + 48*a^5*b + 473*a^4*b^2 + 970*a^3*b^3 + 3684*a^2*b^4 + 1070*a*b^5 - 525*b^6)*e^(6*d*x + 6*c) - (384*a^6 + 1127*a^5*b - 861*a^4*b^2 - 7146*a^3*b^3 - 11386*a^2*b^4 - 1965*a*b^5 + 1575*b^6)*e^(4*d*x + 4*c) + 2*(136*a^6 - 96*a^5*b - 1309*a^4*b^2 - 2996*a^3*b^3 - 2238*a^2*b^4 - 4*a*b^5 + 315*b^6)*e^(2*d*x + 2*c))/((a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5 - (a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*e^(14*d*x + 14*c) - (a^9 - 3*a^8*b - 22*a^7*b^2 - 38*a^6*b^3 - 27*a^5*b^4 - 7*a^4*b^5)*e^(12*d*x + 12*c) + (3*a^9 + 7*a^8*b - 18*a^7*b^2 - 66*a^6*b^3 - 65*a^5*b^4 - 21*a^4*b^5)*e^(10*d*x + 10*c) + (3*a^9 - a^8*b + 14*a^7*b^2 + 78*a^6*b^3 + 95*a^5*b^4 + 35*a^4*b^5)*e^(8*d*x + 8*c) - (3*a^9 - a^8*b + 14*a^7*b^2 + 78*a^6*b^3 + 95*a^5*b^4 + 35*a^4*b^5)*e^(6*d*x + 6*c) - (3*a^9 + 7*a^8*b - 18*a^7*b^2 - 66*a^6*b^3 - 65*a^5*b^4 - 21*a^4*b^5)*e^(4*d*x + 4*c) + (a^9 - 3*a^8*b - 22*a^7*b^2 - 38*a^6*b^3 - 27*a^5*b^4 - 7*a^4*b^5)*e^(2*d*x + 2*c))*d) - 1/192*(176*a^6 + 781*a^5*b + 1571*a^4*b^2 + 1538*a^3*b^3 + 502*a^2*b^4 - 175*a*b^5 - 105*b^6 + 2*(136*a^6 - 96*a^5*b - 1309*a^4*b^2 - 2996*a^3*b^3 - 2238*a^2*b^4 - 4*a*b^5 + 315*b^6)*e^(-2*d*x - 2*c) - (384*a^6 + 1127*a^5*b - 861*a^4*b^2 - 7146*a^3*b^3 - 11386*a^2*b^4 - 1965*a*b^5 + 1575*b^6)*e^(-4*d*x - 4*c) - 4*(184*a^6 + 48*a^5*b + 473*a^4*b^2 + 970*a^3*b^3 + 3684*a^2*b^4 + 1070*a*b^5 - 525*b^6)*e^(-6*d*x - 6*c) + (176*a^6 - 281*a^5*b + 3509*a^4*b^2 + 3950*a^3*b^3 + 12226*a^2*b^4 + 3755*a*b^5 - 1575*b^6)*e^(-8*d*x - 8*c) + 6*(120*a^6 + 192*a^5*b - 315*a^4*b^2 - 728*a^3*b^3 - 1070*a^2*b^4 - 240*a*b^5 + 105*b^6)*e^(-10*d*x - 10*c) + 3*(96*a^6 + 465*a^5*b + 665*a^4*b^2 + 706*a^3*b^3 + 506*a^2*b^4 + 61*a*b^5 - 35*b^6)*e^(-12*d*x - 12*c))/((a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5 + (a^9 - 3*a^8*b - 22*a^7*b^2 - 38*a^6*b^3 - 27*a^5*b^4 - 7*a^4*b^5)*e^(-2*d*x - 2*c) - (3*a^9 + 7*a^8*b - 18*a^7*b^2 - 66*a^6*b^3 - 65*a^5*b^4 - 21*a^4*b^5)*e^(-4*d*x - 4*c) - (3*a^9 - a^8*b + 14*a^7*b^2 + 78*a^6*b^3 + 95*a^5*b^4 + 35*a^4*b^5)*e^(-6*d*x - 6*c) + (3*a^9 - a^8*b + 14*a^7*b^2 + 78*a^6*b^3 + 95*a^5*b^4 + 35*a^4*b^5)*e^(-8*d*x - 8*c) + (3*a^9 + 7*a^8*b - 18*a^7*b^2 - 66*a^6*b^3 - 65*a^5*b^4 - 21*a^4*b^5)*e^(-10*d*x - 10*c) - (a^9 - 3*a^8*b - 22*a^7*b^2 - 38*a^6*b^3 - 27*a^5*b^4 - 7*a^4*b^5)*e^(-12*d*x - 12*c) - (a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*e^(-14*d*x - 14*c))*d) + 1/48*(32*a^5 + 83*a^4*b - 60*a^3*b^2 - 346*a^2*b^3 - 340*a*b^4 - 105*b^5 + 3*(32*a^5 + 95*a^4*b + 154*a^3*b^2 + 84*a^2*b^3 - 42*a*b^4 - 35*b^5)*e^(12*d*x + 12*c) + 6*(48*a^5 + 40*a^4*b - 117*a^3*b^2 - 201*a^2*b^3 + 45*a*b^4 + 105*b^5)*e^(10*d*x + 10*c) + (224*a^5 + 281*a^4*b + 384*a^3*b^2 + 2318*a^2*b^3 - 160*a*b^4 - 1575*b^5)*e^(8*d*x + 8*c) - 4*(16*a^5 - 136*a^4*b - 9*a^3*b^2 + 697*a^2*b^3 - 115*a*b^4 - 525*b^5)*e^(6*d*x + 6*c) - (96*a^5 + 137*a^4*b - 1262*a^3*b^2 - 1840*a^2*b^3 + 1230*a*b^4 + 1575*b^5)*e^(4*d*x + 4*c) + 2*(16*a^5 - 136*a^4*b - 435*a^3*b^2 - 35*a^2*b^3 + 563*a*b^4 + 315*b^5)*e^(2*d*x + 2*c))/((a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4 - (a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4)*e^(14*d*x + 14*c) - (a^8 - 4*a^7*b - 18*a^6*b^2 - 20*a^5*b^3 - 7*a^4*b^4)*e^(12*d*x + 12*c) + (3*a^8 + 4*a^7*b - 22*a^6*b^2 - 44*a^5*b^3 - 21*a^4*b^4)*e^(10*d*x + 10*c) + (3*a^8 - 4*a^7*b + 18*a^6*b^2 + 60*a^5*b^3 + 35*a^4*b^4)*e^(8*d*x + 8*c) - (3*a^8 - 4*a^7*b + 18*a^6*b^2 + 60*a^5*b^3 + 35*a^4*b^4)*e^(6*d*x + 6*c) - (3*a^8 + 4*a^7*b - 22*a^6*b^2 - 44*a^5*b^3 - 21*a^4*b^4)*e^(4*d*x + 4*c) + (a^8 - 4*a^7*b - 18*a^6*b^2 - 20*a^5*b^3 - 7*a^4*b^4)*e^(2*d*x + 2*c))*d) - 1/48*(32*a^5 + 83*a^4*b - 60*a^3*b^2 - 346*a^2*b^3 - 340*a*b^4 - 105*b^5 + 2*(16*a^5 - 136*a^4*b - 435*a^3*b^2 - 35*a^2*b^3 + 563*a*b^4 + 315*b^5)*e^(-2*d*x - 2*c) - (96*a^5 + 137*a^4*b - 1262*a^3*b^2 - 1840*a^2*b^3 + 1230*a*b^4 + 1575*b^5)*e^(-4*d*x - 4*c) - 4*(16*a^5 - 136*a^4*b - 9*a^3*b^2 + 697*a^2*b^3 - 115*a*b^4 - 525*b^5)*e^(-6*d*x - 6*c) + (224*a^5 + 281*a^4*b + 384*a^3*b^2 + 2318*a^2*b^3 - 160*a*b^4 - 1575*b^5)*e^(-8*d*x - 8*c) + 6*(48*a^5 + 40*a^4*b - 117*a^3*b^2 - 201*a^2*b^3 + 45*a*b^4 + 105*b^5)*e^(-10*d*x - 10*c) + 3*(32*a^5 + 95*a^4*b + 154*a^3*b^2 + 84*a^2*b^3 - 42*a*b^4 - 35*b^5)*e^(-12*d*x - 12*c))/((a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4 + (a^8 - 4*a^7*b - 18*a^6*b^2 - 20*a^5*b^3 - 7*a^4*b^4)*e^(-2*d*x - 2*c) - (3*a^8 + 4*a^7*b - 22*a^6*b^2 - 44*a^5*b^3 - 21*a^4*b^4)*e^(-4*d*x - 4*c) - (3*a^8 - 4*a^7*b + 18*a^6*b^2 + 60*a^5*b^3 + 35*a^4*b^4)*e^(-6*d*x - 6*c) + (3*a^8 - 4*a^7*b + 18*a^6*b^2 + 60*a^5*b^3 + 35*a^4*b^4)*e^(-8*d*x - 8*c) + (3*a^8 + 4*a^7*b - 22*a^6*b^2 - 44*a^5*b^3 - 21*a^4*b^4)*e^(-10*d*x - 10*c) - (a^8 - 4*a^7*b - 18*a^6*b^2 - 20*a^5*b^3 - 7*a^4*b^4)*e^(-12*d*x - 12*c) - (a^8 + 4*a^7*b + 6*a^6*b^2 + 4*a^5*b^3 + a^4*b^4)*e^(-14*d*x - 14*c))*d) + 1/32*(16*a^4 + 147*a^3*b + 351*a^2*b^2 + 325*a*b^3 + 105*b^4 + 2*(8*a^4 + 32*a^3*b - 251*a^2*b^2 - 590*a*b^3 - 315*b^4)*e^(-2*d*x - 2*c) - (96*a^4 + 313*a^3*b + 19*a^2*b^2 - 1725*a*b^3 - 1575*b^4)*e^(-4*d*x - 4*c) - 4*(56*a^4 + 80*a^3*b - 65*a^2*b^2 + 400*a*b^3 + 525*b^4)*e^(-6*d*x - 6*c) - (176*a^4 + 135*a^3*b + 15*a^2*b^2 - 1375*a*b^3 - 1575*b^4)*e^(-8*d*x - 8*c) - 6*(8*a^4 + 45*a^2*b^2 + 150*a*b^3 + 105*b^4)*e^(-10*d*x - 10*c) + 15*(3*a^3*b + 13*a^2*b^2 + 17*a*b^3 + 7*b^4)*e^(-12*d*x - 12*c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3 + (a^7 - 5*a^6*b - 13*a^5*b^2 - 7*a^4*b^3)*e^(-2*d*x - 2*c) - (3*a^7 + a^6*b - 23*a^5*b^2 - 21*a^4*b^3)*e^(-4*d*x - 4*c) - (3*a^7 - 7*a^6*b + 25*a^5*b^2 + 35*a^4*b^3)*e^(-6*d*x - 6*c) + (3*a^7 - 7*a^6*b + 25*a^5*b^2 + 35*a^4*b^3)*e^(-8*d*x - 8*c) + (3*a^7 + a^6*b - 23*a^5*b^2 - 21*a^4*b^3)*e^(-10*d*x - 10*c) - (a^7 - 5*a^6*b - 13*a^5*b^2 - 7*a^4*b^3)*e^(-12*d*x - 12*c) - (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*e^(-14*d*x - 14*c))*d) + 3/4*b*log((a + b)*e^(4*d*x + 4*c) + 2*(a - b)*e^(2*d*x + 2*c) + a + b)/(a^4*d) - 3/4*b*log(2*(a - b)*e^(-2*d*x - 2*c) + (a + b)*e^(-4*d*x - 4*c) + a + b)/(a^4*d) + 1/4*(2*a - 3*b)*log(e^(2*d*x + 2*c) - 1)/(a^4*d) - 3/2*b*log(e^(2*d*x + 2*c) - 1)/(a^4*d) - 1/4*(2*a - 3*b)*log(e^(-2*d*x - 2*c) - 1)/(a^4*d) + 3/2*b*log(e^(-2*d*x - 2*c) - 1)/(a^4*d) - 5/32*(3*a*b - 7*b^2)*arctan(1/2*((a + b)*e^(2*d*x + 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^4*d) - 15/64*(3*a*b + 7*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^4*d) + 5/32*(3*a*b - 7*b^2)*arctan(1/2*((a + b)*e^(-2*d*x - 2*c) + a - b)/sqrt(a*b))/(sqrt(a*b)*a^4*d)","B",0
201,1,925,0,0.742610," ","integrate(1/(a+b*tanh(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
202,1,5,0,0.474976," ","integrate((1-tanh(x)^2)^(1/2),x, algorithm=""maxima"")","2 \, \arctan\left(e^{x}\right)"," ",0,"2*arctan(e^x)","A",0
203,1,5,0,0.493204," ","integrate((-1+tanh(x)^2)^(1/2),x, algorithm=""maxima"")","2 i \, \arctan\left(e^{x}\right)"," ",0,"2*I*arctan(e^x)","C",0
204,1,28,0,0.478117," ","integrate((1-tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{e^{\left(3 \, x\right)} - e^{x}}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1} + \arctan\left(e^{x}\right)"," ",0,"(e^(3*x) - e^x)/(e^(4*x) + 2*e^(2*x) + 1) + arctan(e^x)","A",0
205,1,32,0,0.460611," ","integrate((-1+tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{-i \, e^{\left(3 \, x\right)} + i \, e^{x}}{e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1} - i \, \arctan\left(e^{x}\right)"," ",0,"(-I*e^(3*x) + I*e^x)/(e^(4*x) + 2*e^(2*x) + 1) - I*arctan(e^x)","C",0
206,1,11,0,0.416529," ","integrate(1/(1-tanh(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
207,1,25,0,0.421305," ","integrate(1/(-1+tanh(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{e^{\left(-2 \, x\right)}}{2 \, \sqrt{-e^{\left(-2 \, x\right)}}} + \frac{1}{2 \, \sqrt{-e^{\left(-2 \, x\right)}}}"," ",0,"-1/2*e^(-2*x)/sqrt(-e^(-2*x)) + 1/2/sqrt(-e^(-2*x))","B",0
208,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^5,x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \tanh\left(x\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*tanh(x)^5, x)","F",0
209,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^4,x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \tanh\left(x\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*tanh(x)^4, x)","F",0
210,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^3,x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \tanh\left(x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*tanh(x)^3, x)","F",0
211,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^2,x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \tanh\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*tanh(x)^2, x)","F",0
212,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \tanh\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*tanh(x), x)","F",0
213,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a), x)","F",0
214,0,0,0,0.000000," ","integrate(coth(x)*(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \coth\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*coth(x), x)","F",0
215,0,0,0,0.000000," ","integrate(coth(x)^2*(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \coth\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*coth(x)^2, x)","F",0
216,0,0,0,0.000000," ","integrate(coth(x)^3*(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \coth\left(x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*coth(x)^3, x)","F",0
217,0,0,0,0.000000," ","integrate(coth(x)^4*(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \coth\left(x\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*coth(x)^4, x)","F",0
218,0,0,0,0.000000," ","integrate(coth(x)^5*(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{2} + a} \coth\left(x\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^2 + a)*coth(x)^5, x)","F",0
219,0,0,0,0.000000," ","integrate(tanh(x)^3*(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)^{3}\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(3/2)*tanh(x)^3, x)","F",0
220,0,0,0,0.000000," ","integrate(tanh(x)^2*(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(3/2)*tanh(x)^2, x)","F",0
221,0,0,0,0.000000," ","integrate(tanh(x)*(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(3/2)*tanh(x), x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(3/2), x)","F",0
223,0,0,0,0.000000," ","integrate(coth(x)*(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(3/2)*coth(x), x)","F",0
224,0,0,0,0.000000," ","integrate(coth(x)^2*(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(3/2)*coth(x)^2, x)","F",0
225,0,0,0,0.000000," ","integrate((1+tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\tanh\left(x\right)^{2} + 1}\,{d x}"," ",0,"integrate(sqrt(tanh(x)^2 + 1), x)","F",0
226,0,0,0,0.000000," ","integrate((-1-tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-\tanh\left(x\right)^{2} - 1}\,{d x}"," ",0,"integrate(sqrt(-tanh(x)^2 - 1), x)","F",0
227,0,0,0,0.000000," ","integrate((1+tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\tanh\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((tanh(x)^2 + 1)^(3/2), x)","F",0
228,0,0,0,0.000000," ","integrate((-1-tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(-\tanh\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-tanh(x)^2 - 1)^(3/2), x)","F",0
229,0,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{5}}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^5/sqrt(b*tanh(x)^2 + a), x)","F",0
230,0,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{4}}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^4/sqrt(b*tanh(x)^2 + a), x)","F",0
231,0,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{3}}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^3/sqrt(b*tanh(x)^2 + a), x)","F",0
232,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^2/sqrt(b*tanh(x)^2 + a), x)","F",0
233,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)/sqrt(b*tanh(x)^2 + a), x)","F",0
234,0,0,0,0.000000," ","integrate(1/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*tanh(x)^2 + a), x)","F",0
235,0,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)/sqrt(b*tanh(x)^2 + a), x)","F",0
236,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)^2/sqrt(b*tanh(x)^2 + a), x)","F",0
237,0,0,0,0.000000," ","integrate(coth(x)^3/(a+b*tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{3}}{\sqrt{b \tanh\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)^3/sqrt(b*tanh(x)^2 + a), x)","F",0
238,0,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{5}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^5/(b*tanh(x)^2 + a)^(3/2), x)","F",0
239,0,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{4}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^4/(b*tanh(x)^2 + a)^(3/2), x)","F",0
240,0,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{3}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^3/(b*tanh(x)^2 + a)^(3/2), x)","F",0
241,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^2/(b*tanh(x)^2 + a)^(3/2), x)","F",0
242,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*tanh(x)^2 + a)^(3/2), x)","F",0
243,0,0,0,0.000000," ","integrate(1/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(-3/2), x)","F",0
244,0,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*tanh(x)^2 + a)^(3/2), x)","F",0
245,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)^2/(b*tanh(x)^2 + a)^(3/2), x)","F",0
246,0,0,0,0.000000," ","integrate(tanh(x)^6/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{6}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^6/(b*tanh(x)^2 + a)^(5/2), x)","F",0
247,0,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{5}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^5/(b*tanh(x)^2 + a)^(5/2), x)","F",0
248,0,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{4}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^4/(b*tanh(x)^2 + a)^(5/2), x)","F",0
249,0,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{3}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^3/(b*tanh(x)^2 + a)^(5/2), x)","F",0
250,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^2/(b*tanh(x)^2 + a)^(5/2), x)","F",0
251,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*tanh(x)^2 + a)^(5/2), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tanh(x)^2 + a)^(-5/2), x)","F",0
253,0,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*tanh(x)^2 + a)^(5/2), x)","F",0
254,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{{\left(b \tanh\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)^2/(b*tanh(x)^2 + a)^(5/2), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(1+tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\tanh\left(x\right)^{2} + 1}}\,{d x}"," ",0,"integrate(1/sqrt(tanh(x)^2 + 1), x)","F",0
256,0,0,0,0.000000," ","integrate(1/(-1-tanh(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\tanh\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-tanh(x)^2 - 1), x)","F",0
257,1,194,0,0.412716," ","integrate((a+b*tanh(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{1}{15} \, b^{2} {\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 b {\left(x + \frac{c}{d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} + 1\right)}}\right)} + a^{2} x"," ",0,"1/15*b^2*(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*b*(x + c/d + log(e^(-2*d*x - 2*c) + 1)/d + 2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) + 1))) + a^2*x","B",0
258,1,73,0,0.412468," ","integrate(1/(1+tanh(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
259,0,0,0,0.000000," ","integrate(tanh(x)*(a+b*tanh(x)^4)^(3/2),x, algorithm=""maxima"")","\int {\left(b \tanh\left(x\right)^{4} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)\,{d x}"," ",0,"integrate((b*tanh(x)^4 + a)^(3/2)*tanh(x), x)","F",0
260,0,0,0,0.000000," ","integrate(tanh(x)*(a+b*tanh(x)^4)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tanh\left(x\right)^{4} + a} \tanh\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*tanh(x)^4 + a)*tanh(x), x)","F",0
261,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{\sqrt{b \tanh\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(tanh(x)/sqrt(b*tanh(x)^4 + a), x)","F",0
262,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \tanh\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*tanh(x)^4 + a)^(3/2), x)","F",0
263,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \tanh\left(x\right)^{4} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*tanh(x)^4 + a)^(5/2), x)","F",0
