1,1,129,0,0.313177," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c)^4,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}{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,"1/64*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) - 1/8*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
2,1,111,0,0.338463," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c)^3,x, algorithm=""maxima"")","\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)} + \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)}"," ",0,"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) + 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))))","B",0
3,1,62,0,0.327085," ","integrate((a+b*sech(d*x+c)^2)*sinh(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)} + b {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)}"," ",0,"-1/8*a*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) + b*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1)))","A",0
4,1,36,0,0.321300," ","integrate((a+b*sech(d*x+c)^2)*sinh(d*x+c),x, algorithm=""maxima"")","\frac{a \cosh\left(d x + c\right)}{d} - \frac{2 \, b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}}"," ",0,"a*cosh(d*x + c)/d - 2*b/(d*(e^(d*x + c) + e^(-d*x - c)))","A",0
5,1,80,0,0.324921," ","integrate(csch(d*x+c)*(a+b*sech(d*x+c)^2),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{2 \, e^{\left(-d x - c\right)}}{d {\left(e^{\left(-2 \, d x - 2 \, 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*(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))) + a*log(tanh(1/2*d*x + 1/2*c))/d","B",0
6,1,39,0,0.333146," ","integrate(csch(d*x+c)^2*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, a}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} + \frac{4 \, b}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"2*a/(d*(e^(-2*d*x - 2*c) - 1)) + 4*b/(d*(e^(-4*d*x - 4*c) - 1))","A",0
7,1,198,0,0.341986," ","integrate(csch(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\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(3 \, e^{\left(-d x - c\right)} - 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)}\right)}}{d {\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)} - 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,"1/2*b*(3*log(e^(-d*x - c) + 1)/d - 3*log(e^(-d*x - c) - 1)/d + 2*(3*e^(-d*x - c) - 2*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c))/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) - e^(-6*d*x - 6*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
8,1,187,0,0.339499," ","integrate(csch(d*x+c)^4*(a+b*sech(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{16}{3} \, b {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}} - \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\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))) + 16/3*b*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1)) - 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1)))","B",0
9,1,211,0,0.338016," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c)^4,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}{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)} - \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,"1/64*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) + 1/3*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))) - 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
10,1,266,0,0.340122," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c)^3,x, algorithm=""maxima"")","\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)} + 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{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)}"," ",0,"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) + 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)))) - 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)))","B",0
11,1,160,0,0.332283," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c)^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)} + 2 \, a b {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} + \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)}"," ",0,"-1/8*a^2*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) + 2*a*b*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + 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)))","B",0
12,1,65,0,0.321059," ","integrate((a+b*sech(d*x+c)^2)^2*sinh(d*x+c),x, algorithm=""maxima"")","\frac{a^{2} \cosh\left(d x + c\right)}{d} - \frac{4 \, a b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}} - \frac{8 \, b^{2}}{3 \, d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{3}}"," ",0,"a^2*cosh(d*x + c)/d - 4*a*b/(d*(e^(d*x + c) + e^(-d*x - c))) - 8/3*b^2/(d*(e^(d*x + c) + e^(-d*x - c))^3)","A",0
13,1,197,0,0.337288," ","integrate(csch(d*x+c)*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, b^{2} {\left(\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(3 \, e^{\left(-d x - c\right)} + 10 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)}\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(\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{a^{2} \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-1/3*b^2*(3*log(e^(-d*x - c) + 1)/d - 3*log(e^(-d*x - c) - 1)/d - 2*(3*e^(-d*x - c) + 10*e^(-3*d*x - 3*c) + 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))) - 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))) + a^2*log(tanh(1/2*d*x + 1/2*c))/d","B",0
14,1,140,0,0.337089," ","integrate(csch(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{16}{3} \, b^{2} {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}} + \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + \frac{2 \, a^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} + \frac{8 \, a b}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"-16/3*b^2*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) + 1)) + 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) + 1))) + 2*a^2/(d*(e^(-2*d*x - 2*c) - 1)) + 8*a*b/(d*(e^(-4*d*x - 4*c) - 1))","B",0
15,1,354,0,0.338994," ","integrate(csch(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} {\left(\frac{15 \, \log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{15 \, \log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, {\left(15 \, e^{\left(-d x - c\right)} + 20 \, e^{\left(-3 \, d x - 3 \, c\right)} - 22 \, e^{\left(-5 \, d x - 5 \, c\right)} + 20 \, e^{\left(-7 \, d x - 7 \, c\right)} + 15 \, e^{\left(-9 \, d x - 9 \, c\right)}\right)}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, 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)} + e^{\left(-10 \, d x - 10 \, c\right)} + 1\right)}}\right)} + a b {\left(\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(3 \, e^{\left(-d x - c\right)} - 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)}\right)}}{d {\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)} - 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)}"," ",0,"1/6*b^2*(15*log(e^(-d*x - c) + 1)/d - 15*log(e^(-d*x - c) - 1)/d - 2*(15*e^(-d*x - c) + 20*e^(-3*d*x - 3*c) - 22*e^(-5*d*x - 5*c) + 20*e^(-7*d*x - 7*c) + 15*e^(-9*d*x - 9*c))/(d*(e^(-2*d*x - 2*c) - 2*e^(-4*d*x - 4*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c) + 1))) + a*b*(3*log(e^(-d*x - c) + 1)/d - 3*log(e^(-d*x - c) - 1)/d + 2*(3*e^(-d*x - c) - 2*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c))/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) - e^(-6*d*x - 6*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)))","B",0
16,1,285,0,0.342833," ","integrate(csch(d*x+c)^4*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\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{32}{3} \, a b {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}} - \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + \frac{32}{3} \, b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, c\right)}}{d {\left(3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 3 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} - 1\right)}} - \frac{1}{d {\left(3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 3 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} - 1\right)}}\right)}"," ",0,"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))) + 32/3*a*b*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1)) - 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1))) + 32/3*b^2*(3*e^(-4*d*x - 4*c)/(d*(3*e^(-4*d*x - 4*c) - 3*e^(-8*d*x - 8*c) + e^(-12*d*x - 12*c) - 1)) - 1/(d*(3*e^(-4*d*x - 4*c) - 3*e^(-8*d*x - 8*c) + e^(-12*d*x - 12*c) - 1)))","B",0
17,1,422,0,0.344517," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c)^4,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)} + 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)} - \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)} + \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)}"," ",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) + 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))) - 3/8*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)))) + 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)))","B",0
18,1,489,0,0.341655," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c)^3,x, algorithm=""maxima"")","\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)} + \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)} - 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{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)}"," ",0,"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) + 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)))) - 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))) - 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)))","B",0
19,1,443,0,0.338703," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c)^2,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)} + 3 \, a^{2} b {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} + \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)} + 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)}"," ",0,"-1/8*a^3*(4*x - e^(2*d*x + 2*c)/d + e^(-2*d*x - 2*c)/d) + 3*a^2*b*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + 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))) + 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)))","B",0
20,1,94,0,0.321785," ","integrate((a+b*sech(d*x+c)^2)^3*sinh(d*x+c),x, algorithm=""maxima"")","\frac{a^{3} \cosh\left(d x + c\right)}{d} - \frac{6 \, a^{2} b}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}} - \frac{8 \, a b^{2}}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{3}} - \frac{32 \, b^{3}}{5 \, d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{5}}"," ",0,"a^3*cosh(d*x + c)/d - 6*a^2*b/(d*(e^(d*x + c) + e^(-d*x - c))) - 8*a*b^2/(d*(e^(d*x + c) + e^(-d*x - c))^3) - 32/5*b^3/(d*(e^(d*x + c) + e^(-d*x - c))^5)","A",0
21,1,358,0,0.328735," ","integrate(csch(d*x+c)*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{15} \, b^{3} {\left(\frac{15 \, \log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{15 \, \log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, {\left(15 \, e^{\left(-d x - c\right)} + 80 \, e^{\left(-3 \, d x - 3 \, c\right)} + 178 \, e^{\left(-5 \, d x - 5 \, c\right)} + 80 \, e^{\left(-7 \, d x - 7 \, c\right)} + 15 \, e^{\left(-9 \, d x - 9 \, c\right)}\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(\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(3 \, e^{\left(-d x - c\right)} + 10 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)}\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(\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{a^{3} \log\left(\tanh\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-1/15*b^3*(15*log(e^(-d*x - c) + 1)/d - 15*log(e^(-d*x - c) - 1)/d - 2*(15*e^(-d*x - c) + 80*e^(-3*d*x - 3*c) + 178*e^(-5*d*x - 5*c) + 80*e^(-7*d*x - 7*c) + 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*b^2*(3*log(e^(-d*x - c) + 1)/d - 3*log(e^(-d*x - c) - 1)/d - 2*(3*e^(-d*x - c) + 10*e^(-3*d*x - 3*c) + 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))) - 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))) + a^3*log(tanh(1/2*d*x + 1/2*c))/d","B",0
22,1,358,0,0.335411," ","integrate(csch(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{32}{5} \, b^{3} {\left(\frac{4 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 5 \, e^{\left(-4 \, d x - 4 \, c\right)} - 5 \, e^{\left(-8 \, d x - 8 \, c\right)} - 4 \, e^{\left(-10 \, d x - 10 \, c\right)} - e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}} + \frac{5 \, e^{\left(-4 \, d x - 4 \, c\right)}}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 5 \, e^{\left(-4 \, d x - 4 \, c\right)} - 5 \, e^{\left(-8 \, d x - 8 \, c\right)} - 4 \, e^{\left(-10 \, d x - 10 \, c\right)} - e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}} + \frac{1}{d {\left(4 \, e^{\left(-2 \, d x - 2 \, c\right)} + 5 \, e^{\left(-4 \, d x - 4 \, c\right)} - 5 \, e^{\left(-8 \, d x - 8 \, c\right)} - 4 \, e^{\left(-10 \, d x - 10 \, c\right)} - e^{\left(-12 \, d x - 12 \, c\right)} + 1\right)}}\right)} - 16 \, a b^{2} {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}} + \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + \frac{2 \, a^{3}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} + \frac{12 \, a^{2} b}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"-32/5*b^3*(4*e^(-2*d*x - 2*c)/(d*(4*e^(-2*d*x - 2*c) + 5*e^(-4*d*x - 4*c) - 5*e^(-8*d*x - 8*c) - 4*e^(-10*d*x - 10*c) - e^(-12*d*x - 12*c) + 1)) + 5*e^(-4*d*x - 4*c)/(d*(4*e^(-2*d*x - 2*c) + 5*e^(-4*d*x - 4*c) - 5*e^(-8*d*x - 8*c) - 4*e^(-10*d*x - 10*c) - e^(-12*d*x - 12*c) + 1)) + 1/(d*(4*e^(-2*d*x - 2*c) + 5*e^(-4*d*x - 4*c) - 5*e^(-8*d*x - 8*c) - 4*e^(-10*d*x - 10*c) - e^(-12*d*x - 12*c) + 1))) - 16*a*b^2*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) + 1)) + 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) + 1))) + 2*a^3/(d*(e^(-2*d*x - 2*c) - 1)) + 12*a^2*b/(d*(e^(-4*d*x - 4*c) - 1))","B",0
23,1,556,0,0.338464," ","integrate(csch(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{1}{30} \, b^{3} {\left(\frac{105 \, \log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{105 \, \log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, {\left(105 \, e^{\left(-d x - c\right)} + 350 \, e^{\left(-3 \, d x - 3 \, c\right)} + 231 \, e^{\left(-5 \, d x - 5 \, c\right)} - 412 \, e^{\left(-7 \, d x - 7 \, c\right)} + 231 \, e^{\left(-9 \, d x - 9 \, c\right)} + 350 \, e^{\left(-11 \, d x - 11 \, c\right)} + 105 \, e^{\left(-13 \, d x - 13 \, c\right)}\right)}}{d {\left(3 \, e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-4 \, d x - 4 \, c\right)} - 5 \, 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)} + 3 \, e^{\left(-12 \, d x - 12 \, c\right)} + e^{\left(-14 \, d x - 14 \, c\right)} + 1\right)}}\right)} + \frac{1}{2} \, a b^{2} {\left(\frac{15 \, \log\left(e^{\left(-d x - c\right)} + 1\right)}{d} - \frac{15 \, \log\left(e^{\left(-d x - c\right)} - 1\right)}{d} - \frac{2 \, {\left(15 \, e^{\left(-d x - c\right)} + 20 \, e^{\left(-3 \, d x - 3 \, c\right)} - 22 \, e^{\left(-5 \, d x - 5 \, c\right)} + 20 \, e^{\left(-7 \, d x - 7 \, c\right)} + 15 \, e^{\left(-9 \, d x - 9 \, c\right)}\right)}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, 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)} + e^{\left(-10 \, d x - 10 \, c\right)} + 1\right)}}\right)} + \frac{3}{2} \, a^{2} b {\left(\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(3 \, e^{\left(-d x - c\right)} - 2 \, e^{\left(-3 \, d x - 3 \, c\right)} + 3 \, e^{\left(-5 \, d x - 5 \, c\right)}\right)}}{d {\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)} - 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)}"," ",0,"1/30*b^3*(105*log(e^(-d*x - c) + 1)/d - 105*log(e^(-d*x - c) - 1)/d - 2*(105*e^(-d*x - c) + 350*e^(-3*d*x - 3*c) + 231*e^(-5*d*x - 5*c) - 412*e^(-7*d*x - 7*c) + 231*e^(-9*d*x - 9*c) + 350*e^(-11*d*x - 11*c) + 105*e^(-13*d*x - 13*c))/(d*(3*e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) - 5*e^(-6*d*x - 6*c) - 5*e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c) + 3*e^(-12*d*x - 12*c) + e^(-14*d*x - 14*c) + 1))) + 1/2*a*b^2*(15*log(e^(-d*x - c) + 1)/d - 15*log(e^(-d*x - c) - 1)/d - 2*(15*e^(-d*x - c) + 20*e^(-3*d*x - 3*c) - 22*e^(-5*d*x - 5*c) + 20*e^(-7*d*x - 7*c) + 15*e^(-9*d*x - 9*c))/(d*(e^(-2*d*x - 2*c) - 2*e^(-4*d*x - 4*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) + e^(-10*d*x - 10*c) + 1))) + 3/2*a^2*b*(3*log(e^(-d*x - c) + 1)/d - 3*log(e^(-d*x - c) - 1)/d + 2*(3*e^(-d*x - c) - 2*e^(-3*d*x - 3*c) + 3*e^(-5*d*x - 5*c))/(d*(e^(-2*d*x - 2*c) + e^(-4*d*x - 4*c) - e^(-6*d*x - 6*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)))","B",0
24,1,664,0,0.344083," ","integrate(csch(d*x+c)^4*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\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{256}{15} \, b^{3} {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, e^{\left(-6 \, d x - 6 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + 2 \, e^{\left(-12 \, d x - 12 \, c\right)} - 2 \, e^{\left(-14 \, d x - 14 \, c\right)} - e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} - \frac{2 \, e^{\left(-4 \, d x - 4 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, e^{\left(-6 \, d x - 6 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + 2 \, e^{\left(-12 \, d x - 12 \, c\right)} - 2 \, e^{\left(-14 \, d x - 14 \, c\right)} - e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} - \frac{6 \, e^{\left(-6 \, d x - 6 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, e^{\left(-6 \, d x - 6 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + 2 \, e^{\left(-12 \, d x - 12 \, c\right)} - 2 \, e^{\left(-14 \, d x - 14 \, c\right)} - e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}} + \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, e^{\left(-6 \, d x - 6 \, c\right)} + 6 \, e^{\left(-10 \, d x - 10 \, c\right)} + 2 \, e^{\left(-12 \, d x - 12 \, c\right)} - 2 \, e^{\left(-14 \, d x - 14 \, c\right)} - e^{\left(-16 \, d x - 16 \, c\right)} + 1\right)}}\right)} + 16 \, a^{2} b {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}} - \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + 32 \, a b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, c\right)}}{d {\left(3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 3 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} - 1\right)}} - \frac{1}{d {\left(3 \, e^{\left(-4 \, d x - 4 \, c\right)} - 3 \, e^{\left(-8 \, d x - 8 \, c\right)} + e^{\left(-12 \, d x - 12 \, c\right)} - 1\right)}}\right)}"," ",0,"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))) + 256/15*b^3*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-4*d*x - 4*c) - 6*e^(-6*d*x - 6*c) + 6*e^(-10*d*x - 10*c) + 2*e^(-12*d*x - 12*c) - 2*e^(-14*d*x - 14*c) - e^(-16*d*x - 16*c) + 1)) - 2*e^(-4*d*x - 4*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-4*d*x - 4*c) - 6*e^(-6*d*x - 6*c) + 6*e^(-10*d*x - 10*c) + 2*e^(-12*d*x - 12*c) - 2*e^(-14*d*x - 14*c) - e^(-16*d*x - 16*c) + 1)) - 6*e^(-6*d*x - 6*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-4*d*x - 4*c) - 6*e^(-6*d*x - 6*c) + 6*e^(-10*d*x - 10*c) + 2*e^(-12*d*x - 12*c) - 2*e^(-14*d*x - 14*c) - e^(-16*d*x - 16*c) + 1)) + 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-4*d*x - 4*c) - 6*e^(-6*d*x - 6*c) + 6*e^(-10*d*x - 10*c) + 2*e^(-12*d*x - 12*c) - 2*e^(-14*d*x - 14*c) - e^(-16*d*x - 16*c) + 1))) + 16*a^2*b*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1)) - 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1))) + 32*a*b^2*(3*e^(-4*d*x - 4*c)/(d*(3*e^(-4*d*x - 4*c) - 3*e^(-8*d*x - 8*c) + e^(-12*d*x - 12*c) - 1)) - 1/(d*(3*e^(-4*d*x - 4*c) - 3*e^(-8*d*x - 8*c) + e^(-12*d*x - 12*c) - 1)))","B",0
25,1,526,0,0.462381," ","integrate(sinh(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} a d} + \frac{3 \, {\left(d x + c\right)}}{8 \, a d} - \frac{{\left(8 \, b e^{\left(-2 \, d x - 2 \, c\right)} - a\right)} e^{\left(4 \, d x + 4 \, c\right)}}{64 \, a^{2} d} - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a d} + \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{2} d} - \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{2} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d} + \frac{{\left(a b + 2 \, b^{2}\right)} {\left(d x + c\right)}}{2 \, a^{3} d} + \frac{8 \, b e^{\left(-2 \, d x - 2 \, c\right)} - a e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, a^{2} d} + \frac{{\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} a^{3} d}"," ",0,"3/16*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) + 3/8*(d*x + c)/(a*d) - 1/64*(8*b*e^(-2*d*x - 2*c) - a)*e^(4*d*x + 4*c)/(a^2*d) - 1/8*e^(2*d*x + 2*c)/(a*d) + 1/8*e^(-2*d*x - 2*c)/(a*d) + 1/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^2*d) - 1/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d) - 1/8*(a*b + 2*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d) + 1/8*(a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d) + 1/2*(a*b + 2*b^2)*(d*x + c)/(a^3*d) + 1/64*(8*b*e^(-2*d*x - 2*c) - a*e^(-4*d*x - 4*c))/(a^2*d) + 1/16*(a^2*b + 8*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^3*d)","B",0
26,0,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(3 \, {\left(3 \, a e^{\left(4 \, c\right)} + 4 \, b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(3 \, a e^{\left(2 \, c\right)} + 4 \, b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} - a e^{\left(6 \, d x + 6 \, c\right)} - a\right)} e^{\left(-3 \, d x - 3 \, c\right)}}{24 \, a^{2} d} + \frac{1}{8} \, \int \frac{16 \, {\left({\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)}\right)}}{a^{3} e^{\left(4 \, d x + 4 \, c\right)} + a^{3} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-1/24*(3*(3*a*e^(4*c) + 4*b*e^(4*c))*e^(4*d*x) + 3*(3*a*e^(2*c) + 4*b*e^(2*c))*e^(2*d*x) - a*e^(6*d*x + 6*c) - a)*e^(-3*d*x - 3*c)/(a^2*d) + 1/8*integrate(16*((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*e^(4*d*x + 4*c) + a^3 + 2*(a^3*e^(2*c) + 2*a^2*b*e^(2*c))*e^(2*d*x)), x)","F",0
27,1,352,0,0.423601," ","integrate(sinh(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, \sqrt{{\left(a + b\right)} b} a d} - \frac{d x + c}{2 \, a d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{2} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{2} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d}"," ",0,"-1/4*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) - 1/2*(d*x + c)/(a*d) + 1/8*e^(2*d*x + 2*c)/(a*d) - 1/8*e^(-2*d*x - 2*c)/(a*d) - 1/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^2*d) + 1/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d) + 1/8*(a*b + 2*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d) - 1/8*(a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d)","B",0
28,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(e^{\left(2 \, d x + 2 \, c\right)} + 1\right)} e^{\left(-d x - c\right)}}{2 \, a d} - \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} e^{\left(4 \, d x + 4 \, c\right)} + a^{2} + 2 \, {\left(a^{2} e^{\left(2 \, c\right)} + 2 \, a b 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 - c)/(a*d) - 1/2*integrate(4*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^2*e^(4*d*x + 4*c) + a^2 + 2*(a^2*e^(2*c) + 2*a*b*e^(2*c))*e^(2*d*x)), x)","F",0
29,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*sech(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 + b d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a d + b 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)} + 3 \, a b e^{\left(2 \, c\right)} + 2 \, b^{2} 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 + b*d) + log((e^(d*x + c) - 1)*e^(-c))/(a*d + b*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) + 3*a*b*e^(2*c) + 2*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
30,1,100,0,0.426013," ","integrate(csch(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} {\left(a + b\right)} d} + \frac{2}{{\left({\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - a - b\right)} d}"," ",0,"-1/2*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a + b)*d) + 2/(((a + b)*e^(-2*d*x - 2*c) - a - b)*d)","B",0
31,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(a - b\right)} \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, {\left(a^{2} d + 2 \, a b d + b^{2} d\right)}} - \frac{{\left(a - b\right)} \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, {\left(a^{2} d + 2 \, a b d + b^{2} d\right)}} - \frac{e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(d x + c\right)}}{a d + b d + {\left(a d e^{\left(4 \, c\right)} + b d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - 2 \, {\left(a d e^{\left(2 \, c\right)} + b d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} - 8 \, \int \frac{a b e^{\left(3 \, d x + 3 \, c\right)} - a b e^{\left(d x + c\right)}}{4 \, {\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)} + 4 \, a^{2} b e^{\left(2 \, c\right)} + 5 \, a b^{2} e^{\left(2 \, c\right)} + 2 \, b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/2*(a - b)*log((e^(d*x + c) + 1)*e^(-c))/(a^2*d + 2*a*b*d + b^2*d) - 1/2*(a - b)*log((e^(d*x + c) - 1)*e^(-c))/(a^2*d + 2*a*b*d + b^2*d) - (e^(3*d*x + 3*c) + e^(d*x + c))/(a*d + b*d + (a*d*e^(4*c) + b*d*e^(4*c))*e^(4*d*x) - 2*(a*d*e^(2*c) + b*d*e^(2*c))*e^(2*d*x)) - 8*integrate(1/4*(a*b*e^(3*d*x + 3*c) - a*b*e^(d*x + c))/(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) + 4*a^2*b*e^(2*c) + 5*a*b^2*e^(2*c) + 2*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
32,1,195,0,0.456376," ","integrate(csch(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{a b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{2 \, {\left(6 \, a e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, b e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, a + b\right)}}{3 \, {\left(a^{2} + 2 \, a b + b^{2} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d}"," ",0,"1/2*a*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) - 2/3*(6*a*e^(-2*d*x - 2*c) + 3*b*e^(-4*d*x - 4*c) - 2*a + b)/((a^2 + 2*a*b + b^2 - 3*(a^2 + 2*a*b + b^2)*e^(-2*d*x - 2*c) + 3*(a^2 + 2*a*b + b^2)*e^(-4*d*x - 4*c) - (a^2 + 2*a*b + b^2)*e^(-6*d*x - 6*c))*d)","B",0
33,1,1299,0,0.513935," ","integrate(sinh(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{3} b + 42 \, a^{2} b^{2} + 88 \, a b^{3} + 48 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{5} + a^{4} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(3 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a^{3} b + 42 \, a^{2} b^{2} + 88 \, a b^{3} + 48 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{5} + a^{4} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, {\left(3 \, a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3} + {\left(a^{3} b + 18 \, a^{2} b^{2} + 48 \, a b^{3} + 32 \, b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{6} + a^{5} b + {\left(a^{6} + a^{5} b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3} + {\left(a^{3} b + 18 \, a^{2} b^{2} + 48 \, a b^{3} + 32 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{16 \, {\left(a^{6} + a^{5} b + 2 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{6} + a^{5} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{a^{2} b + 2 \, a b^{2} + {\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + a^{4} b + {\left(a^{5} + a^{4} b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{2} b + 2 \, a b^{2} + {\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{5} + a^{4} b + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{5} + a^{4} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{3 \, {\left(a b + {\left(a b + 2 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}\right)}}{8 \, {\left(a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{3 \, {\left(d x + c\right)}}{8 \, a^{2} d} - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a^{2} d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a^{2} d} + \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{2 \, a^{3} d} - \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{3} d} + \frac{a e^{\left(4 \, d x + 4 \, c\right)} - 16 \, b e^{\left(2 \, d x + 2 \, c\right)}}{64 \, a^{3} d} + \frac{16 \, b e^{\left(-2 \, d x - 2 \, c\right)} - a e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, a^{3} d} + \frac{{\left(a b + 3 \, b^{2}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{4} d} - \frac{{\left(a b + 3 \, b^{2}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{4} d}"," ",0,"-1/64*(3*a^3*b + 42*a^2*b^2 + 88*a*b^3 + 48*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + a^4*b)*sqrt((a + b)*b)*d) - 1/16*(3*a^2*b + 12*a*b^2 + 8*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)*d) + 1/64*(3*a^3*b + 42*a^2*b^2 + 88*a*b^3 + 48*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + a^4*b)*sqrt((a + b)*b)*d) + 1/16*(3*a^2*b + 12*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)*d) + 3/32*(3*a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)*d) + 1/16*(a^3*b + 8*a^2*b^2 + 8*a*b^3 + (a^3*b + 18*a^2*b^2 + 48*a*b^3 + 32*b^4)*e^(2*d*x + 2*c))/((a^6 + a^5*b + (a^6 + a^5*b)*e^(4*d*x + 4*c) + 2*(a^6 + 3*a^5*b + 2*a^4*b^2)*e^(2*d*x + 2*c))*d) - 1/16*(a^3*b + 8*a^2*b^2 + 8*a*b^3 + (a^3*b + 18*a^2*b^2 + 48*a*b^3 + 32*b^4)*e^(-2*d*x - 2*c))/((a^6 + a^5*b + 2*(a^6 + 3*a^5*b + 2*a^4*b^2)*e^(-2*d*x - 2*c) + (a^6 + a^5*b)*e^(-4*d*x - 4*c))*d) + 1/4*(a^2*b + 2*a*b^2 + (a^2*b + 8*a*b^2 + 8*b^3)*e^(2*d*x + 2*c))/((a^5 + a^4*b + (a^5 + a^4*b)*e^(4*d*x + 4*c) + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*e^(2*d*x + 2*c))*d) - 1/4*(a^2*b + 2*a*b^2 + (a^2*b + 8*a*b^2 + 8*b^3)*e^(-2*d*x - 2*c))/((a^5 + a^4*b + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*e^(-2*d*x - 2*c) + (a^5 + a^4*b)*e^(-4*d*x - 4*c))*d) - 3/8*(a*b + (a*b + 2*b^2)*e^(-2*d*x - 2*c))/((a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c) + (a^4 + a^3*b)*e^(-4*d*x - 4*c))*d) + 3/8*(d*x + c)/(a^2*d) - 1/8*e^(2*d*x + 2*c)/(a^2*d) + 1/8*e^(-2*d*x - 2*c)/(a^2*d) + 1/2*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^3*d) - 1/2*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d) + 1/64*(a*e^(4*d*x + 4*c) - 16*b*e^(2*d*x + 2*c))/(a^3*d) + 1/64*(16*b*e^(-2*d*x - 2*c) - a*e^(-4*d*x - 4*c))/(a^3*d) + 1/4*(a*b + 3*b^2)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^4*d) - 1/4*(a*b + 3*b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^4*d)","B",0
34,0,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{a^{2} e^{\left(10 \, d x + 10 \, c\right)} + a^{2} - {\left(7 \, a^{2} e^{\left(8 \, c\right)} + 20 \, a b e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - 2 \, {\left(13 \, a^{2} e^{\left(6 \, c\right)} + 66 \, a b e^{\left(6 \, c\right)} + 60 \, b^{2} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - 2 \, {\left(13 \, a^{2} e^{\left(4 \, c\right)} + 66 \, a b e^{\left(4 \, c\right)} + 60 \, b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - {\left(7 \, a^{2} e^{\left(2 \, c\right)} + 20 \, a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{24 \, {\left(a^{4} d e^{\left(7 \, d x + 7 \, c\right)} + a^{4} d e^{\left(3 \, d x + 3 \, c\right)} + 2 \, {\left(a^{4} d e^{\left(5 \, c\right)} + 2 \, a^{3} b d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)}\right)}} + \frac{1}{8} \, \int \frac{8 \, {\left({\left(3 \, a b e^{\left(3 \, c\right)} + 5 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(3 \, a b e^{c} + 5 \, b^{2} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{4} e^{\left(4 \, d x + 4 \, c\right)} + a^{4} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/24*(a^2*e^(10*d*x + 10*c) + a^2 - (7*a^2*e^(8*c) + 20*a*b*e^(8*c))*e^(8*d*x) - 2*(13*a^2*e^(6*c) + 66*a*b*e^(6*c) + 60*b^2*e^(6*c))*e^(6*d*x) - 2*(13*a^2*e^(4*c) + 66*a*b*e^(4*c) + 60*b^2*e^(4*c))*e^(4*d*x) - (7*a^2*e^(2*c) + 20*a*b*e^(2*c))*e^(2*d*x))/(a^4*d*e^(7*d*x + 7*c) + a^4*d*e^(3*d*x + 3*c) + 2*(a^4*d*e^(5*c) + 2*a^3*b*d*e^(5*c))*e^(5*d*x)) + 1/8*integrate(8*((3*a*b*e^(3*c) + 5*b^2*e^(3*c))*e^(3*d*x) - (3*a*b*e^c + 5*b^2*e^c)*e^(d*x))/(a^4*e^(4*d*x + 4*c) + a^4 + 2*(a^4*e^(2*c) + 2*a^3*b*e^(2*c))*e^(2*d*x)), x)","F",0
35,1,696,0,0.458579," ","integrate(sinh(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(3 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{a^{2} b + 2 \, a b^{2} + {\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + a^{4} b + {\left(a^{5} + a^{4} b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{2} b + 2 \, a b^{2} + {\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{5} + a^{4} b + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{5} + a^{4} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{a b + {\left(a b + 2 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{2 \, {\left(a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{d x + c}{2 \, a^{2} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a^{2} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a^{2} d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{2 \, a^{3} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{3} d}"," ",0,"1/16*(3*a^2*b + 12*a*b^2 + 8*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)*d) - 1/16*(3*a^2*b + 12*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)*d) - 1/8*(3*a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)*d) - 1/4*(a^2*b + 2*a*b^2 + (a^2*b + 8*a*b^2 + 8*b^3)*e^(2*d*x + 2*c))/((a^5 + a^4*b + (a^5 + a^4*b)*e^(4*d*x + 4*c) + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*e^(2*d*x + 2*c))*d) + 1/4*(a^2*b + 2*a*b^2 + (a^2*b + 8*a*b^2 + 8*b^3)*e^(-2*d*x - 2*c))/((a^5 + a^4*b + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*e^(-2*d*x - 2*c) + (a^5 + a^4*b)*e^(-4*d*x - 4*c))*d) + 1/2*(a*b + (a*b + 2*b^2)*e^(-2*d*x - 2*c))/((a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c) + (a^4 + a^3*b)*e^(-4*d*x - 4*c))*d) - 1/2*(d*x + c)/(a^2*d) + 1/8*e^(2*d*x + 2*c)/(a^2*d) - 1/8*e^(-2*d*x - 2*c)/(a^2*d) - 1/2*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^3*d) + 1/2*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
36,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(a e^{\left(4 \, c\right)} + 2 \, b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 3 \, {\left(a e^{\left(2 \, c\right)} + 2 \, b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a e^{\left(6 \, d x + 6 \, c\right)} + a}{2 \, {\left(a^{3} d e^{\left(5 \, d x + 5 \, c\right)} + a^{3} d e^{\left(d x + c\right)} + 2 \, {\left(a^{3} d e^{\left(3 \, c\right)} + 2 \, a^{2} b d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, 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} e^{\left(4 \, d x + 4 \, c\right)} + a^{3} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/2*(3*(a*e^(4*c) + 2*b*e^(4*c))*e^(4*d*x) + 3*(a*e^(2*c) + 2*b*e^(2*c))*e^(2*d*x) + a*e^(6*d*x + 6*c) + a)/(a^3*d*e^(5*d*x + 5*c) + a^3*d*e^(d*x + c) + 2*(a^3*d*e^(3*c) + 2*a^2*b*d*e^(3*c))*e^(3*d*x)) - 1/2*integrate(6*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^3*e^(4*d*x + 4*c) + a^3 + 2*(a^3*e^(2*c) + 2*a^2*b*e^(2*c))*e^(2*d*x)), x)","F",0
37,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*sech(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 + a^{2} b d + {\left(a^{3} d e^{\left(4 \, c\right)} + a^{2} b d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(2 \, c\right)} + 3 \, a^{2} b d e^{\left(2 \, c\right)} + 2 \, 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 + 2 \, a b d + b^{2} d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a^{2} d + 2 \, a b d + b^{2} d} + 2 \, \int \frac{{\left(3 \, a b e^{\left(3 \, c\right)} + b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(3 \, a b e^{c} + 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)} + 4 \, a^{3} b e^{\left(2 \, c\right)} + 5 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 2 \, a b^{3} 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 + a^2*b*d + (a^3*d*e^(4*c) + a^2*b*d*e^(4*c))*e^(4*d*x) + 2*(a^3*d*e^(2*c) + 3*a^2*b*d*e^(2*c) + 2*a*b^2*d*e^(2*c))*e^(2*d*x)) - log((e^(d*x + c) + 1)*e^(-c))/(a^2*d + 2*a*b*d + b^2*d) + log((e^(d*x + c) - 1)*e^(-c))/(a^2*d + 2*a*b*d + b^2*d) + 2*integrate(1/2*((3*a*b*e^(3*c) + b^2*e^(3*c))*e^(3*d*x) - (3*a*b*e^c + 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) + 4*a^3*b*e^(2*c) + 5*a^2*b^2*e^(2*c) + 2*a*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
38,1,262,0,0.461302," ","integrate(csch(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{3 \, b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{2 \, a^{2} - a b + 2 \, {\left(2 \, a^{2} + 4 \, a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a^{2} + a b + 2 \, 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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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}"," ",0,"-3/4*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) - (2*a^2 - a*b + 2*(2*a^2 + 4*a*b - b^2)*e^(-2*d*x - 2*c) + (2*a^2 + a*b + 2*b^2)*e^(-4*d*x - 4*c))/((a^4 + 2*a^3*b + a^2*b^2 + (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*e^(-2*d*x - 2*c) - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*e^(-4*d*x - 4*c) - (a^4 + 2*a^3*b + a^2*b^2)*e^(-6*d*x - 6*c))*d)","B",0
39,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a - 3 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, {\left(a^{3} d + 3 \, a^{2} b d + 3 \, a b^{2} d + b^{3} d\right)}} - \frac{{\left(a - 3 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, {\left(a^{3} d + 3 \, a^{2} b d + 3 \, a b^{2} d + b^{3} d\right)}} - \frac{{\left(a e^{\left(7 \, c\right)} - b e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(3 \, a e^{\left(5 \, c\right)} + 5 \, b e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(3 \, a e^{\left(3 \, c\right)} + 5 \, 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(8 \, c\right)} + 2 \, a^{2} b d e^{\left(8 \, c\right)} + a b^{2} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{2} b d e^{\left(6 \, c\right)} + 2 \, a b^{2} d e^{\left(6 \, c\right)} + b^{3} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} - 2 \, {\left(a^{3} d e^{\left(4 \, c\right)} + 6 \, a^{2} b d e^{\left(4 \, c\right)} + 9 \, a b^{2} d e^{\left(4 \, c\right)} + 4 \, b^{3} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{2} b d e^{\left(2 \, c\right)} + 2 \, a b^{2} d e^{\left(2 \, c\right)} + b^{3} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} - 8 \, \int \frac{{\left(3 \, a b e^{\left(3 \, c\right)} - b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(3 \, a b e^{c} - b^{2} e^{c}\right)} e^{\left(d x\right)}}{8 \, {\left(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)} + 5 \, a^{3} b e^{\left(2 \, c\right)} + 9 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 7 \, a b^{3} e^{\left(2 \, c\right)} + 2 \, b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/2*(a - 3*b)*log((e^(d*x + c) + 1)*e^(-c))/(a^3*d + 3*a^2*b*d + 3*a*b^2*d + b^3*d) - 1/2*(a - 3*b)*log((e^(d*x + c) - 1)*e^(-c))/(a^3*d + 3*a^2*b*d + 3*a*b^2*d + b^3*d) - ((a*e^(7*c) - b*e^(7*c))*e^(7*d*x) + (3*a*e^(5*c) + 5*b*e^(5*c))*e^(5*d*x) + (3*a*e^(3*c) + 5*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^(8*c) + 2*a^2*b*d*e^(8*c) + a*b^2*d*e^(8*c))*e^(8*d*x) + 4*(a^2*b*d*e^(6*c) + 2*a*b^2*d*e^(6*c) + b^3*d*e^(6*c))*e^(6*d*x) - 2*(a^3*d*e^(4*c) + 6*a^2*b*d*e^(4*c) + 9*a*b^2*d*e^(4*c) + 4*b^3*d*e^(4*c))*e^(4*d*x) + 4*(a^2*b*d*e^(2*c) + 2*a*b^2*d*e^(2*c) + b^3*d*e^(2*c))*e^(2*d*x)) - 8*integrate(1/8*((3*a*b*e^(3*c) - b^2*e^(3*c))*e^(3*d*x) - (3*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) + 5*a^3*b*e^(2*c) + 9*a^2*b^2*e^(2*c) + 7*a*b^3*e^(2*c) + 2*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
40,1,430,0,0.520203," ","integrate(csch(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a b - 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{4 \, a^{2} - 11 \, a b - 2 \, {\left(2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - 3 \, {\left(3 \, a b - 2 \, b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d}"," ",0,"1/4*(3*a*b - 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)*d) + 1/3*(4*a^2 - 11*a*b - 2*(2*a^2 - 9*a*b + 19*b^2)*e^(-2*d*x - 2*c) - 2*(10*a^2 + 22*a*b - 33*b^2)*e^(-4*d*x - 4*c) - 6*(2*a^2 + 3*a*b + 11*b^2)*e^(-6*d*x - 6*c) - 3*(3*a*b - 2*b^2)*e^(-8*d*x - 8*c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*e^(-2*d*x - 2*c) - 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*e^(-4*d*x - 4*c) + 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*e^(-6*d*x - 6*c) + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*e^(-8*d*x - 8*c) - (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*e^(-10*d*x - 10*c))*d)","B",0
41,1,2468,0,0.603307," ","integrate(sinh(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(5 \, a^{4} b + 100 \, a^{3} b^{2} + 320 \, a^{2} b^{3} + 352 \, a b^{4} + 128 \, b^{5}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, {\left(5 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, {\left(5 \, a^{4} b + 100 \, a^{3} b^{2} + 320 \, a^{2} b^{3} + 352 \, a b^{4} + 128 \, b^{5}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, {\left(5 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, {\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{128 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{9 \, a^{5} b + 110 \, a^{4} b^{2} + 216 \, a^{3} b^{3} + 112 \, a^{2} b^{4} + {\left(9 \, a^{5} b + 228 \, a^{4} b^{2} + 920 \, a^{3} b^{3} + 1216 \, a^{2} b^{4} + 512 \, a b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{5} b + 594 \, a^{4} b^{2} + 2816 \, a^{3} b^{3} + 5696 \, a^{2} b^{4} + 5248 \, a b^{5} + 1792 \, b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{5} b + 476 \, a^{4} b^{2} + 1720 \, a^{3} b^{3} + 2176 \, a^{2} b^{4} + 896 \, a b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{64 \, {\left(a^{9} + 2 \, a^{8} b + a^{7} b^{2} + {\left(a^{9} + 2 \, a^{8} b + a^{7} b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} + 2 \, a^{6} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{9} + 14 \, a^{8} b + 27 \, a^{7} b^{2} + 24 \, a^{6} b^{3} + 8 \, a^{5} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} + 2 \, a^{6} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{9 \, a^{5} b + 110 \, a^{4} b^{2} + 216 \, a^{3} b^{3} + 112 \, a^{2} b^{4} + {\left(27 \, a^{5} b + 476 \, a^{4} b^{2} + 1720 \, a^{3} b^{3} + 2176 \, a^{2} b^{4} + 896 \, a b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{5} b + 594 \, a^{4} b^{2} + 2816 \, a^{3} b^{3} + 5696 \, a^{2} b^{4} + 5248 \, a b^{5} + 1792 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(9 \, a^{5} b + 228 \, a^{4} b^{2} + 920 \, a^{3} b^{3} + 1216 \, a^{2} b^{4} + 512 \, a b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{64 \, {\left(a^{9} + 2 \, a^{8} b + a^{7} b^{2} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} + 2 \, a^{6} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{9} + 14 \, a^{8} b + 27 \, a^{7} b^{2} + 24 \, a^{6} b^{3} + 8 \, a^{5} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} + 2 \, a^{6} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{9} + 2 \, a^{8} b + a^{7} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{9 \, a^{4} b + 32 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 3 \, {\left(3 \, a^{4} b + 34 \, a^{3} b^{2} + 64 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{4} b + 264 \, a^{3} b^{2} + 740 \, a^{2} b^{3} + 832 \, a b^{4} + 320 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{4} b + 194 \, a^{3} b^{2} + 336 \, a^{2} b^{3} + 160 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{9 \, a^{4} b + 32 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + {\left(27 \, a^{4} b + 194 \, a^{3} b^{2} + 336 \, a^{2} b^{3} + 160 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{4} b + 264 \, a^{3} b^{2} + 740 \, a^{2} b^{3} + 832 \, a b^{4} + 320 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(3 \, a^{4} b + 34 \, a^{3} b^{2} + 64 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{3 \, {\left(9 \, a^{3} b + 6 \, a^{2} b^{2} + {\left(27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(9 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(9 \, a^{3} b + 28 \, a^{2} b^{2} + 16 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{32 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{3 \, {\left(d x + c\right)}}{8 \, a^{3} d} - \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a^{3} d} + \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a^{3} d} + \frac{3 \, b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{4} d} - \frac{3 \, b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{4} d} + \frac{a e^{\left(4 \, d x + 4 \, c\right)} - 24 \, b e^{\left(2 \, d x + 2 \, c\right)}}{64 \, a^{4} d} + \frac{24 \, b e^{\left(-2 \, d x - 2 \, c\right)} - a e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, a^{4} d} + \frac{3 \, {\left(a b + 4 \, b^{2}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{8 \, a^{5} d} - \frac{3 \, {\left(a b + 4 \, b^{2}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{8 \, a^{5} d}"," ",0,"-3/256*(5*a^4*b + 100*a^3*b^2 + 320*a^2*b^3 + 352*a*b^4 + 128*b^5)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^7 + 2*a^6*b + a^5*b^2)*sqrt((a + b)*b)*d) - 3/64*(5*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)*d) + 3/256*(5*a^4*b + 100*a^3*b^2 + 320*a^2*b^3 + 352*a*b^4 + 128*b^5)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^7 + 2*a^6*b + a^5*b^2)*sqrt((a + b)*b)*d) + 3/64*(5*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)*d) + 3/128*(15*a^2*b + 20*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)*d) + 1/64*(9*a^5*b + 110*a^4*b^2 + 216*a^3*b^3 + 112*a^2*b^4 + (9*a^5*b + 228*a^4*b^2 + 920*a^3*b^3 + 1216*a^2*b^4 + 512*a*b^5)*e^(6*d*x + 6*c) + (27*a^5*b + 594*a^4*b^2 + 2816*a^3*b^3 + 5696*a^2*b^4 + 5248*a*b^5 + 1792*b^6)*e^(4*d*x + 4*c) + (27*a^5*b + 476*a^4*b^2 + 1720*a^3*b^3 + 2176*a^2*b^4 + 896*a*b^5)*e^(2*d*x + 2*c))/((a^9 + 2*a^8*b + a^7*b^2 + (a^9 + 2*a^8*b + a^7*b^2)*e^(8*d*x + 8*c) + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 + 2*a^6*b^3)*e^(6*d*x + 6*c) + 2*(3*a^9 + 14*a^8*b + 27*a^7*b^2 + 24*a^6*b^3 + 8*a^5*b^4)*e^(4*d*x + 4*c) + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 + 2*a^6*b^3)*e^(2*d*x + 2*c))*d) - 1/64*(9*a^5*b + 110*a^4*b^2 + 216*a^3*b^3 + 112*a^2*b^4 + (27*a^5*b + 476*a^4*b^2 + 1720*a^3*b^3 + 2176*a^2*b^4 + 896*a*b^5)*e^(-2*d*x - 2*c) + (27*a^5*b + 594*a^4*b^2 + 2816*a^3*b^3 + 5696*a^2*b^4 + 5248*a*b^5 + 1792*b^6)*e^(-4*d*x - 4*c) + (9*a^5*b + 228*a^4*b^2 + 920*a^3*b^3 + 1216*a^2*b^4 + 512*a*b^5)*e^(-6*d*x - 6*c))/((a^9 + 2*a^8*b + a^7*b^2 + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 + 2*a^6*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^9 + 14*a^8*b + 27*a^7*b^2 + 24*a^6*b^3 + 8*a^5*b^4)*e^(-4*d*x - 4*c) + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 + 2*a^6*b^3)*e^(-6*d*x - 6*c) + (a^9 + 2*a^8*b + a^7*b^2)*e^(-8*d*x - 8*c))*d) + 1/16*(9*a^4*b + 32*a^3*b^2 + 20*a^2*b^3 + 3*(3*a^4*b + 34*a^3*b^2 + 64*a^2*b^3 + 32*a*b^4)*e^(6*d*x + 6*c) + (27*a^4*b + 264*a^3*b^2 + 740*a^2*b^3 + 832*a*b^4 + 320*b^5)*e^(4*d*x + 4*c) + (27*a^4*b + 194*a^3*b^2 + 336*a^2*b^3 + 160*a*b^4)*e^(2*d*x + 2*c))/((a^8 + 2*a^7*b + a^6*b^2 + (a^8 + 2*a^7*b + a^6*b^2)*e^(8*d*x + 8*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(6*d*x + 6*c) + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*e^(4*d*x + 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(2*d*x + 2*c))*d) - 1/16*(9*a^4*b + 32*a^3*b^2 + 20*a^2*b^3 + (27*a^4*b + 194*a^3*b^2 + 336*a^2*b^3 + 160*a*b^4)*e^(-2*d*x - 2*c) + (27*a^4*b + 264*a^3*b^2 + 740*a^2*b^3 + 832*a*b^4 + 320*b^5)*e^(-4*d*x - 4*c) + 3*(3*a^4*b + 34*a^3*b^2 + 64*a^2*b^3 + 32*a*b^4)*e^(-6*d*x - 6*c))/((a^8 + 2*a^7*b + a^6*b^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*e^(-4*d*x - 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(-6*d*x - 6*c) + (a^8 + 2*a^7*b + a^6*b^2)*e^(-8*d*x - 8*c))*d) - 3/32*(9*a^3*b + 6*a^2*b^2 + (27*a^3*b + 68*a^2*b^2 + 32*a*b^3)*e^(-2*d*x - 2*c) + 3*(9*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*e^(-4*d*x - 4*c) + (9*a^3*b + 28*a^2*b^2 + 16*a*b^3)*e^(-6*d*x - 6*c))/((a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(-4*d*x - 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-6*d*x - 6*c) + (a^7 + 2*a^6*b + a^5*b^2)*e^(-8*d*x - 8*c))*d) + 3/8*(d*x + c)/(a^3*d) - 1/8*e^(2*d*x + 2*c)/(a^3*d) + 1/8*e^(-2*d*x - 2*c)/(a^3*d) + 3/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^4*d) - 3/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^4*d) + 1/64*(a*e^(4*d*x + 4*c) - 24*b*e^(2*d*x + 2*c))/(a^4*d) + 1/64*(24*b*e^(-2*d*x - 2*c) - a*e^(-4*d*x - 4*c))/(a^4*d) + 3/8*(a*b + 4*b^2)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^5*d) - 3/8*(a*b + 4*b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^5*d)","B",0
42,-2,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*sech(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
43,1,1373,0,0.532935," ","integrate(sinh(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, {\left(5 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{9 \, a^{4} b + 32 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 3 \, {\left(3 \, a^{4} b + 34 \, a^{3} b^{2} + 64 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{4} b + 264 \, a^{3} b^{2} + 740 \, a^{2} b^{3} + 832 \, a b^{4} + 320 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{4} b + 194 \, a^{3} b^{2} + 336 \, a^{2} b^{3} + 160 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{9 \, a^{4} b + 32 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + {\left(27 \, a^{4} b + 194 \, a^{3} b^{2} + 336 \, a^{2} b^{3} + 160 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{4} b + 264 \, a^{3} b^{2} + 740 \, a^{2} b^{3} + 832 \, a b^{4} + 320 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(3 \, a^{4} b + 34 \, a^{3} b^{2} + 64 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{9 \, a^{3} b + 6 \, a^{2} b^{2} + {\left(27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(9 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(9 \, a^{3} b + 28 \, a^{2} b^{2} + 16 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{8 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{d x + c}{2 \, a^{3} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a^{3} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a^{3} d} - \frac{3 \, b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{4} d} + \frac{3 \, b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{4} d}"," ",0,"3/64*(5*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)*d) - 3/64*(5*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)*d) - 1/32*(15*a^2*b + 20*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)*d) - 1/16*(9*a^4*b + 32*a^3*b^2 + 20*a^2*b^3 + 3*(3*a^4*b + 34*a^3*b^2 + 64*a^2*b^3 + 32*a*b^4)*e^(6*d*x + 6*c) + (27*a^4*b + 264*a^3*b^2 + 740*a^2*b^3 + 832*a*b^4 + 320*b^5)*e^(4*d*x + 4*c) + (27*a^4*b + 194*a^3*b^2 + 336*a^2*b^3 + 160*a*b^4)*e^(2*d*x + 2*c))/((a^8 + 2*a^7*b + a^6*b^2 + (a^8 + 2*a^7*b + a^6*b^2)*e^(8*d*x + 8*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(6*d*x + 6*c) + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*e^(4*d*x + 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(2*d*x + 2*c))*d) + 1/16*(9*a^4*b + 32*a^3*b^2 + 20*a^2*b^3 + (27*a^4*b + 194*a^3*b^2 + 336*a^2*b^3 + 160*a*b^4)*e^(-2*d*x - 2*c) + (27*a^4*b + 264*a^3*b^2 + 740*a^2*b^3 + 832*a*b^4 + 320*b^5)*e^(-4*d*x - 4*c) + 3*(3*a^4*b + 34*a^3*b^2 + 64*a^2*b^3 + 32*a*b^4)*e^(-6*d*x - 6*c))/((a^8 + 2*a^7*b + a^6*b^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*e^(-4*d*x - 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(-6*d*x - 6*c) + (a^8 + 2*a^7*b + a^6*b^2)*e^(-8*d*x - 8*c))*d) + 1/8*(9*a^3*b + 6*a^2*b^2 + (27*a^3*b + 68*a^2*b^2 + 32*a*b^3)*e^(-2*d*x - 2*c) + 3*(9*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*e^(-4*d*x - 4*c) + (9*a^3*b + 28*a^2*b^2 + 16*a*b^3)*e^(-6*d*x - 6*c))/((a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(-4*d*x - 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-6*d*x - 6*c) + (a^7 + 2*a^6*b + a^5*b^2)*e^(-8*d*x - 8*c))*d) - 1/2*(d*x + c)/(a^3*d) + 1/8*e^(2*d*x + 2*c)/(a^3*d) - 1/8*e^(-2*d*x - 2*c)/(a^3*d) - 3/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^4*d) + 3/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^4*d)","B",0
44,0,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{2 \, a^{2} e^{\left(10 \, d x + 10 \, c\right)} + 2 \, a^{2} + 5 \, {\left(2 \, a^{2} e^{\left(8 \, c\right)} + 5 \, a b e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 5 \, {\left(4 \, a^{2} e^{\left(6 \, c\right)} + 15 \, a b e^{\left(6 \, c\right)} + 12 \, b^{2} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 5 \, {\left(4 \, a^{2} e^{\left(4 \, c\right)} + 15 \, a b e^{\left(4 \, c\right)} + 12 \, b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 5 \, {\left(2 \, a^{2} e^{\left(2 \, c\right)} + 5 \, a b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{4 \, {\left(a^{5} d e^{\left(9 \, d x + 9 \, c\right)} + a^{5} d e^{\left(d x + c\right)} + 4 \, {\left(a^{5} d e^{\left(7 \, c\right)} + 2 \, a^{4} b d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(3 \, a^{5} d e^{\left(5 \, c\right)} + 8 \, a^{4} b d e^{\left(5 \, c\right)} + 8 \, a^{3} b^{2} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(3 \, c\right)} + 2 \, a^{4} b d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, 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} e^{\left(4 \, d x + 4 \, c\right)} + a^{4} + 2 \, {\left(a^{4} e^{\left(2 \, c\right)} + 2 \, a^{3} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*(2*a^2*e^(10*d*x + 10*c) + 2*a^2 + 5*(2*a^2*e^(8*c) + 5*a*b*e^(8*c))*e^(8*d*x) + 5*(4*a^2*e^(6*c) + 15*a*b*e^(6*c) + 12*b^2*e^(6*c))*e^(6*d*x) + 5*(4*a^2*e^(4*c) + 15*a*b*e^(4*c) + 12*b^2*e^(4*c))*e^(4*d*x) + 5*(2*a^2*e^(2*c) + 5*a*b*e^(2*c))*e^(2*d*x))/(a^5*d*e^(9*d*x + 9*c) + a^5*d*e^(d*x + c) + 4*(a^5*d*e^(7*c) + 2*a^4*b*d*e^(7*c))*e^(7*d*x) + 2*(3*a^5*d*e^(5*c) + 8*a^4*b*d*e^(5*c) + 8*a^3*b^2*d*e^(5*c))*e^(5*d*x) + 4*(a^5*d*e^(3*c) + 2*a^4*b*d*e^(3*c))*e^(3*d*x)) - 1/2*integrate(15/2*(b*e^(3*d*x + 3*c) - b*e^(d*x + c))/(a^4*e^(4*d*x + 4*c) + a^4 + 2*(a^4*e^(2*c) + 2*a^3*b*e^(2*c))*e^(2*d*x)), x)","F",0
45,0,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(9 \, a^{2} b e^{\left(7 \, c\right)} + 5 \, a b^{2} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(27 \, a^{2} b e^{\left(5 \, c\right)} + 43 \, a b^{2} e^{\left(5 \, c\right)} + 12 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(27 \, a^{2} b e^{\left(3 \, c\right)} + 43 \, a b^{2} e^{\left(3 \, c\right)} + 12 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(9 \, a^{2} b e^{c} + 5 \, a b^{2} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{6} d + 2 \, a^{5} b d + a^{4} b^{2} d + {\left(a^{6} d e^{\left(8 \, c\right)} + 2 \, a^{5} b d e^{\left(8 \, c\right)} + a^{4} b^{2} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{6} d e^{\left(6 \, c\right)} + 4 \, a^{5} b d e^{\left(6 \, c\right)} + 5 \, a^{4} b^{2} d e^{\left(6 \, c\right)} + 2 \, a^{3} b^{3} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{6} d e^{\left(4 \, c\right)} + 14 \, a^{5} b d e^{\left(4 \, c\right)} + 27 \, a^{4} b^{2} d e^{\left(4 \, c\right)} + 24 \, a^{3} b^{3} d e^{\left(4 \, c\right)} + 8 \, 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)} + 4 \, a^{5} b d e^{\left(2 \, c\right)} + 5 \, a^{4} b^{2} d e^{\left(2 \, c\right)} + 2 \, a^{3} b^{3} 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 + 3 \, a^{2} b d + 3 \, a b^{2} d + b^{3} d} + \frac{\log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{a^{3} d + 3 \, a^{2} b d + 3 \, a b^{2} d + b^{3} d} + 2 \, \int \frac{{\left(15 \, a^{2} b e^{\left(3 \, c\right)} + 10 \, a b^{2} e^{\left(3 \, c\right)} + 3 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(15 \, a^{2} b e^{c} + 10 \, a b^{2} e^{c} + 3 \, 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)} + 5 \, a^{5} b e^{\left(2 \, c\right)} + 9 \, a^{4} b^{2} e^{\left(2 \, c\right)} + 7 \, a^{3} b^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b^{4} 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) + 5*a*b^2*e^(7*c))*e^(7*d*x) + (27*a^2*b*e^(5*c) + 43*a*b^2*e^(5*c) + 12*b^3*e^(5*c))*e^(5*d*x) + (27*a^2*b*e^(3*c) + 43*a*b^2*e^(3*c) + 12*b^3*e^(3*c))*e^(3*d*x) + (9*a^2*b*e^c + 5*a*b^2*e^c)*e^(d*x))/(a^6*d + 2*a^5*b*d + a^4*b^2*d + (a^6*d*e^(8*c) + 2*a^5*b*d*e^(8*c) + a^4*b^2*d*e^(8*c))*e^(8*d*x) + 4*(a^6*d*e^(6*c) + 4*a^5*b*d*e^(6*c) + 5*a^4*b^2*d*e^(6*c) + 2*a^3*b^3*d*e^(6*c))*e^(6*d*x) + 2*(3*a^6*d*e^(4*c) + 14*a^5*b*d*e^(4*c) + 27*a^4*b^2*d*e^(4*c) + 24*a^3*b^3*d*e^(4*c) + 8*a^2*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^6*d*e^(2*c) + 4*a^5*b*d*e^(2*c) + 5*a^4*b^2*d*e^(2*c) + 2*a^3*b^3*d*e^(2*c))*e^(2*d*x)) - log((e^(d*x + c) + 1)*e^(-c))/(a^3*d + 3*a^2*b*d + 3*a*b^2*d + b^3*d) + log((e^(d*x + c) - 1)*e^(-c))/(a^3*d + 3*a^2*b*d + 3*a*b^2*d + b^3*d) + 2*integrate(1/8*((15*a^2*b*e^(3*c) + 10*a*b^2*e^(3*c) + 3*b^3*e^(3*c))*e^(3*d*x) - (15*a^2*b*e^c + 10*a*b^2*e^c + 3*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) + 5*a^5*b*e^(2*c) + 9*a^4*b^2*e^(2*c) + 7*a^3*b^3*e^(2*c) + 2*a^2*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
46,1,533,0,0.528244," ","integrate(csch(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{15 \, b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{8 \, a^{4} - 9 \, a^{3} b - 2 \, a^{2} b^{2} + 2 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{4 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d}"," ",0,"-15/16*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)*d) - 1/4*(8*a^4 - 9*a^3*b - 2*a^2*b^2 + 2*(16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3)*e^(-2*d*x - 2*c) + 2*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*e^(-4*d*x - 4*c) + 2*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*e^(-6*d*x - 6*c) + (8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*e^(-8*d*x - 8*c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*e^(-2*d*x - 2*c) + 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*e^(-4*d*x - 4*c) - 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*e^(-6*d*x - 6*c) - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*e^(-8*d*x - 8*c) - (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*e^(-10*d*x - 10*c))*d)","B",0
47,0,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(a - 5 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} + 1\right)} e^{\left(-c\right)}\right)}{2 \, {\left(a^{4} d + 4 \, a^{3} b d + 6 \, a^{2} b^{2} d + 4 \, a b^{3} d + b^{4} d\right)}} - \frac{{\left(a - 5 \, b\right)} \log\left({\left(e^{\left(d x + c\right)} - 1\right)} e^{\left(-c\right)}\right)}{2 \, {\left(a^{4} d + 4 \, a^{3} b d + 6 \, a^{2} b^{2} d + 4 \, a b^{3} d + b^{4} d\right)}} - \frac{{\left(4 \, a^{3} e^{\left(11 \, c\right)} - 9 \, a^{2} b e^{\left(11 \, c\right)} - a b^{2} e^{\left(11 \, c\right)}\right)} e^{\left(11 \, d x\right)} + {\left(20 \, a^{3} e^{\left(9 \, c\right)} + 23 \, a^{2} b e^{\left(9 \, c\right)} - 29 \, a b^{2} e^{\left(9 \, c\right)} + 4 \, b^{3} e^{\left(9 \, c\right)}\right)} e^{\left(9 \, d x\right)} + 2 \, {\left(20 \, a^{3} e^{\left(7 \, c\right)} + 57 \, a^{2} b e^{\left(7 \, c\right)} + 47 \, a b^{2} e^{\left(7 \, c\right)} - 2 \, b^{3} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(20 \, a^{3} e^{\left(5 \, c\right)} + 57 \, a^{2} b e^{\left(5 \, c\right)} + 47 \, a b^{2} e^{\left(5 \, c\right)} - 2 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(20 \, a^{3} e^{\left(3 \, c\right)} + 23 \, a^{2} b e^{\left(3 \, c\right)} - 29 \, a b^{2} e^{\left(3 \, c\right)} + 4 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a^{3} e^{c} - 9 \, a^{2} b e^{c} - a b^{2} 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)} + 7 \, a^{5} b d e^{\left(10 \, c\right)} + 15 \, a^{4} b^{2} d e^{\left(10 \, c\right)} + 13 \, a^{3} b^{3} d e^{\left(10 \, c\right)} + 4 \, a^{2} b^{4} 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)} - 47 \, a^{3} b^{3} d e^{\left(8 \, c\right)} - 48 \, a^{2} b^{4} d e^{\left(8 \, c\right)} - 16 \, a b^{5} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - 4 \, {\left(a^{6} d e^{\left(6 \, c\right)} + 7 \, a^{5} b d e^{\left(6 \, c\right)} + 23 \, a^{4} b^{2} d e^{\left(6 \, c\right)} + 37 \, a^{3} b^{3} d e^{\left(6 \, c\right)} + 28 \, a^{2} b^{4} d e^{\left(6 \, c\right)} + 8 \, a b^{5} 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)} - 47 \, a^{3} b^{3} d e^{\left(4 \, c\right)} - 48 \, a^{2} b^{4} d e^{\left(4 \, c\right)} - 16 \, a b^{5} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{6} d e^{\left(2 \, c\right)} + 7 \, a^{5} b d e^{\left(2 \, c\right)} + 15 \, a^{4} b^{2} d e^{\left(2 \, c\right)} + 13 \, a^{3} b^{3} d e^{\left(2 \, c\right)} + 4 \, a^{2} b^{4} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}} - 8 \, \int \frac{{\left(15 \, a^{2} b e^{\left(3 \, c\right)} - 10 \, a b^{2} e^{\left(3 \, c\right)} - b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(15 \, a^{2} b e^{c} - 10 \, a b^{2} e^{c} - b^{3} e^{c}\right)} e^{\left(d x\right)}}{32 \, {\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)} + 6 \, a^{5} b e^{\left(2 \, c\right)} + 14 \, a^{4} b^{2} e^{\left(2 \, c\right)} + 16 \, a^{3} b^{3} e^{\left(2 \, c\right)} + 9 \, a^{2} b^{4} e^{\left(2 \, c\right)} + 2 \, a b^{5} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/2*(a - 5*b)*log((e^(d*x + c) + 1)*e^(-c))/(a^4*d + 4*a^3*b*d + 6*a^2*b^2*d + 4*a*b^3*d + b^4*d) - 1/2*(a - 5*b)*log((e^(d*x + c) - 1)*e^(-c))/(a^4*d + 4*a^3*b*d + 6*a^2*b^2*d + 4*a*b^3*d + b^4*d) - 1/4*((4*a^3*e^(11*c) - 9*a^2*b*e^(11*c) - a*b^2*e^(11*c))*e^(11*d*x) + (20*a^3*e^(9*c) + 23*a^2*b*e^(9*c) - 29*a*b^2*e^(9*c) + 4*b^3*e^(9*c))*e^(9*d*x) + 2*(20*a^3*e^(7*c) + 57*a^2*b*e^(7*c) + 47*a*b^2*e^(7*c) - 2*b^3*e^(7*c))*e^(7*d*x) + 2*(20*a^3*e^(5*c) + 57*a^2*b*e^(5*c) + 47*a*b^2*e^(5*c) - 2*b^3*e^(5*c))*e^(5*d*x) + (20*a^3*e^(3*c) + 23*a^2*b*e^(3*c) - 29*a*b^2*e^(3*c) + 4*b^3*e^(3*c))*e^(3*d*x) + (4*a^3*e^c - 9*a^2*b*e^c - a*b^2*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) + 7*a^5*b*d*e^(10*c) + 15*a^4*b^2*d*e^(10*c) + 13*a^3*b^3*d*e^(10*c) + 4*a^2*b^4*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) - 47*a^3*b^3*d*e^(8*c) - 48*a^2*b^4*d*e^(8*c) - 16*a*b^5*d*e^(8*c))*e^(8*d*x) - 4*(a^6*d*e^(6*c) + 7*a^5*b*d*e^(6*c) + 23*a^4*b^2*d*e^(6*c) + 37*a^3*b^3*d*e^(6*c) + 28*a^2*b^4*d*e^(6*c) + 8*a*b^5*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) - 47*a^3*b^3*d*e^(4*c) - 48*a^2*b^4*d*e^(4*c) - 16*a*b^5*d*e^(4*c))*e^(4*d*x) + 2*(a^6*d*e^(2*c) + 7*a^5*b*d*e^(2*c) + 15*a^4*b^2*d*e^(2*c) + 13*a^3*b^3*d*e^(2*c) + 4*a^2*b^4*d*e^(2*c))*e^(2*d*x)) - 8*integrate(1/32*((15*a^2*b*e^(3*c) - 10*a*b^2*e^(3*c) - b^3*e^(3*c))*e^(3*d*x) - (15*a^2*b*e^c - 10*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) + 6*a^5*b*e^(2*c) + 14*a^4*b^2*e^(2*c) + 16*a^3*b^3*e^(2*c) + 9*a^2*b^4*e^(2*c) + 2*a*b^5*e^(2*c))*e^(2*d*x)), x)","F",0
48,1,782,0,0.595057," ","integrate(csch(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{5 \, {\left(3 \, a b - 4 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{16 \, a^{4} - 83 \, a^{3} b + 6 \, a^{2} b^{2} + 2 \, {\left(8 \, a^{4} - 299 \, a^{2} b^{2} + 24 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(96 \, a^{4} + 71 \, a^{3} b - 344 \, a^{2} b^{2} + 1208 \, a b^{3} - 48 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(56 \, a^{4} + 144 \, a^{3} b + 31 \, a^{2} b^{2} - 546 \, a b^{3} + 36 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(176 \, a^{4} + 569 \, a^{3} b + 666 \, a^{2} b^{2} + 1704 \, a b^{3} - 144 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - 6 \, {\left(8 \, a^{4} + 32 \, a^{3} b + 93 \, a^{2} b^{2} - 28 \, a b^{3} + 8 \, b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - 15 \, {\left(3 \, a^{3} b - 4 \, a^{2} b^{2}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{12 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(a^{7} + 12 \, a^{6} b + 38 \, a^{5} b^{2} + 52 \, a^{4} b^{3} + 33 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{7} + 20 \, a^{6} b + 34 \, a^{5} b^{2} - 4 \, a^{4} b^{3} - 61 \, a^{3} b^{4} - 56 \, a^{2} b^{5} - 16 \, a b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{7} + 28 \, a^{6} b + 130 \, a^{5} b^{2} + 300 \, a^{4} b^{3} + 355 \, a^{3} b^{4} + 208 \, a^{2} b^{5} + 48 \, a b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{7} + 28 \, a^{6} b + 130 \, a^{5} b^{2} + 300 \, a^{4} b^{3} + 355 \, a^{3} b^{4} + 208 \, a^{2} b^{5} + 48 \, a b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{7} + 20 \, a^{6} b + 34 \, a^{5} b^{2} - 4 \, a^{4} b^{3} - 61 \, a^{3} b^{4} - 56 \, a^{2} b^{5} - 16 \, a b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{7} + 12 \, a^{6} b + 38 \, a^{5} b^{2} + 52 \, a^{4} b^{3} + 33 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-12 \, d x - 12 \, 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(-14 \, d x - 14 \, c\right)}\right)} d}"," ",0,"5/16*(3*a*b - 4*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*b)*d) + 1/12*(16*a^4 - 83*a^3*b + 6*a^2*b^2 + 2*(8*a^4 - 299*a^2*b^2 + 24*a*b^3)*e^(-2*d*x - 2*c) - (96*a^4 + 71*a^3*b - 344*a^2*b^2 + 1208*a*b^3 - 48*b^4)*e^(-4*d*x - 4*c) - 4*(56*a^4 + 144*a^3*b + 31*a^2*b^2 - 546*a*b^3 + 36*b^4)*e^(-6*d*x - 6*c) - (176*a^4 + 569*a^3*b + 666*a^2*b^2 + 1704*a*b^3 - 144*b^4)*e^(-8*d*x - 8*c) - 6*(8*a^4 + 32*a^3*b + 93*a^2*b^2 - 28*a*b^3 + 8*b^4)*e^(-10*d*x - 10*c) - 15*(3*a^3*b - 4*a^2*b^2)*e^(-12*d*x - 12*c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (a^7 + 12*a^6*b + 38*a^5*b^2 + 52*a^4*b^3 + 33*a^3*b^4 + 8*a^2*b^5)*e^(-2*d*x - 2*c) - (3*a^7 + 20*a^6*b + 34*a^5*b^2 - 4*a^4*b^3 - 61*a^3*b^4 - 56*a^2*b^5 - 16*a*b^6)*e^(-4*d*x - 4*c) - (3*a^7 + 28*a^6*b + 130*a^5*b^2 + 300*a^4*b^3 + 355*a^3*b^4 + 208*a^2*b^5 + 48*a*b^6)*e^(-6*d*x - 6*c) + (3*a^7 + 28*a^6*b + 130*a^5*b^2 + 300*a^4*b^3 + 355*a^3*b^4 + 208*a^2*b^5 + 48*a*b^6)*e^(-8*d*x - 8*c) + (3*a^7 + 20*a^6*b + 34*a^5*b^2 - 4*a^4*b^3 - 61*a^3*b^4 - 56*a^2*b^5 - 16*a*b^6)*e^(-10*d*x - 10*c) - (a^7 + 12*a^6*b + 38*a^5*b^2 + 52*a^4*b^3 + 33*a^3*b^4 + 8*a^2*b^5)*e^(-12*d*x - 12*c) - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*e^(-14*d*x - 14*c))*d)","B",0
49,1,97,0,0.307737," ","integrate(cosh(d*x+c)^4*(a+b*sech(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}{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,"1/64*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) + 1/8*b*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d)","A",0
50,1,85,0,0.308600," ","integrate(cosh(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\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)} + \frac{1}{2} \, b {\left(\frac{e^{\left(d x + c\right)}}{d} - \frac{e^{\left(-d x - c\right)}}{d}\right)}"," ",0,"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) + 1/2*b*(e^(d*x + c)/d - e^(-d*x - c)/d)","B",0
51,1,38,0,0.309769," ","integrate(cosh(d*x+c)^2*(a+b*sech(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)} + b x"," ",0,"1/8*a*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) + b*x","A",0
52,1,28,0,0.412121," ","integrate(cosh(d*x+c)*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{2 \, b \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{a \sinh\left(d x + c\right)}{d}"," ",0,"-2*b*arctan(e^(-d*x - c))/d + a*sinh(d*x + c)/d","A",0
53,1,81,0,0.402853," ","integrate(sech(d*x+c)*(a+b*sech(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
54,1,112,0,0.317003," ","integrate(sech(d*x+c)^2*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{4}{3} \, b {\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{2 \, a}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"4/3*b*(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))) + 2*a/(d*(e^(-2*d*x - 2*c) + 1))","B",0
55,1,184,0,0.409988," ","integrate(sech(d*x+c)^3*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{1}{4} \, b {\left(\frac{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{3 \, e^{\left(-d x - c\right)} + 11 \, e^{\left(-3 \, d x - 3 \, c\right)} - 11 \, e^{\left(-5 \, d x - 5 \, c\right)} - 3 \, 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*(3*arctan(e^(-d*x - c))/d - (3*e^(-d*x - c) + 11*e^(-3*d*x - 3*c) - 11*e^(-5*d*x - 5*c) - 3*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
56,1,300,0,0.320799," ","integrate(sech(d*x+c)^4*(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{16}{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{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{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,"16/15*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)) + 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)) + 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
57,1,105,0,0.305705," ","integrate(cosh(d*x+c)^4*(a+b*sech(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}{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)} + b^{2} x"," ",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) + 1/4*a*b*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) + b^2*x","A",0
58,1,105,0,0.411588," ","integrate(cosh(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\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)} + a b {\left(\frac{e^{\left(d x + c\right)}}{d} - \frac{e^{\left(-d x - c\right)}}{d}\right)} - \frac{2 \, b^{2} \arctan\left(e^{\left(-d x - c\right)}\right)}{d}"," ",0,"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) + a*b*(e^(d*x + c)/d - e^(-d*x - c)/d) - 2*b^2*arctan(e^(-d*x - c))/d","B",0
59,1,63,0,0.321816," ","integrate(cosh(d*x+c)^2*(a+b*sech(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)} + 2 \, a b x + \frac{2 \, b^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"1/8*a^2*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) + 2*a*b*x + 2*b^2/(d*(e^(-2*d*x - 2*c) + 1))","A",0
60,1,101,0,0.420269," ","integrate(cosh(d*x+c)*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-b^{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)} - \frac{4 \, a b \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{a^{2} \sinh\left(d x + c\right)}{d}"," ",0,"-b^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))) - 4*a*b*arctan(e^(-d*x - c))/d + a^2*sinh(d*x + c)/d","A",0
61,1,201,0,0.423306," ","integrate(sech(d*x+c)*(a+b*sech(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{3 \, e^{\left(-d x - c\right)} + 11 \, e^{\left(-3 \, d x - 3 \, c\right)} - 11 \, e^{\left(-5 \, d x - 5 \, c\right)} - 3 \, 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 - (3*e^(-d*x - c) + 11*e^(-3*d*x - 3*c) - 11*e^(-5*d*x - 5*c) - 3*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
62,1,324,0,0.334891," ","integrate(sech(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{16}{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{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{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{8}{3} \, a b {\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{2 \, a^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"16/15*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)) + 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)) + 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))) + 8/3*a*b*(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))) + 2*a^2/(d*(e^(-2*d*x - 2*c) + 1))","B",0
63,1,348,0,0.420159," ","integrate(sech(d*x+c)^3*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{1}{24} \, b^{2} {\left(\frac{15 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{15 \, e^{\left(-d x - c\right)} + 85 \, e^{\left(-3 \, d x - 3 \, c\right)} + 198 \, e^{\left(-5 \, d x - 5 \, c\right)} - 198 \, e^{\left(-7 \, d x - 7 \, c\right)} - 85 \, e^{\left(-9 \, d x - 9 \, c\right)} - 15 \, 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{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{3 \, e^{\left(-d x - c\right)} + 11 \, e^{\left(-3 \, d x - 3 \, c\right)} - 11 \, e^{\left(-5 \, d x - 5 \, c\right)} - 3 \, 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*(15*arctan(e^(-d*x - c))/d - (15*e^(-d*x - c) + 85*e^(-3*d*x - 3*c) + 198*e^(-5*d*x - 5*c) - 198*e^(-7*d*x - 7*c) - 85*e^(-9*d*x - 9*c) - 15*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*(3*arctan(e^(-d*x - c))/d - (3*e^(-d*x - c) + 11*e^(-3*d*x - 3*c) - 11*e^(-5*d*x - 5*c) - 3*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
64,1,671,0,0.329060," ","integrate(sech(d*x+c)^4*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{32}{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{21 \, 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{35 \, 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{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{32}{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{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{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,"32/35*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)) + 21*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)) + 35*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)) + 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))) + 32/15*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)) + 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)) + 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
65,1,130,0,0.324143," ","integrate(cosh(d*x+c)^4*(a+b*sech(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}{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)} + 3 \, a b^{2} x + \frac{2 \, b^{3}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\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) + 3/8*a^2*b*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) + 3*a*b^2*x + 2*b^3/(d*(e^(-2*d*x - 2*c) + 1))","A",0
66,1,179,0,0.415363," ","integrate(cosh(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-b^{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)} + \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)} + \frac{3}{2} \, a^{2} b {\left(\frac{e^{\left(d x + c\right)}}{d} - \frac{e^{\left(-d x - c\right)}}{d}\right)} - \frac{6 \, a b^{2} \arctan\left(e^{\left(-d x - c\right)}\right)}{d}"," ",0,"-b^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))) + 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) + 3/2*a^2*b*(e^(d*x + c)/d - e^(-d*x - c)/d) - 6*a*b^2*arctan(e^(-d*x - c))/d","B",0
67,1,160,0,0.318600," ","integrate(cosh(d*x+c)^2*(a+b*sech(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)} + 3 \, a^{2} b x + \frac{4}{3} \, b^{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{6 \, a b^{2}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"1/8*a^3*(4*x + e^(2*d*x + 2*c)/d - e^(-2*d*x - 2*c)/d) + 3*a^2*b*x + 4/3*b^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))) + 6*a*b^2/(d*(e^(-2*d*x - 2*c) + 1))","B",0
68,1,221,0,0.411840," ","integrate(cosh(d*x+c)*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, b^{3} {\left(\frac{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{3 \, e^{\left(-d x - c\right)} + 11 \, e^{\left(-3 \, d x - 3 \, c\right)} - 11 \, e^{\left(-5 \, d x - 5 \, c\right)} - 3 \, 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 b^{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)} - \frac{6 \, a^{2} b \arctan\left(e^{\left(-d x - c\right)}\right)}{d} + \frac{a^{3} \sinh\left(d x + c\right)}{d}"," ",0,"-1/4*b^3*(3*arctan(e^(-d*x - c))/d - (3*e^(-d*x - c) + 11*e^(-3*d*x - 3*c) - 11*e^(-5*d*x - 5*c) - 3*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*b^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))) - 6*a^2*b*arctan(e^(-d*x - c))/d + a^3*sinh(d*x + c)/d","B",0
69,1,365,0,0.414413," ","integrate(sech(d*x+c)*(a+b*sech(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{15 \, e^{\left(-d x - c\right)} + 85 \, e^{\left(-3 \, d x - 3 \, c\right)} + 198 \, e^{\left(-5 \, d x - 5 \, c\right)} - 198 \, e^{\left(-7 \, d x - 7 \, c\right)} - 85 \, e^{\left(-9 \, d x - 9 \, c\right)} - 15 \, 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{3 \, e^{\left(-d x - c\right)} + 11 \, e^{\left(-3 \, d x - 3 \, c\right)} - 11 \, e^{\left(-5 \, d x - 5 \, c\right)} - 3 \, 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 - (15*e^(-d*x - c) + 85*e^(-3*d*x - 3*c) + 198*e^(-5*d*x - 5*c) - 198*e^(-7*d*x - 7*c) - 85*e^(-9*d*x - 9*c) - 15*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 - (3*e^(-d*x - c) + 11*e^(-3*d*x - 3*c) - 11*e^(-5*d*x - 5*c) - 3*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
70,1,695,0,0.329442," ","integrate(sech(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{32}{35} \, b^{3} {\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{21 \, 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{35 \, 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{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{16}{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{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{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^{2} b {\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{2 \, a^{3}}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"32/35*b^3*(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)) + 21*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)) + 35*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)) + 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))) + 16/5*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)) + 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)) + 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^2*b*(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))) + 2*a^3/(d*(e^(-2*d*x - 2*c) + 1))","B",0
71,1,556,0,0.420720," ","integrate(sech(d*x+c)^3*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{1}{192} \, b^{3} {\left(\frac{105 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{105 \, e^{\left(-d x - c\right)} + 805 \, e^{\left(-3 \, d x - 3 \, c\right)} + 2681 \, e^{\left(-5 \, d x - 5 \, c\right)} + 5053 \, e^{\left(-7 \, d x - 7 \, c\right)} - 5053 \, e^{\left(-9 \, d x - 9 \, c\right)} - 2681 \, e^{\left(-11 \, d x - 11 \, c\right)} - 805 \, e^{\left(-13 \, d x - 13 \, c\right)} - 105 \, 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{15 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{15 \, e^{\left(-d x - c\right)} + 85 \, e^{\left(-3 \, d x - 3 \, c\right)} + 198 \, e^{\left(-5 \, d x - 5 \, c\right)} - 198 \, e^{\left(-7 \, d x - 7 \, c\right)} - 85 \, e^{\left(-9 \, d x - 9 \, c\right)} - 15 \, 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{3 \, \arctan\left(e^{\left(-d x - c\right)}\right)}{d} - \frac{3 \, e^{\left(-d x - c\right)} + 11 \, e^{\left(-3 \, d x - 3 \, c\right)} - 11 \, e^{\left(-5 \, d x - 5 \, c\right)} - 3 \, 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*(105*arctan(e^(-d*x - c))/d - (105*e^(-d*x - c) + 805*e^(-3*d*x - 3*c) + 2681*e^(-5*d*x - 5*c) + 5053*e^(-7*d*x - 7*c) - 5053*e^(-9*d*x - 9*c) - 2681*e^(-11*d*x - 11*c) - 805*e^(-13*d*x - 13*c) - 105*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*(15*arctan(e^(-d*x - c))/d - (15*e^(-d*x - c) + 85*e^(-3*d*x - 3*c) + 198*e^(-5*d*x - 5*c) - 198*e^(-7*d*x - 7*c) - 85*e^(-9*d*x - 9*c) - 15*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*(3*arctan(e^(-d*x - c))/d - (3*e^(-d*x - c) + 11*e^(-3*d*x - 3*c) - 11*e^(-5*d*x - 5*c) - 3*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
72,1,1245,0,0.342854," ","integrate(sech(d*x+c)^4*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{256}{315} \, 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{36 \, 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{84 \, 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{126 \, 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{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{96}{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{21 \, 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{35 \, 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{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{16}{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{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{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,"256/315*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)) + 36*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)) + 84*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)) + 126*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)) + 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))) + 96/35*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)) + 21*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)) + 35*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)) + 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))) + 16/5*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)) + 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)) + 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
73,1,526,0,0.456528," ","integrate(cosh(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} a d} + \frac{3 \, {\left(d x + c\right)}}{8 \, a d} - \frac{{\left(8 \, b e^{\left(-2 \, d x - 2 \, c\right)} - a\right)} e^{\left(4 \, d x + 4 \, c\right)}}{64 \, a^{2} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{2} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{2} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d} + \frac{{\left(a b + 2 \, b^{2}\right)} {\left(d x + c\right)}}{2 \, a^{3} d} + \frac{8 \, b e^{\left(-2 \, d x - 2 \, c\right)} - a e^{\left(-4 \, d x - 4 \, c\right)}}{64 \, a^{2} d} + \frac{{\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} a^{3} d}"," ",0,"3/16*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) + 3/8*(d*x + c)/(a*d) - 1/64*(8*b*e^(-2*d*x - 2*c) - a)*e^(4*d*x + 4*c)/(a^2*d) + 1/8*e^(2*d*x + 2*c)/(a*d) - 1/8*e^(-2*d*x - 2*c)/(a*d) - 1/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^2*d) + 1/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d) + 1/8*(a*b + 2*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d) - 1/8*(a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d) + 1/2*(a*b + 2*b^2)*(d*x + c)/(a^3*d) + 1/64*(8*b*e^(-2*d*x - 2*c) - a*e^(-4*d*x - 4*c))/(a^2*d) + 1/16*(a^2*b + 8*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^3*d)","B",0
74,0,0,0,0.000000," ","integrate(cosh(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(3 \, {\left(3 \, a e^{\left(4 \, c\right)} - 4 \, b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} - 3 \, {\left(3 \, a e^{\left(2 \, c\right)} - 4 \, b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)} + a e^{\left(6 \, d x + 6 \, c\right)} - a\right)} e^{\left(-3 \, d x - 3 \, c\right)}}{24 \, a^{2} d} + \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} e^{\left(4 \, d x + 4 \, c\right)} + a^{3} + 2 \, {\left(a^{3} e^{\left(2 \, c\right)} + 2 \, a^{2} b e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"1/24*(3*(3*a*e^(4*c) - 4*b*e^(4*c))*e^(4*d*x) - 3*(3*a*e^(2*c) - 4*b*e^(2*c))*e^(2*d*x) + a*e^(6*d*x + 6*c) - a)*e^(-3*d*x - 3*c)/(a^2*d) + 1/8*integrate(16*(b^2*e^(3*d*x + 3*c) + b^2*e^(d*x + c))/(a^3*e^(4*d*x + 4*c) + a^3 + 2*(a^3*e^(2*c) + 2*a^2*b*e^(2*c))*e^(2*d*x)), x)","F",0
75,1,352,0,0.423994," ","integrate(cosh(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, \sqrt{{\left(a + b\right)} b} a d} + \frac{d x + c}{2 \, a d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{2} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{2} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a^{2} d}"," ",0,"1/4*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) + 1/2*(d*x + c)/(a*d) + 1/8*e^(2*d*x + 2*c)/(a*d) - 1/8*e^(-2*d*x - 2*c)/(a*d) - 1/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^2*d) + 1/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d) + 1/8*(a*b + 2*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d) - 1/8*(a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a^2*d)","B",0
76,0,0,0,0.000000," ","integrate(cosh(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{{\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)} e^{\left(-d x - c\right)}}{2 \, a d} - \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} e^{\left(4 \, d x + 4 \, c\right)} + a^{2} + 2 \, {\left(a^{2} e^{\left(2 \, c\right)} + 2 \, a b 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 - c)/(a*d) - 1/2*integrate(4*(b*e^(3*d*x + 3*c) + b*e^(d*x + c))/(a^2*e^(4*d*x + 4*c) + a^2 + 2*(a^2*e^(2*c) + 2*a*b*e^(2*c))*e^(2*d*x)), x)","F",0
77,0,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\int \frac{\operatorname{sech}\left(d x + c\right)}{b \operatorname{sech}\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(sech(d*x + c)/(b*sech(d*x + c)^2 + a), x)","F",0
78,1,66,0,0.416645," ","integrate(sech(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} d}"," ",0,"-1/2*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*d)","B",0
79,0,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{2 \, \arctan\left(e^{\left(d x + c\right)}\right)}{b d} - 8 \, \int \frac{a e^{\left(3 \, d x + 3 \, c\right)} + a e^{\left(d x + c\right)}}{4 \, {\left(a b e^{\left(4 \, d x + 4 \, c\right)} + a b + 2 \, {\left(a b e^{\left(2 \, c\right)} + 2 \, 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*d*x + 3*c) + a*e^(d*x + c))/(a*b*e^(4*d*x + 4*c) + a*b + 2*(a*b*e^(2*c) + 2*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
80,1,91,0,0.425819," ","integrate(sech(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{a \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} b d} + \frac{2}{{\left(b e^{\left(-2 \, d x - 2 \, c\right)} + b\right)} d}"," ",0,"1/2*a*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*b*d) + 2/((b*e^(-2*d*x - 2*c) + b)*d)","B",0
81,0,0,0,0.000000," ","integrate(sech(d*x+c)^5/(a+b*sech(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} - b e^{c}\right)} \arctan\left(e^{\left(d x + c\right)}\right) e^{\left(-c\right)}}{b^{2} d} + 32 \, \int \frac{a^{2} e^{\left(3 \, d x + 3 \, c\right)} + a^{2} e^{\left(d x + c\right)}}{16 \, {\left(a b^{2} e^{\left(4 \, d x + 4 \, c\right)} + a b^{2} + 2 \, {\left(a b^{2} e^{\left(2 \, c\right)} + 2 \, 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 - b*e^c)*arctan(e^(d*x + c))*e^(-c)/(b^2*d) + 32*integrate(1/16*(a^2*e^(3*d*x + 3*c) + a^2*e^(d*x + c))/(a*b^2*e^(4*d*x + 4*c) + a*b^2 + 2*(a*b^2*e^(2*c) + 2*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
82,1,160,0,0.461389," ","integrate(sech(d*x+c)^6/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} b^{2} d} - \frac{2 \, {\left(6 \, {\left(a - b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, a e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, a - 2 \, 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}"," ",0,"-1/2*a^2*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*b^2*d) - 2/3*(6*(a - b)*e^(-2*d*x - 2*c) + 3*a*e^(-4*d*x - 4*c) + 3*a - 2*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)","B",0
83,0,0,0,0.000000," ","integrate(cosh(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{a^{3} + a^{2} b - {\left(a^{3} e^{\left(10 \, c\right)} + a^{2} b e^{\left(10 \, c\right)}\right)} e^{\left(10 \, d x\right)} - {\left(11 \, a^{3} e^{\left(8 \, c\right)} - 9 \, a^{2} b e^{\left(8 \, c\right)} - 20 \, 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)} + 11 \, a^{2} b e^{\left(6 \, c\right)} - 42 \, a b^{2} e^{\left(6 \, c\right)} - 60 \, b^{3} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(5 \, a^{3} e^{\left(4 \, c\right)} + 11 \, a^{2} b e^{\left(4 \, c\right)} - 42 \, a b^{2} e^{\left(4 \, c\right)} - 60 \, b^{3} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + {\left(11 \, a^{3} e^{\left(2 \, c\right)} - 9 \, a^{2} b e^{\left(2 \, c\right)} - 20 \, 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)} + a^{4} b d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(a^{5} d e^{\left(5 \, c\right)} + 3 \, a^{4} b d e^{\left(5 \, c\right)} + 2 \, a^{3} b^{2} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + {\left(a^{5} d e^{\left(3 \, c\right)} + a^{4} b 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)} + 5 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(6 \, a b^{2} e^{c} + 5 \, b^{3} e^{c}\right)} e^{\left(d x\right)}\right)}}{a^{5} + a^{4} b + {\left(a^{5} e^{\left(4 \, c\right)} + a^{4} b e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{5} e^{\left(2 \, c\right)} + 3 \, a^{4} b e^{\left(2 \, c\right)} + 2 \, a^{3} b^{2} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}\,{d x}"," ",0,"-1/24*(a^3 + a^2*b - (a^3*e^(10*c) + a^2*b*e^(10*c))*e^(10*d*x) - (11*a^3*e^(8*c) - 9*a^2*b*e^(8*c) - 20*a*b^2*e^(8*c))*e^(8*d*x) - 2*(5*a^3*e^(6*c) + 11*a^2*b*e^(6*c) - 42*a*b^2*e^(6*c) - 60*b^3*e^(6*c))*e^(6*d*x) + 2*(5*a^3*e^(4*c) + 11*a^2*b*e^(4*c) - 42*a*b^2*e^(4*c) - 60*b^3*e^(4*c))*e^(4*d*x) + (11*a^3*e^(2*c) - 9*a^2*b*e^(2*c) - 20*a*b^2*e^(2*c))*e^(2*d*x))/((a^5*d*e^(7*c) + a^4*b*d*e^(7*c))*e^(7*d*x) + 2*(a^5*d*e^(5*c) + 3*a^4*b*d*e^(5*c) + 2*a^3*b^2*d*e^(5*c))*e^(5*d*x) + (a^5*d*e^(3*c) + a^4*b*d*e^(3*c))*e^(3*d*x)) + 1/8*integrate(8*((6*a*b^2*e^(3*c) + 5*b^3*e^(3*c))*e^(3*d*x) + (6*a*b^2*e^c + 5*b^3*e^c)*e^(d*x))/(a^5 + a^4*b + (a^5*e^(4*c) + a^4*b*e^(4*c))*e^(4*d*x) + 2*(a^5*e^(2*c) + 3*a^4*b*e^(2*c) + 2*a^3*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
84,1,696,0,0.465720," ","integrate(cosh(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(3 \, a^{2} b + 12 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + a^{3} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{a^{2} b + 2 \, a b^{2} + {\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{5} + a^{4} b + {\left(a^{5} + a^{4} b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{a^{2} b + 2 \, a b^{2} + {\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{5} + a^{4} b + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{5} + a^{4} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{a b + {\left(a b + 2 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{2 \, {\left(a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{d x + c}{2 \, a^{2} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a^{2} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a^{2} d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{2 \, a^{3} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{3} d}"," ",0,"1/16*(3*a^2*b + 12*a*b^2 + 8*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)*d) - 1/16*(3*a^2*b + 12*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + a^3*b)*sqrt((a + b)*b)*d) + 1/8*(3*a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)*d) - 1/4*(a^2*b + 2*a*b^2 + (a^2*b + 8*a*b^2 + 8*b^3)*e^(2*d*x + 2*c))/((a^5 + a^4*b + (a^5 + a^4*b)*e^(4*d*x + 4*c) + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*e^(2*d*x + 2*c))*d) + 1/4*(a^2*b + 2*a*b^2 + (a^2*b + 8*a*b^2 + 8*b^3)*e^(-2*d*x - 2*c))/((a^5 + a^4*b + 2*(a^5 + 3*a^4*b + 2*a^3*b^2)*e^(-2*d*x - 2*c) + (a^5 + a^4*b)*e^(-4*d*x - 4*c))*d) - 1/2*(a*b + (a*b + 2*b^2)*e^(-2*d*x - 2*c))/((a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c) + (a^4 + a^3*b)*e^(-4*d*x - 4*c))*d) + 1/2*(d*x + c)/(a^2*d) + 1/8*e^(2*d*x + 2*c)/(a^2*d) - 1/8*e^(-2*d*x - 2*c)/(a^2*d) - 1/2*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^3*d) + 1/2*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
85,0,0,0,0.000000," ","integrate(cosh(d*x+c)/(a+b*sech(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)} + 5 \, a b e^{\left(4 \, c\right)} + 6 \, b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + {\left(a^{2} e^{\left(2 \, c\right)} + 5 \, a b e^{\left(2 \, c\right)} + 6 \, 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)} + a^{3} b d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 2 \, {\left(a^{4} d e^{\left(3 \, c\right)} + 3 \, a^{3} b d e^{\left(3 \, c\right)} + 2 \, a^{2} b^{2} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{4} d e^{c} + a^{3} b 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)} + 3 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a b e^{c} + 3 \, b^{2} e^{c}\right)} e^{\left(d x\right)}\right)}}{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)} + 3 \, a^{3} b e^{\left(2 \, c\right)} + 2 \, a^{2} b^{2} 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) + 5*a*b*e^(4*c) + 6*b^2*e^(4*c))*e^(4*d*x) + (a^2*e^(2*c) + 5*a*b*e^(2*c) + 6*b^2*e^(2*c))*e^(2*d*x))/((a^4*d*e^(5*c) + a^3*b*d*e^(5*c))*e^(5*d*x) + 2*(a^4*d*e^(3*c) + 3*a^3*b*d*e^(3*c) + 2*a^2*b^2*d*e^(3*c))*e^(3*d*x) + (a^4*d*e^c + a^3*b*d*e^c)*e^(d*x)) - 1/2*integrate(2*((4*a*b*e^(3*c) + 3*b^2*e^(3*c))*e^(3*d*x) + (4*a*b*e^c + 3*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) + 3*a^3*b*e^(2*c) + 2*a^2*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
86,0,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*sech(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 + a^{2} b d + {\left(a^{3} d e^{\left(4 \, c\right)} + a^{2} b d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} d e^{\left(2 \, c\right)} + 3 \, a^{2} b d e^{\left(2 \, c\right)} + 2 \, 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} + 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)} + 3 \, a^{2} b e^{\left(2 \, c\right)} + 2 \, 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 + a^2*b*d + (a^3*d*e^(4*c) + a^2*b*d*e^(4*c))*e^(4*d*x) + 2*(a^3*d*e^(2*c) + 3*a^2*b*d*e^(2*c) + 2*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 + a^2*b + (a^3*e^(4*c) + a^2*b*e^(4*c))*e^(4*d*x) + 2*(a^3*e^(2*c) + 3*a^2*b*e^(2*c) + 2*a*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
87,1,150,0,0.456140," ","integrate(sech(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a}{{\left(a^{3} + a^{2} b + 2 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} + a^{2} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{\log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, \sqrt{{\left(a + b\right)} b} {\left(a + b\right)} d}"," ",0,"((a + 2*b)*e^(-2*d*x - 2*c) + a)/((a^3 + a^2*b + 2*(a^3 + 3*a^2*b + 2*a*b^2)*e^(-2*d*x - 2*c) + (a^3 + a^2*b)*e^(-4*d*x - 4*c))*d) - 1/4*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a + b)*d)","B",0
88,0,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{e^{\left(3 \, d x + 3 \, c\right)} - e^{\left(d x + c\right)}}{a^{2} d + a b d + {\left(a^{2} d e^{\left(4 \, c\right)} + a b d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\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)} 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)} + 3 \, a b e^{\left(2 \, c\right)} + 2 \, b^{2} 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^2*d + a*b*d + (a^2*d*e^(4*c) + a*b*d*e^(4*c))*e^(4*d*x) + 2*(a^2*d*e^(2*c) + 3*a*b*d*e^(2*c) + 2*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) + 3*a*b*e^(2*c) + 2*b^2*e^(2*c))*e^(2*d*x)), x)","F",0
89,1,165,0,0.478288," ","integrate(sech(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(a + 2 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, \sqrt{{\left(a + b\right)} b} {\left(a b + b^{2}\right)} d} - \frac{{\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a}{{\left(a^{2} b + a b^{2} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\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}"," ",0,"-1/4*(a + 2*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a*b + b^2)*d) - ((a + 2*b)*e^(-2*d*x - 2*c) + a)/((a^2*b + a*b^2 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*e^(-2*d*x - 2*c) + (a^2*b + a*b^2)*e^(-4*d*x - 4*c))*d)","B",0
90,0,0,0,0.000000," ","integrate(sech(d*x+c)^5/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{a e^{\left(3 \, d x + 3 \, c\right)} - a e^{\left(d x + c\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)} + 3 \, a b^{2} d e^{\left(2 \, c\right)} + 2 \, b^{3} 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)} + 3 \, a b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(2 \, a^{2} e^{c} + 3 \, a b 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)} + 3 \, a b^{3} e^{\left(2 \, c\right)} + 2 \, b^{4} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-(a*e^(3*d*x + 3*c) - a*e^(d*x + c))/(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) + 3*a*b^2*d*e^(2*c) + 2*b^3*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) + 3*a*b*e^(3*c))*e^(3*d*x) + (2*a^2*e^c + 3*a*b*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) + 3*a*b^3*e^(2*c) + 2*b^4*e^(2*c))*e^(2*d*x)), x)","F",0
91,1,244,0,0.553649," ","integrate(sech(d*x+c)^6/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a + 4 \, b\right)} a \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, {\left(a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, a^{2} + 2 \, a b + 2 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{2} + 4 \, a b\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{{\left(a^{2} b^{2} + a b^{3} + {\left(3 \, a^{2} b^{2} + 7 \, a b^{3} + 4 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{2} b^{2} + 7 \, a b^{3} + 4 \, b^{4}\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}"," ",0,"1/4*(3*a + 4*b)*a*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a*b^2 + b^3)*sqrt((a + b)*b)*d) + (3*a^2 + 2*a*b + 2*(3*a^2 + 7*a*b + 4*b^2)*e^(-2*d*x - 2*c) + (3*a^2 + 4*a*b)*e^(-4*d*x - 4*c))/((a^2*b^2 + a*b^3 + (3*a^2*b^2 + 7*a*b^3 + 4*b^4)*e^(-2*d*x - 2*c) + (3*a^2*b^2 + 7*a*b^3 + 4*b^4)*e^(-4*d*x - 4*c) + (a^2*b^2 + a*b^3)*e^(-6*d*x - 6*c))*d)","B",0
92,0,0,0,0.000000," ","integrate(sech(d*x+c)^7/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{2} e^{\left(7 \, c\right)} + a b e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(2 \, a^{2} e^{\left(5 \, c\right)} + 5 \, a b e^{\left(5 \, c\right)} + 4 \, b^{2} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(2 \, a^{2} e^{\left(3 \, c\right)} + 5 \, a b e^{\left(3 \, c\right)} + 4 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(2 \, a^{2} e^{c} + a b e^{c}\right)} e^{\left(d x\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)} + 4 \, {\left(a^{2} b^{2} d e^{\left(6 \, c\right)} + 2 \, a b^{3} d e^{\left(6 \, c\right)} + b^{4} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{2} b^{2} d e^{\left(4 \, c\right)} + 7 \, a b^{3} d e^{\left(4 \, c\right)} + 4 \, b^{4} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{2} b^{2} d e^{\left(2 \, c\right)} + 2 \, a b^{3} d e^{\left(2 \, c\right)} + b^{4} d e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}} - \frac{{\left(4 \, a e^{c} - 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)} + 5 \, a^{2} b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a^{3} e^{c} + 5 \, a^{2} b 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)} + 3 \, a b^{4} e^{\left(2 \, c\right)} + 2 \, b^{5} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"((2*a^2*e^(7*c) + a*b*e^(7*c))*e^(7*d*x) + (2*a^2*e^(5*c) + 5*a*b*e^(5*c) + 4*b^2*e^(5*c))*e^(5*d*x) - (2*a^2*e^(3*c) + 5*a*b*e^(3*c) + 4*b^2*e^(3*c))*e^(3*d*x) - (2*a^2*e^c + a*b*e^c)*e^(d*x))/(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) + 4*(a^2*b^2*d*e^(6*c) + 2*a*b^3*d*e^(6*c) + b^4*d*e^(6*c))*e^(6*d*x) + 2*(3*a^2*b^2*d*e^(4*c) + 7*a*b^3*d*e^(4*c) + 4*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^2*b^2*d*e^(2*c) + 2*a*b^3*d*e^(2*c) + b^4*d*e^(2*c))*e^(2*d*x)) - (4*a*e^c - b*e^c)*arctan(e^(d*x + c))*e^(-c)/(b^3*d) + 128*integrate(1/128*((4*a^3*e^(3*c) + 5*a^2*b*e^(3*c))*e^(3*d*x) + (4*a^3*e^c + 5*a^2*b*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) + 3*a*b^4*e^(2*c) + 2*b^5*e^(2*c))*e^(2*d*x)), x)","F",0
93,1,1373,0,0.546255," ","integrate(cosh(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, {\left(5 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{9 \, a^{4} b + 32 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + 3 \, {\left(3 \, a^{4} b + 34 \, a^{3} b^{2} + 64 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(27 \, a^{4} b + 264 \, a^{3} b^{2} + 740 \, a^{2} b^{3} + 832 \, a b^{4} + 320 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(27 \, a^{4} b + 194 \, a^{3} b^{2} + 336 \, a^{2} b^{3} + 160 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{9 \, a^{4} b + 32 \, a^{3} b^{2} + 20 \, a^{2} b^{3} + {\left(27 \, a^{4} b + 194 \, a^{3} b^{2} + 336 \, a^{2} b^{3} + 160 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(27 \, a^{4} b + 264 \, a^{3} b^{2} + 740 \, a^{2} b^{3} + 832 \, a b^{4} + 320 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(3 \, a^{4} b + 34 \, a^{3} b^{2} + 64 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{8} + 14 \, a^{7} b + 27 \, a^{6} b^{2} + 24 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} + 2 \, a^{5} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{8} + 2 \, a^{7} b + a^{6} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{9 \, a^{3} b + 6 \, a^{2} b^{2} + {\left(27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(9 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(9 \, a^{3} b + 28 \, a^{2} b^{2} + 16 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{8 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{d x + c}{2 \, a^{3} d} + \frac{e^{\left(2 \, d x + 2 \, c\right)}}{8 \, a^{3} d} - \frac{e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a^{3} d} - \frac{3 \, b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{4} d} + \frac{3 \, b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{4} d}"," ",0,"3/64*(5*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)*d) - 3/64*(5*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 2*a^5*b + a^4*b^2)*sqrt((a + b)*b)*d) + 1/32*(15*a^2*b + 20*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)*d) - 1/16*(9*a^4*b + 32*a^3*b^2 + 20*a^2*b^3 + 3*(3*a^4*b + 34*a^3*b^2 + 64*a^2*b^3 + 32*a*b^4)*e^(6*d*x + 6*c) + (27*a^4*b + 264*a^3*b^2 + 740*a^2*b^3 + 832*a*b^4 + 320*b^5)*e^(4*d*x + 4*c) + (27*a^4*b + 194*a^3*b^2 + 336*a^2*b^3 + 160*a*b^4)*e^(2*d*x + 2*c))/((a^8 + 2*a^7*b + a^6*b^2 + (a^8 + 2*a^7*b + a^6*b^2)*e^(8*d*x + 8*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(6*d*x + 6*c) + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*e^(4*d*x + 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(2*d*x + 2*c))*d) + 1/16*(9*a^4*b + 32*a^3*b^2 + 20*a^2*b^3 + (27*a^4*b + 194*a^3*b^2 + 336*a^2*b^3 + 160*a*b^4)*e^(-2*d*x - 2*c) + (27*a^4*b + 264*a^3*b^2 + 740*a^2*b^3 + 832*a*b^4 + 320*b^5)*e^(-4*d*x - 4*c) + 3*(3*a^4*b + 34*a^3*b^2 + 64*a^2*b^3 + 32*a*b^4)*e^(-6*d*x - 6*c))/((a^8 + 2*a^7*b + a^6*b^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^8 + 14*a^7*b + 27*a^6*b^2 + 24*a^5*b^3 + 8*a^4*b^4)*e^(-4*d*x - 4*c) + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 + 2*a^5*b^3)*e^(-6*d*x - 6*c) + (a^8 + 2*a^7*b + a^6*b^2)*e^(-8*d*x - 8*c))*d) - 1/8*(9*a^3*b + 6*a^2*b^2 + (27*a^3*b + 68*a^2*b^2 + 32*a*b^3)*e^(-2*d*x - 2*c) + 3*(9*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*e^(-4*d*x - 4*c) + (9*a^3*b + 28*a^2*b^2 + 16*a*b^3)*e^(-6*d*x - 6*c))/((a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(-4*d*x - 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-6*d*x - 6*c) + (a^7 + 2*a^6*b + a^5*b^2)*e^(-8*d*x - 8*c))*d) + 1/2*(d*x + c)/(a^3*d) + 1/8*e^(2*d*x + 2*c)/(a^3*d) - 1/8*e^(-2*d*x - 2*c)/(a^3*d) - 3/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^4*d) + 3/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^4*d)","B",0
94,0,0,0,0.000000," ","integrate(cosh(d*x+c)/(a+b*sech(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)} + 28 \, a^{3} b e^{\left(8 \, c\right)} + 50 \, a^{2} b^{2} e^{\left(8 \, c\right)} + 25 \, a b^{3} e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} - {\left(4 \, a^{4} e^{\left(6 \, c\right)} + 24 \, a^{3} b e^{\left(6 \, c\right)} + 80 \, a^{2} b^{2} e^{\left(6 \, c\right)} + 129 \, a b^{3} e^{\left(6 \, c\right)} + 60 \, b^{4} e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + {\left(4 \, a^{4} e^{\left(4 \, c\right)} + 24 \, a^{3} b e^{\left(4 \, c\right)} + 80 \, a^{2} b^{2} e^{\left(4 \, c\right)} + 129 \, a b^{3} e^{\left(4 \, c\right)} + 60 \, b^{4} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + {\left(6 \, a^{4} e^{\left(2 \, c\right)} + 28 \, a^{3} b e^{\left(2 \, c\right)} + 50 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 25 \, a b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}}{4 \, {\left({\left(a^{7} d e^{\left(9 \, c\right)} + 2 \, a^{6} b d e^{\left(9 \, c\right)} + a^{5} b^{2} d e^{\left(9 \, c\right)}\right)} e^{\left(9 \, d x\right)} + 4 \, {\left(a^{7} d e^{\left(7 \, c\right)} + 4 \, a^{6} b d e^{\left(7 \, c\right)} + 5 \, a^{5} b^{2} d e^{\left(7 \, c\right)} + 2 \, a^{4} b^{3} d e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + 2 \, {\left(3 \, a^{7} d e^{\left(5 \, c\right)} + 14 \, a^{6} b d e^{\left(5 \, c\right)} + 27 \, a^{5} b^{2} d e^{\left(5 \, c\right)} + 24 \, a^{4} b^{3} d e^{\left(5 \, c\right)} + 8 \, a^{3} b^{4} d e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} + 4 \, {\left(a^{7} d e^{\left(3 \, c\right)} + 4 \, a^{6} b d e^{\left(3 \, c\right)} + 5 \, a^{5} b^{2} d e^{\left(3 \, c\right)} + 2 \, a^{4} b^{3} d e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(a^{7} d e^{c} + 2 \, a^{6} b d e^{c} + a^{5} b^{2} 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)} + 12 \, a b^{2} e^{\left(3 \, c\right)} + 5 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(8 \, a^{2} b e^{c} + 12 \, a b^{2} e^{c} + 5 \, b^{3} e^{c}\right)} e^{\left(d x\right)}\right)}}{2 \, {\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)} + 4 \, a^{5} b e^{\left(2 \, c\right)} + 5 \, a^{4} b^{2} e^{\left(2 \, c\right)} + 2 \, a^{3} b^{3} 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) + 28*a^3*b*e^(8*c) + 50*a^2*b^2*e^(8*c) + 25*a*b^3*e^(8*c))*e^(8*d*x) - (4*a^4*e^(6*c) + 24*a^3*b*e^(6*c) + 80*a^2*b^2*e^(6*c) + 129*a*b^3*e^(6*c) + 60*b^4*e^(6*c))*e^(6*d*x) + (4*a^4*e^(4*c) + 24*a^3*b*e^(4*c) + 80*a^2*b^2*e^(4*c) + 129*a*b^3*e^(4*c) + 60*b^4*e^(4*c))*e^(4*d*x) + (6*a^4*e^(2*c) + 28*a^3*b*e^(2*c) + 50*a^2*b^2*e^(2*c) + 25*a*b^3*e^(2*c))*e^(2*d*x))/((a^7*d*e^(9*c) + 2*a^6*b*d*e^(9*c) + a^5*b^2*d*e^(9*c))*e^(9*d*x) + 4*(a^7*d*e^(7*c) + 4*a^6*b*d*e^(7*c) + 5*a^5*b^2*d*e^(7*c) + 2*a^4*b^3*d*e^(7*c))*e^(7*d*x) + 2*(3*a^7*d*e^(5*c) + 14*a^6*b*d*e^(5*c) + 27*a^5*b^2*d*e^(5*c) + 24*a^4*b^3*d*e^(5*c) + 8*a^3*b^4*d*e^(5*c))*e^(5*d*x) + 4*(a^7*d*e^(3*c) + 4*a^6*b*d*e^(3*c) + 5*a^5*b^2*d*e^(3*c) + 2*a^4*b^3*d*e^(3*c))*e^(3*d*x) + (a^7*d*e^c + 2*a^6*b*d*e^c + a^5*b^2*d*e^c)*e^(d*x)) - 1/2*integrate(3/2*((8*a^2*b*e^(3*c) + 12*a*b^2*e^(3*c) + 5*b^3*e^(3*c))*e^(3*d*x) + (8*a^2*b*e^c + 12*a*b^2*e^c + 5*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) + 4*a^5*b*e^(2*c) + 5*a^4*b^2*e^(2*c) + 2*a^3*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
95,0,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(8 \, a^{2} b e^{\left(7 \, c\right)} + 5 \, a b^{2} e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(8 \, a^{2} b e^{\left(5 \, c\right)} + 29 \, a b^{2} e^{\left(5 \, c\right)} + 12 \, b^{3} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(8 \, a^{2} b e^{\left(3 \, c\right)} + 29 \, a b^{2} e^{\left(3 \, c\right)} + 12 \, b^{3} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(8 \, a^{2} b e^{c} + 5 \, a b^{2} e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{6} d + 2 \, a^{5} b d + a^{4} b^{2} d + {\left(a^{6} d e^{\left(8 \, c\right)} + 2 \, a^{5} b d e^{\left(8 \, c\right)} + a^{4} b^{2} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{6} d e^{\left(6 \, c\right)} + 4 \, a^{5} b d e^{\left(6 \, c\right)} + 5 \, a^{4} b^{2} d e^{\left(6 \, c\right)} + 2 \, a^{3} b^{3} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{6} d e^{\left(4 \, c\right)} + 14 \, a^{5} b d e^{\left(4 \, c\right)} + 27 \, a^{4} b^{2} d e^{\left(4 \, c\right)} + 24 \, a^{3} b^{3} d e^{\left(4 \, c\right)} + 8 \, 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)} + 4 \, a^{5} b d e^{\left(2 \, c\right)} + 5 \, a^{4} b^{2} d e^{\left(2 \, c\right)} + 2 \, a^{3} b^{3} 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} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} e^{\left(4 \, c\right)} + 2 \, a^{4} b e^{\left(4 \, c\right)} + a^{3} b^{2} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{5} e^{\left(2 \, c\right)} + 4 \, a^{4} b e^{\left(2 \, c\right)} + 5 \, a^{3} b^{2} e^{\left(2 \, c\right)} + 2 \, 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) + 5*a*b^2*e^(7*c))*e^(7*d*x) + (8*a^2*b*e^(5*c) + 29*a*b^2*e^(5*c) + 12*b^3*e^(5*c))*e^(5*d*x) - (8*a^2*b*e^(3*c) + 29*a*b^2*e^(3*c) + 12*b^3*e^(3*c))*e^(3*d*x) - (8*a^2*b*e^c + 5*a*b^2*e^c)*e^(d*x))/(a^6*d + 2*a^5*b*d + a^4*b^2*d + (a^6*d*e^(8*c) + 2*a^5*b*d*e^(8*c) + a^4*b^2*d*e^(8*c))*e^(8*d*x) + 4*(a^6*d*e^(6*c) + 4*a^5*b*d*e^(6*c) + 5*a^4*b^2*d*e^(6*c) + 2*a^3*b^3*d*e^(6*c))*e^(6*d*x) + 2*(3*a^6*d*e^(4*c) + 14*a^5*b*d*e^(4*c) + 27*a^4*b^2*d*e^(4*c) + 24*a^3*b^3*d*e^(4*c) + 8*a^2*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^6*d*e^(2*c) + 4*a^5*b*d*e^(2*c) + 5*a^4*b^2*d*e^(2*c) + 2*a^3*b^3*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 + 2*a^4*b + a^3*b^2 + (a^5*e^(4*c) + 2*a^4*b*e^(4*c) + a^3*b^2*e^(4*c))*e^(4*d*x) + 2*(a^5*e^(2*c) + 4*a^4*b*e^(2*c) + 5*a^3*b^2*e^(2*c) + 2*a^2*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
96,1,353,0,0.514261," ","integrate(sech(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{5 \, a^{3} + 2 \, a^{2} b + {\left(15 \, a^{3} + 32 \, a^{2} b + 8 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(15 \, a^{3} + 46 \, a^{2} b + 56 \, a b^{2} + 16 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(5 \, a^{3} + 16 \, a^{2} b + 8 \, a b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2} + 4 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} + 14 \, a^{5} b + 27 \, a^{4} b^{2} + 24 \, a^{3} b^{3} + 8 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{3 \, \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d}"," ",0,"1/4*(5*a^3 + 2*a^2*b + (15*a^3 + 32*a^2*b + 8*a*b^2)*e^(-2*d*x - 2*c) + (15*a^3 + 46*a^2*b + 56*a*b^2 + 16*b^3)*e^(-4*d*x - 4*c) + (5*a^3 + 16*a^2*b + 8*a*b^2)*e^(-6*d*x - 6*c))/((a^6 + 2*a^5*b + a^4*b^2 + 4*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^6 + 14*a^5*b + 27*a^4*b^2 + 24*a^3*b^3 + 8*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*e^(-6*d*x - 6*c) + (a^6 + 2*a^5*b + a^4*b^2)*e^(-8*d*x - 8*c))*d) - 3/16*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d)","B",0
97,0,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(4 \, a^{2} e^{\left(7 \, c\right)} + a b e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(4 \, a^{2} e^{\left(5 \, c\right)} + 9 \, a b e^{\left(5 \, c\right)} - 4 \, b^{2} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(4 \, a^{2} e^{\left(3 \, c\right)} + 9 \, a b e^{\left(3 \, c\right)} - 4 \, b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(4 \, a^{2} e^{c} + a b e^{c}\right)} e^{\left(d x\right)}}{4 \, {\left(a^{5} d + 2 \, a^{4} b d + a^{3} b^{2} d + {\left(a^{5} d e^{\left(8 \, c\right)} + 2 \, a^{4} b d e^{\left(8 \, c\right)} + a^{3} b^{2} d e^{\left(8 \, c\right)}\right)} e^{\left(8 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(6 \, c\right)} + 4 \, a^{4} b d e^{\left(6 \, c\right)} + 5 \, a^{3} b^{2} d e^{\left(6 \, c\right)} + 2 \, 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)} + 14 \, a^{4} b d e^{\left(4 \, c\right)} + 27 \, a^{3} b^{2} d e^{\left(4 \, c\right)} + 24 \, a^{2} b^{3} d e^{\left(4 \, c\right)} + 8 \, a b^{4} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{5} d e^{\left(2 \, c\right)} + 4 \, a^{4} b d e^{\left(2 \, c\right)} + 5 \, a^{3} b^{2} d e^{\left(2 \, c\right)} + 2 \, 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)} + b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(4 \, a e^{c} + 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)} + 4 \, a^{3} b e^{\left(2 \, c\right)} + 5 \, a^{2} b^{2} e^{\left(2 \, c\right)} + 2 \, a b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*((4*a^2*e^(7*c) + a*b*e^(7*c))*e^(7*d*x) + (4*a^2*e^(5*c) + 9*a*b*e^(5*c) - 4*b^2*e^(5*c))*e^(5*d*x) - (4*a^2*e^(3*c) + 9*a*b*e^(3*c) - 4*b^2*e^(3*c))*e^(3*d*x) - (4*a^2*e^c + a*b*e^c)*e^(d*x))/(a^5*d + 2*a^4*b*d + a^3*b^2*d + (a^5*d*e^(8*c) + 2*a^4*b*d*e^(8*c) + a^3*b^2*d*e^(8*c))*e^(8*d*x) + 4*(a^5*d*e^(6*c) + 4*a^4*b*d*e^(6*c) + 5*a^3*b^2*d*e^(6*c) + 2*a^2*b^3*d*e^(6*c))*e^(6*d*x) + 2*(3*a^5*d*e^(4*c) + 14*a^4*b*d*e^(4*c) + 27*a^3*b^2*d*e^(4*c) + 24*a^2*b^3*d*e^(4*c) + 8*a*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^5*d*e^(2*c) + 4*a^4*b*d*e^(2*c) + 5*a^3*b^2*d*e^(2*c) + 2*a^2*b^3*d*e^(2*c))*e^(2*d*x)) + 8*integrate(1/32*((4*a*e^(3*c) + b*e^(3*c))*e^(3*d*x) + (4*a*e^c + 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) + 4*a^3*b*e^(2*c) + 5*a^2*b^2*e^(2*c) + 2*a*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
98,1,369,0,0.534860," ","integrate(sech(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(a + 4 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{a^{3} - 2 \, a^{2} b + {\left(3 \, a^{3} - 4 \, a^{2} b - 16 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{3} + 2 \, a^{2} b - 8 \, a b^{2} - 16 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} + 4 \, a^{2} b\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3} + 4 \, {\left(a^{5} b + 4 \, a^{4} b^{2} + 5 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} b + 14 \, a^{4} b^{2} + 27 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 8 \, a b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} b + 4 \, a^{4} b^{2} + 5 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d}"," ",0,"-1/16*(a + 4*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b + 2*a*b^2 + b^3)*sqrt((a + b)*b)*d) - 1/4*(a^3 - 2*a^2*b + (3*a^3 - 4*a^2*b - 16*a*b^2)*e^(-2*d*x - 2*c) + (3*a^3 + 2*a^2*b - 8*a*b^2 - 16*b^3)*e^(-4*d*x - 4*c) + (a^3 + 4*a^2*b)*e^(-6*d*x - 6*c))/((a^5*b + 2*a^4*b^2 + a^3*b^3 + 4*(a^5*b + 4*a^4*b^2 + 5*a^3*b^3 + 2*a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^5*b + 14*a^4*b^2 + 27*a^3*b^3 + 24*a^2*b^4 + 8*a*b^5)*e^(-4*d*x - 4*c) + 4*(a^5*b + 4*a^4*b^2 + 5*a^3*b^3 + 2*a^2*b^4)*e^(-6*d*x - 6*c) + (a^5*b + 2*a^4*b^2 + a^3*b^3)*e^(-8*d*x - 8*c))*d)","B",0
99,0,0,0,0.000000," ","integrate(sech(d*x+c)^5/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(11 \, a e^{\left(5 \, c\right)} + 20 \, b e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(11 \, a e^{\left(3 \, c\right)} + 20 \, b e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + 3 \, a e^{\left(7 \, d x + 7 \, c\right)} - 3 \, a e^{\left(d x + c\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)} + 4 \, a^{3} b d e^{\left(6 \, c\right)} + 5 \, a^{2} b^{2} d e^{\left(6 \, c\right)} + 2 \, a b^{3} d e^{\left(6 \, c\right)}\right)} e^{\left(6 \, d x\right)} + 2 \, {\left(3 \, a^{4} d e^{\left(4 \, c\right)} + 14 \, a^{3} b d e^{\left(4 \, c\right)} + 27 \, a^{2} b^{2} d e^{\left(4 \, c\right)} + 24 \, a b^{3} d e^{\left(4 \, c\right)} + 8 \, b^{4} d e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 4 \, {\left(a^{4} d e^{\left(2 \, c\right)} + 4 \, a^{3} b d e^{\left(2 \, c\right)} + 5 \, a^{2} b^{2} d e^{\left(2 \, c\right)} + 2 \, a b^{3} 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} + 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)} + 4 \, a^{2} b e^{\left(2 \, c\right)} + 5 \, a b^{2} e^{\left(2 \, c\right)} + 2 \, b^{3} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"1/4*((11*a*e^(5*c) + 20*b*e^(5*c))*e^(5*d*x) - (11*a*e^(3*c) + 20*b*e^(3*c))*e^(3*d*x) + 3*a*e^(7*d*x + 7*c) - 3*a*e^(d*x + c))/(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) + 4*a^3*b*d*e^(6*c) + 5*a^2*b^2*d*e^(6*c) + 2*a*b^3*d*e^(6*c))*e^(6*d*x) + 2*(3*a^4*d*e^(4*c) + 14*a^3*b*d*e^(4*c) + 27*a^2*b^2*d*e^(4*c) + 24*a*b^3*d*e^(4*c) + 8*b^4*d*e^(4*c))*e^(4*d*x) + 4*(a^4*d*e^(2*c) + 4*a^3*b*d*e^(2*c) + 5*a^2*b^2*d*e^(2*c) + 2*a*b^3*d*e^(2*c))*e^(2*d*x)) + 32*integrate(3/128*(e^(3*d*x + 3*c) + e^(d*x + c))/(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) + 4*a^2*b*e^(2*c) + 5*a*b^2*e^(2*c) + 2*b^3*e^(2*c))*e^(2*d*x)), x)","F",0
100,1,395,0,1.367087," ","integrate(sech(d*x+c)^6/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, a^{3} + 6 \, a^{2} b + {\left(9 \, a^{3} + 40 \, a^{2} b + 40 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(3 \, a^{3} + 14 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\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} + 4 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + 2 \, a b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 27 \, a^{2} b^{4} + 24 \, a b^{5} + 8 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{4} b^{2} + 4 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + 2 \, a b^{5}\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}"," ",0,"-1/16*(3*a^2 + 8*a*b + 8*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)*d) - 1/4*(3*a^3 + 6*a^2*b + (9*a^3 + 40*a^2*b + 40*a*b^2)*e^(-2*d*x - 2*c) + 3*(3*a^3 + 14*a^2*b + 24*a*b^2 + 16*b^3)*e^(-4*d*x - 4*c) + (3*a^3 + 8*a^2*b + 8*a*b^2)*e^(-6*d*x - 6*c))/((a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + 4*(a^4*b^2 + 4*a^3*b^3 + 5*a^2*b^4 + 2*a*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^4*b^2 + 14*a^3*b^3 + 27*a^2*b^4 + 24*a*b^5 + 8*b^6)*e^(-4*d*x - 4*c) + 4*(a^4*b^2 + 4*a^3*b^3 + 5*a^2*b^4 + 2*a*b^5)*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)","B",0
101,0,0,0,0.000000," ","integrate(sech(d*x+c)^7/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, a^{3} e^{\left(7 \, c\right)} + 7 \, a^{2} b e^{\left(7 \, c\right)}\right)} e^{\left(7 \, d x\right)} + {\left(4 \, a^{3} e^{\left(5 \, c\right)} + 31 \, a^{2} b e^{\left(5 \, c\right)} + 36 \, a b^{2} e^{\left(5 \, c\right)}\right)} e^{\left(5 \, d x\right)} - {\left(4 \, a^{3} e^{\left(3 \, c\right)} + 31 \, a^{2} b e^{\left(3 \, c\right)} + 36 \, a b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} - {\left(4 \, a^{3} e^{c} + 7 \, a^{2} b 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)} + 4 \, a^{3} b^{3} d e^{\left(6 \, c\right)} + 5 \, a^{2} b^{4} d e^{\left(6 \, c\right)} + 2 \, a b^{5} 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)} + 14 \, a^{3} b^{3} d e^{\left(4 \, c\right)} + 27 \, a^{2} b^{4} d e^{\left(4 \, c\right)} + 24 \, a b^{5} d e^{\left(4 \, c\right)} + 8 \, b^{6} 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)} + 4 \, a^{3} b^{3} d e^{\left(2 \, c\right)} + 5 \, a^{2} b^{4} d e^{\left(2 \, c\right)} + 2 \, a b^{5} 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)} + 20 \, a^{2} b e^{\left(3 \, c\right)} + 15 \, a b^{2} e^{\left(3 \, c\right)}\right)} e^{\left(3 \, d x\right)} + {\left(8 \, a^{3} e^{c} + 20 \, a^{2} b e^{c} + 15 \, a b^{2} e^{c}\right)} e^{\left(d x\right)}}{512 \, {\left(a^{3} b^{3} + 2 \, a^{2} b^{4} + a b^{5} + {\left(a^{3} b^{3} e^{\left(4 \, c\right)} + 2 \, a^{2} b^{4} e^{\left(4 \, c\right)} + a b^{5} e^{\left(4 \, c\right)}\right)} e^{\left(4 \, d x\right)} + 2 \, {\left(a^{3} b^{3} e^{\left(2 \, c\right)} + 4 \, a^{2} b^{4} e^{\left(2 \, c\right)} + 5 \, a b^{5} e^{\left(2 \, c\right)} + 2 \, b^{6} e^{\left(2 \, c\right)}\right)} e^{\left(2 \, d x\right)}\right)}}\,{d x}"," ",0,"-1/4*((4*a^3*e^(7*c) + 7*a^2*b*e^(7*c))*e^(7*d*x) + (4*a^3*e^(5*c) + 31*a^2*b*e^(5*c) + 36*a*b^2*e^(5*c))*e^(5*d*x) - (4*a^3*e^(3*c) + 31*a^2*b*e^(3*c) + 36*a*b^2*e^(3*c))*e^(3*d*x) - (4*a^3*e^c + 7*a^2*b*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) + 4*a^3*b^3*d*e^(6*c) + 5*a^2*b^4*d*e^(6*c) + 2*a*b^5*d*e^(6*c))*e^(6*d*x) + 2*(3*a^4*b^2*d*e^(4*c) + 14*a^3*b^3*d*e^(4*c) + 27*a^2*b^4*d*e^(4*c) + 24*a*b^5*d*e^(4*c) + 8*b^6*d*e^(4*c))*e^(4*d*x) + 4*(a^4*b^2*d*e^(2*c) + 4*a^3*b^3*d*e^(2*c) + 5*a^2*b^4*d*e^(2*c) + 2*a*b^5*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) + 20*a^2*b*e^(3*c) + 15*a*b^2*e^(3*c))*e^(3*d*x) + (8*a^3*e^c + 20*a^2*b*e^c + 15*a*b^2*e^c)*e^(d*x))/(a^3*b^3 + 2*a^2*b^4 + a*b^5 + (a^3*b^3*e^(4*c) + 2*a^2*b^4*e^(4*c) + a*b^5*e^(4*c))*e^(4*d*x) + 2*(a^3*b^3*e^(2*c) + 4*a^2*b^4*e^(2*c) + 5*a*b^5*e^(2*c) + 2*b^6*e^(2*c))*e^(2*d*x)), x)","F",0
102,1,92,0,0.614736," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c)^4,x, algorithm=""maxima"")","\frac{b \tanh\left(d x + c\right)^{5}}{5 \, d} + \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,"1/5*b*tanh(d*x + c)^5/d + 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
103,1,78,0,0.747439," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c)^3,x, algorithm=""maxima"")","\frac{b \tanh\left(d x + c\right)^{4}}{4 \, d} + 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,"1/4*b*tanh(d*x + c)^4/d + 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)))","A",0
104,1,42,0,0.404751," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c)^2,x, algorithm=""maxima"")","\frac{b \tanh\left(d x + c\right)^{3}}{3 \, d} + 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*tanh(d*x + c)^3/d + a*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1)))","A",0
105,1,27,0,0.331446," ","integrate((a+b*sech(d*x+c)^2)*tanh(d*x+c),x, algorithm=""maxima"")","\frac{b \tanh\left(d x + c\right)^{2}}{2 \, d} + \frac{a \log\left(\cosh\left(d x + c\right)\right)}{d}"," ",0,"1/2*b*tanh(d*x + c)^2/d + a*log(cosh(d*x + c))/d","A",0
106,1,23,0,0.369754," ","integrate(a+b*sech(d*x+c)^2,x, algorithm=""maxima"")","a x + \frac{2 \, b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"a*x + 2*b/(d*(e^(-2*d*x - 2*c) + 1))","A",0
107,1,65,0,0.533633," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c)^2),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}\right)} + \frac{a \log\left(\sinh\left(d x + c\right)\right)}{d}"," ",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) + a*log(sinh(d*x + c))/d","B",0
108,1,47,0,0.336197," ","integrate(coth(d*x+c)^2*(a+b*sech(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)} + \frac{2 \, b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}"," ",0,"a*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + 2*b/(d*(e^(-2*d*x - 2*c) - 1))","B",0
109,1,108,0,0.332866," ","integrate(coth(d*x+c)^3*(a+b*sech(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{2 \, b}{d {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{2}}"," ",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))) - 2*b/(d*(e^(d*x + c) - e^(-d*x - c))^2)","B",0
110,1,170,0,0.344078," ","integrate(coth(d*x+c)^4*(a+b*sech(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)} + \frac{2}{3} \, b {\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)}"," ",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))) + 2/3*b*(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)))","B",0
111,1,251,0,0.512141," ","integrate(coth(d*x+c)^5*(a+b*sech(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)} + 2 \, b {\left(\frac{e^{\left(-2 \, d x - 2 \, 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)}} + \frac{e^{\left(-6 \, d x - 6 \, 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)}"," ",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))) + 2*b*(e^(-2*d*x - 2*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)) + 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",0
112,1,649,0,0.548074," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c)^4,x, algorithm=""maxima"")","\frac{2 \, a b \tanh\left(d x + c\right)^{5}}{5 \, d} + \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)} + \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)}"," ",0,"2/5*a*b*tanh(d*x + c)^5/d + 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))) + 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)))","B",0
113,1,333,0,0.438870," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c)^3,x, algorithm=""maxima"")","\frac{a b \tanh\left(d x + c\right)^{4}}{2 \, d} + 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)} - \frac{4}{3} \, b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, 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)}} - \frac{2 \, e^{\left(-6 \, d x - 6 \, 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)}} + \frac{3 \, e^{\left(-8 \, d x - 8 \, 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)}"," ",0,"1/2*a*b*tanh(d*x + c)^4/d + 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))) - 4/3*b^2*(3*e^(-4*d*x - 4*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*e^(-6*d*x - 6*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*e^(-8*d*x - 8*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)))","B",0
114,1,325,0,0.523614," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c)^2,x, algorithm=""maxima"")","\frac{2 \, a b \tanh\left(d x + c\right)^{3}}{3 \, d} + a^{2} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, 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)}"," ",0,"2/3*a*b*tanh(d*x + c)^3/d + a^2*(x + c/d - 2/(d*(e^(-2*d*x - 2*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)))","B",0
115,1,55,0,0.482004," ","integrate((a+b*sech(d*x+c)^2)^2*tanh(d*x+c),x, algorithm=""maxima"")","\frac{a b \tanh\left(d x + c\right)^{2}}{d} + \frac{a^{2} \log\left(\cosh\left(d x + c\right)\right)}{d} - \frac{4 \, b^{2}}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{4}}"," ",0,"a*b*tanh(d*x + c)^2/d + a^2*log(cosh(d*x + c))/d - 4*b^2/(d*(e^(d*x + c) + e^(-d*x - c))^4)","A",0
116,1,120,0,0.457052," ","integrate((a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} x + \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 \, a b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"a^2*x + 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*a*b/(d*(e^(-2*d*x - 2*c) + 1))","B",0
117,1,161,0,0.698042," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","b^{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{\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)} + 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}\right)} + \frac{a^{2} \log\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"b^2*(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))) + 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) + a^2*log(sinh(d*x + c))/d","B",0
118,1,71,0,0.545150," ","integrate(coth(d*x+c)^2*(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} + \frac{4 \, a b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} + \frac{4 \, b^{2}}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"a^2*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) + 4*a*b/(d*(e^(-2*d*x - 2*c) - 1)) + 4*b^2/(d*(e^(-4*d*x - 4*c) - 1))","A",0
119,1,206,0,0.479573," ","integrate(coth(d*x+c)^3*(a+b*sech(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)} - b^{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{\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 \, a b}{d {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{2}}"," ",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) + 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*a*b/(d*(e^(d*x + c) - e^(-d*x - c))^2)","B",0
120,1,268,0,0.426762," ","integrate(coth(d*x+c)^4*(a+b*sech(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)} + \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 b {\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)}"," ",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))) + 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*b*(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)))","B",0
121,1,282,0,0.448773," ","integrate(coth(d*x+c)^5*(a+b*sech(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)} + 4 \, a b {\left(\frac{e^{\left(-2 \, d x - 2 \, 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)}} + \frac{e^{\left(-6 \, d x - 6 \, 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)} - \frac{4 \, b^{2}}{d {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{4}}"," ",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))) + 4*a*b*(e^(-2*d*x - 2*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)) + 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))) - 4*b^2/(d*(e^(d*x + c) - e^(-d*x - c))^4)","B",0
122,1,613,0,0.542235," ","integrate(coth(d*x+c)^6*(a+b*sech(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{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}{5} \, a b {\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)}"," ",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))) + 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))) + 4/5*a*b*(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)))","B",0
123,1,696,0,0.407599," ","integrate(coth(d*x+c)^7*(a+b*sech(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)} + \frac{4}{3} \, a b {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, 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)}} + \frac{10 \, e^{\left(-6 \, d x - 6 \, 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)}} + \frac{3 \, e^{\left(-10 \, d x - 10 \, 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{4}{3} \, b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, 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)}} + \frac{2 \, e^{\left(-6 \, d x - 6 \, 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)}} + \frac{3 \, e^{\left(-8 \, d x - 8 \, 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)}"," ",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))) + 4/3*a*b*(3*e^(-2*d*x - 2*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)) + 10*e^(-6*d*x - 6*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*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))) + 4/3*b^2*(3*e^(-4*d*x - 4*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*e^(-6*d*x - 6*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*e^(-8*d*x - 8*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)))","B",0
124,1,1453,0,0.385061," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c)^4,x, algorithm=""maxima"")","\frac{3 \, a^{2} b \tanh\left(d x + c\right)^{5}}{5 \, d} + \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)} + \frac{16}{315} \, 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{36 \, 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{126 \, 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{441 \, 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{210 \, 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{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)}"," ",0,"3/5*a^2*b*tanh(d*x + c)^5/d + 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))) + 16/315*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)) + 36*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)) - 126*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)) + 441*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)) + 210*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)) + 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)))","B",0
125,1,652,0,0.462477," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c)^3,x, algorithm=""maxima"")","\frac{3 \, a^{2} b \tanh\left(d x + c\right)^{4}}{4 \, d} + 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)} - 4 \, a b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, 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)}} - \frac{2 \, e^{\left(-6 \, d x - 6 \, 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)}} + \frac{3 \, e^{\left(-8 \, d x - 8 \, 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{32}{3} \, b^{3} {\left(\frac{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{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{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)}}\right)}"," ",0,"3/4*a^2*b*tanh(d*x + c)^4/d + 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))) - 4*a*b^2*(3*e^(-4*d*x - 4*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*e^(-6*d*x - 6*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*e^(-8*d*x - 8*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))) - 32/3*b^3*(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)) - 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)) + 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)))","B",0
126,1,788,0,0.442440," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c)^2,x, algorithm=""maxima"")","\frac{a^{2} b \tanh\left(d x + c\right)^{3}}{d} + a^{3} {\left(x + \frac{c}{d} - \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}\right)} + \frac{16}{105} \, b^{3} {\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{21 \, 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{35 \, 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{70 \, 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{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 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)}"," ",0,"a^2*b*tanh(d*x + c)^3/d + a^3*(x + c/d - 2/(d*(e^(-2*d*x - 2*c) + 1))) + 16/105*b^3*(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)) + 21*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)) - 35*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)) + 70*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)) + 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*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)))","B",0
127,1,85,0,0.431403," ","integrate((a+b*sech(d*x+c)^2)^3*tanh(d*x+c),x, algorithm=""maxima"")","\frac{3 \, a^{2} b \tanh\left(d x + c\right)^{2}}{2 \, d} + \frac{a^{3} \log\left(\cosh\left(d x + c\right)\right)}{d} - \frac{12 \, a b^{2}}{d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{4}} - \frac{32 \, b^{3}}{3 \, d {\left(e^{\left(d x + c\right)} + e^{\left(-d x - c\right)}\right)}^{6}}"," ",0,"3/2*a^2*b*tanh(d*x + c)^2/d + a^3*log(cosh(d*x + c))/d - 12*a*b^2/(d*(e^(d*x + c) + e^(-d*x - c))^4) - 32/3*b^3/(d*(e^(d*x + c) + e^(-d*x - c))^6)","A",0
128,1,332,0,0.410858," ","integrate((a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x + \frac{16}{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{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{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{6 \, a^{2} b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"a^3*x + 16/15*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)) + 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)) + 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))) + 6*a^2*b/(d*(e^(-2*d*x - 2*c) + 1))","B",0
129,1,300,0,0.469136," ","integrate(coth(d*x+c)*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","b^{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{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} + \frac{2 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 4 \, 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(\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)} + 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}\right)} + \frac{a^{3} \log\left(\sinh\left(d x + c\right)\right)}{d}"," ",0,"b^3*(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) + 4*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*(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))) + 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) + a^3*log(sinh(d*x + c))/d","B",0
130,1,172,0,0.413188," ","integrate(coth(d*x+c)^2*(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} {\left(x + \frac{c}{d} + \frac{2}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}}\right)} - \frac{16}{3} \, b^{3} {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}} + \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} + 1\right)}}\right)} + \frac{6 \, a^{2} b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}} + \frac{12 \, a b^{2}}{d {\left(e^{\left(-4 \, d x - 4 \, c\right)} - 1\right)}}"," ",0,"a^3*(x + c/d + 2/(d*(e^(-2*d*x - 2*c) - 1))) - 16/3*b^3*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) + 1)) + 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) - e^(-8*d*x - 8*c) + 1))) + 6*a^2*b/(d*(e^(-2*d*x - 2*c) - 1)) + 12*a*b^2/(d*(e^(-4*d*x - 4*c) - 1))","B",0
131,1,314,0,0.470109," ","integrate(coth(d*x+c)^3*(a+b*sech(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)} - 2 \, b^{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{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{2 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} + e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{d {\left(2 \, e^{\left(-4 \, d x - 4 \, c\right)} - e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} - 3 \, a b^{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{\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{6 \, a^{2} b}{d {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{2}}"," ",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))) - 2*b^3*(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) + e^(-6*d*x - 6*c))/(d*(2*e^(-4*d*x - 4*c) - e^(-8*d*x - 8*c) - 1))) - 3*a*b^2*(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))) - 6*a^2*b/(d*(e^(d*x + c) - e^(-d*x - c))^2)","B",0
132,1,366,0,0.521053," ","integrate(coth(d*x+c)^4*(a+b*sech(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)} + 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{16}{3} \, b^{3} {\left(\frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}} - \frac{1}{d {\left(2 \, e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, e^{\left(-6 \, d x - 6 \, c\right)} + e^{\left(-8 \, d x - 8 \, c\right)} - 1\right)}}\right)} + 2 \, a^{2} b {\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)}"," ",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))) + 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))) + 16/3*b^3*(2*e^(-2*d*x - 2*c)/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1)) - 1/(d*(2*e^(-2*d*x - 2*c) - 2*e^(-6*d*x - 6*c) + e^(-8*d*x - 8*c) - 1))) + 2*a^2*b*(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)))","B",0
133,1,422,0,0.497486," ","integrate(coth(d*x+c)^5*(a+b*sech(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)} + b^{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{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{d} - \frac{2 \, {\left(e^{\left(-2 \, d x - 2 \, c\right)} - 4 \, 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)} + 6 \, a^{2} b {\left(\frac{e^{\left(-2 \, d x - 2 \, 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)}} + \frac{e^{\left(-6 \, d x - 6 \, 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)} - \frac{12 \, a b^{2}}{d {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{4}}"," ",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))) + b^3*(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) - 4*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))) + 6*a^2*b*(e^(-2*d*x - 2*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)) + 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))) - 12*a*b^2/(d*(e^(d*x + c) - e^(-d*x - c))^4)","B",0
134,1,826,0,0.361074," ","integrate(coth(d*x+c)^6*(a+b*sech(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)} + \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{16}{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{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{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{6}{5} \, a^{2} b {\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)}"," ",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))) + 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))) - 16/15*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)) - 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)) - 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))) + 6/5*a^2*b*(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)))","B",0
135,1,727,0,0.419852," ","integrate(coth(d*x+c)^7*(a+b*sech(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)} + 2 \, a^{2} b {\left(\frac{3 \, e^{\left(-2 \, d x - 2 \, 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)}} + \frac{10 \, e^{\left(-6 \, d x - 6 \, 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)}} + \frac{3 \, e^{\left(-10 \, d x - 10 \, 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)} + 4 \, a b^{2} {\left(\frac{3 \, e^{\left(-4 \, d x - 4 \, 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)}} + \frac{2 \, e^{\left(-6 \, d x - 6 \, 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)}} + \frac{3 \, e^{\left(-8 \, d x - 8 \, 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{32 \, b^{3}}{3 \, d {\left(e^{\left(d x + c\right)} - e^{\left(-d x - c\right)}\right)}^{6}}"," ",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))) + 2*a^2*b*(3*e^(-2*d*x - 2*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)) + 10*e^(-6*d*x - 6*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*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))) + 4*a*b^2*(3*e^(-4*d*x - 4*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*e^(-6*d*x - 6*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*e^(-8*d*x - 8*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))) - 32/3*b^3/(d*(e^(d*x + c) - e^(-d*x - c))^6)","B",0
136,1,703,0,0.567435," ","integrate((a+b*sech(d*x+c)^2)^4,x, algorithm=""maxima"")","a^{4} x + \frac{32}{35} \, b^{4} {\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{21 \, 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{35 \, 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{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{64}{15} \, a 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{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{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)} + 8 \, a^{2} 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{8 \, a^{3} b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"a^4*x + 32/35*b^4*(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)) + 21*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)) + 35*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)) + 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))) + 64/15*a*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)) + 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)) + 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))) + 8*a^2*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))) + 8*a^3*b/(d*(e^(-2*d*x - 2*c) + 1))","B",0
137,1,1277,0,0.349475," ","integrate((a+b*sech(d*x+c)^2)^5,x, algorithm=""maxima"")","a^{5} x + \frac{256}{315} \, b^{5} {\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{36 \, 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{84 \, 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{126 \, 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{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{32}{7} \, a b^{4} {\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{21 \, 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{35 \, 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{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{32}{3} \, a^{2} 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{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{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{40}{3} \, a^{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{10 \, a^{4} b}{d {\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}}"," ",0,"a^5*x + 256/315*b^5*(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)) + 36*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)) + 84*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)) + 126*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)) + 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))) + 32/7*a*b^4*(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)) + 21*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)) + 35*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)) + 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))) + 32/3*a^2*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)) + 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)) + 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))) + 40/3*a^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))) + 10*a^4*b/(d*(e^(-2*d*x - 2*c) + 1))","B",0
138,1,131,0,0.459078," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{d x + c}{a 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 + 2 \, b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{b^{2} d} + \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a b^{2} d}"," ",0,"(d*x + c)/(a*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 + 2*b)*log(e^(-2*d*x - 2*c) + 1)/(b^2*d) + 1/2*(a^2 + 2*a*b + b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a*b^2*d)","A",0
139,1,637,0,0.636277," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a + 2 \, b\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} b d} + \frac{{\left(a + 2 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} b d} + \frac{3 \, a \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} b d} + \frac{{\left(a + 2 \, b\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{8 \, a b d} + \frac{\log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, b d} - \frac{{\left(a + 2 \, b\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{8 \, a b d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\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{{\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, \sqrt{{\left(a + b\right)} b} a b d} + \frac{{\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, \sqrt{{\left(a + b\right)} b} a 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 + 2*b)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*b*d) + 1/8*(a + 2*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*b*d) + 3/16*a*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*b*d) + 1/8*(a + 2*b)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a*b*d) + 1/4*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(b*d) - 1/8*(a + 2*b)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a*b*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(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) - 1/32*(a^2 + 8*a*b + 8*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*b*d) + 1/32*(a^2 + 8*a*b + 8*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*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
140,1,77,0,0.473631," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{d x + c}{a d} + \frac{{\left(a + b\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a b d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{b d}"," ",0,"(d*x + c)/(a*d) + 1/2*(a + b)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a*b*d) - log(e^(-2*d*x - 2*c) + 1)/(b*d)","A",0
141,1,291,0,0.497086," ","integrate(tanh(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","-\frac{{\left(a + 2 \, b\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a d} + \frac{\log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a + 2 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} a d} + \frac{\log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a d}"," ",0,"-1/8*(a + 2*b)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) + 1/4*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*d) + 1/8*(a + 2*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) + 1/4*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a*d)","B",0
142,1,51,0,0.377910," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{d x + c}{a d} + \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a d}"," ",0,"(d*x + c)/(a*d) + 1/2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a*d)","B",0
143,1,83,0,0.467338," ","integrate(1/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{2 \, \sqrt{{\left(a + b\right)} b} a d} + \frac{d x + c}{a d}"," ",0,"1/2*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*a*d) + (d*x + c)/(a*d)","B",0
144,1,100,0,0.420940," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{2} + a b\right)} d} + \frac{d x + c}{a d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{{\left(a + b\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{{\left(a + b\right)} d}"," ",0,"1/2*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^2 + a*b)*d) + (d*x + c)/(a*d) + log(e^(-d*x - c) + 1)/((a + b)*d) + log(e^(-d*x - c) - 1)/((a + b)*d)","B",0
145,1,429,0,0.476686," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, {\left(a^{2} + a b\right)} d} - \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, {\left(a^{2} + a b\right)} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{2} + a b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{2} + a b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, \sqrt{{\left(a + b\right)} b} {\left(a + b\right)} d} + \frac{\log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, {\left(a + b\right)} d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, {\left(a + b\right)} d} - \frac{1}{2 \, {\left({\left(a + b\right)} e^{\left(2 \, d x + 2 \, c\right)} - a - b\right)} d} + \frac{3}{2 \, {\left({\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - a - b\right)} d}"," ",0,"1/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^2 + a*b)*d) - 1/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^2 + a*b)*d) - 1/8*(a*b + 2*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + a*b)*sqrt((a + b)*b)*d) + 1/8*(a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + a*b)*sqrt((a + b)*b)*d) - 1/4*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a + b)*d) + 1/2*log(e^(2*d*x + 2*c) - 1)/((a + b)*d) - 1/2*log(e^(-2*d*x - 2*c) - 1)/((a + b)*d) - 1/2/(((a + b)*e^(2*d*x + 2*c) - a - b)*d) + 3/2/(((a + b)*e^(-2*d*x - 2*c) - a - b)*d)","B",0
146,1,187,0,0.435457," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{b^{2} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d} + \frac{{\left(a + 2 \, b\right)} \log\left(e^{\left(-d x - c\right)} + 1\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{{\left(a + 2 \, b\right)} \log\left(e^{\left(-d x - c\right)} - 1\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{d x + c}{a d} + \frac{2 \, e^{\left(-2 \, d x - 2 \, c\right)}}{{\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)} d}"," ",0,"1/2*b^2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^3 + 2*a^2*b + a*b^2)*d) + (a + 2*b)*log(e^(-d*x - c) + 1)/((a^2 + 2*a*b + b^2)*d) + (a + 2*b)*log(e^(-d*x - c) - 1)/((a^2 + 2*a*b + b^2)*d) + (d*x + c)/(a*d) + 2*e^(-2*d*x - 2*c)/((2*(a + b)*e^(-2*d*x - 2*c) - (a + b)*e^(-4*d*x - 4*c) - a - b)*d)","B",0
147,1,1435,0,0.627074," ","integrate(coth(d*x+c)^4/(a+b*sech(d*x+c)^2),x, algorithm=""maxima"")","\frac{3 \, a b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{{\left(2 \, a + 3 \, b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{b \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(2 \, a + 3 \, b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{b \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{{\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, {\left(12 \, a + 13 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 6 \, {\left(9 \, a + 10 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 22 \, a + 25 \, b}{24 \, {\left(a^{2} + 2 \, a b + b^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{3 \, {\left(4 \, a + 5 \, b\right)} e^{\left(4 \, d x + 4 \, c\right)} - 6 \, {\left(2 \, a + 3 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, a + 7 \, b}{6 \, {\left(a^{2} + 2 \, a b + b^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{6 \, {\left(9 \, a + 10 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, {\left(12 \, a + 13 \, b\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 22 \, a - 25 \, b}{24 \, {\left(a^{2} + 2 \, a b + b^{2} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{6 \, {\left(2 \, a + 3 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 3 \, {\left(4 \, a + 5 \, b\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, a - 7 \, b}{6 \, {\left(a^{2} + 2 \, a b + b^{2} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} - \frac{6 \, a e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, b e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, a + b}{4 \, {\left(a^{2} + 2 \, a b + b^{2} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d}"," ",0,"3/16*a*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) + 1/8*(a*b + 2*b^2)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^3 + 2*a^2*b + a*b^2)*d) - 1/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^2 + 2*a*b + b^2)*d) - 1/8*(a*b + 2*b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^3 + 2*a^2*b + a*b^2)*d) + 1/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^2 + 2*a*b + b^2)*d) + 1/4*(2*a + 3*b)*log(e^(2*d*x + 2*c) - 1)/((a^2 + 2*a*b + b^2)*d) + 1/2*b*log(e^(2*d*x + 2*c) - 1)/((a^2 + 2*a*b + b^2)*d) - 1/4*(2*a + 3*b)*log(e^(-2*d*x - 2*c) - 1)/((a^2 + 2*a*b + b^2)*d) - 1/2*b*log(e^(-2*d*x - 2*c) - 1)/((a^2 + 2*a*b + b^2)*d) - 1/32*(a^2*b + 8*a*b^2 + 8*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 2*a^2*b + a*b^2)*sqrt((a + b)*b)*d) + 1/8*(a*b + 2*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) + 1/32*(a^2*b + 8*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 2*a^2*b + a*b^2)*sqrt((a + b)*b)*d) - 1/8*(a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) + 1/24*(3*(12*a + 13*b)*e^(4*d*x + 4*c) - 6*(9*a + 10*b)*e^(2*d*x + 2*c) + 22*a + 25*b)/((a^2 + 2*a*b + b^2 - (a^2 + 2*a*b + b^2)*e^(6*d*x + 6*c) + 3*(a^2 + 2*a*b + b^2)*e^(4*d*x + 4*c) - 3*(a^2 + 2*a*b + b^2)*e^(2*d*x + 2*c))*d) + 1/6*(3*(4*a + 5*b)*e^(4*d*x + 4*c) - 6*(2*a + 3*b)*e^(2*d*x + 2*c) + 4*a + 7*b)/((a^2 + 2*a*b + b^2 - (a^2 + 2*a*b + b^2)*e^(6*d*x + 6*c) + 3*(a^2 + 2*a*b + b^2)*e^(4*d*x + 4*c) - 3*(a^2 + 2*a*b + b^2)*e^(2*d*x + 2*c))*d) + 1/24*(6*(9*a + 10*b)*e^(-2*d*x - 2*c) - 3*(12*a + 13*b)*e^(-4*d*x - 4*c) - 22*a - 25*b)/((a^2 + 2*a*b + b^2 - 3*(a^2 + 2*a*b + b^2)*e^(-2*d*x - 2*c) + 3*(a^2 + 2*a*b + b^2)*e^(-4*d*x - 4*c) - (a^2 + 2*a*b + b^2)*e^(-6*d*x - 6*c))*d) + 1/6*(6*(2*a + 3*b)*e^(-2*d*x - 2*c) - 3*(4*a + 5*b)*e^(-4*d*x - 4*c) - 4*a - 7*b)/((a^2 + 2*a*b + b^2 - 3*(a^2 + 2*a*b + b^2)*e^(-2*d*x - 2*c) + 3*(a^2 + 2*a*b + b^2)*e^(-4*d*x - 4*c) - (a^2 + 2*a*b + b^2)*e^(-6*d*x - 6*c))*d) - 1/4*(6*a*e^(-2*d*x - 2*c) + 3*b*e^(-4*d*x - 4*c) - 2*a + b)/((a^2 + 2*a*b + b^2 - 3*(a^2 + 2*a*b + b^2)*e^(-2*d*x - 2*c) + 3*(a^2 + 2*a*b + b^2)*e^(-4*d*x - 4*c) - (a^2 + 2*a*b + b^2)*e^(-6*d*x - 6*c))*d)","B",0
148,1,154,0,0.446372," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{3} b e^{\left(-4 \, d x - 4 \, c\right)} + a^{3} b + 2 \, {\left(a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}\right)} d} + \frac{d x + c}{a^{2} d} + \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} + 1\right)}{b^{2} d} - \frac{{\left(a^{2} - b^{2}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{2} b^{2} d}"," ",0,"2*(a^2 + 2*a*b + b^2)*e^(-2*d*x - 2*c)/((a^3*b*e^(-4*d*x - 4*c) + a^3*b + 2*(a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c))*d) + (d*x + c)/(a^2*d) + log(e^(-2*d*x - 2*c) + 1)/(b^2*d) - 1/2*(a^2 - b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*b^2*d)","B",0
149,1,1053,0,0.836732," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a^{3} - 6 \, a^{2} b - 24 \, a b^{2} - 16 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{a \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} {\left(a b + b^{2}\right)} d} - \frac{{\left(a^{3} - 6 \, a^{2} b - 24 \, a b^{2} - 16 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, {\left(a + 2 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, \sqrt{{\left(a + b\right)} b} {\left(a b + b^{2}\right)} d} - \frac{a \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, \sqrt{{\left(a + b\right)} b} {\left(a b + b^{2}\right)} d} + \frac{a^{3} + 8 \, a^{2} b + 8 \, a b^{2} + {\left(a^{3} + 18 \, a^{2} b + 48 \, a b^{2} + 32 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{4} b + a^{3} b^{2} + {\left(a^{4} b + a^{3} b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{3} + 8 \, a^{2} b + 8 \, a b^{2} + {\left(a^{3} + 18 \, a^{2} b + 48 \, a b^{2} + 32 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{16 \, {\left(a^{4} b + a^{3} b^{2} + 2 \, {\left(a^{4} b + 3 \, a^{3} b^{2} + 2 \, a^{2} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} b + a^{3} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{a^{2} + 2 \, a b + {\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{3} b + a^{2} b^{2} + {\left(a^{3} b + a^{2} b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{2} + 2 \, a b + {\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{3} b + a^{2} b^{2} + 2 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} b + a^{2} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{3 \, {\left({\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a\right)}}{8 \, {\left(a^{2} b + a b^{2} + 2 \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\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(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{2} d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{2} d}"," ",0,"1/64*(a^3 - 6*a^2*b - 24*a*b^2 - 16*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3*b + a^2*b^2)*sqrt((a + b)*b)*d) + 1/16*a*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a*b + b^2)*d) - 1/64*(a^3 - 6*a^2*b - 24*a*b^2 - 16*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3*b + a^2*b^2)*sqrt((a + b)*b)*d) - 3/32*(a + 2*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a*b + b^2)*d) - 1/16*a*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a*b + b^2)*d) + 1/16*(a^3 + 8*a^2*b + 8*a*b^2 + (a^3 + 18*a^2*b + 48*a*b^2 + 32*b^3)*e^(2*d*x + 2*c))/((a^4*b + a^3*b^2 + (a^4*b + a^3*b^2)*e^(4*d*x + 4*c) + 2*(a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*e^(2*d*x + 2*c))*d) - 1/16*(a^3 + 8*a^2*b + 8*a*b^2 + (a^3 + 18*a^2*b + 48*a*b^2 + 32*b^3)*e^(-2*d*x - 2*c))/((a^4*b + a^3*b^2 + 2*(a^4*b + 3*a^3*b^2 + 2*a^2*b^3)*e^(-2*d*x - 2*c) + (a^4*b + a^3*b^2)*e^(-4*d*x - 4*c))*d) + 1/4*(a^2 + 2*a*b + (a^2 + 8*a*b + 8*b^2)*e^(2*d*x + 2*c))/((a^3*b + a^2*b^2 + (a^3*b + a^2*b^2)*e^(4*d*x + 4*c) + 2*(a^3*b + 3*a^2*b^2 + 2*a*b^3)*e^(2*d*x + 2*c))*d) - 1/4*(a^2 + 2*a*b + (a^2 + 8*a*b + 8*b^2)*e^(-2*d*x - 2*c))/((a^3*b + a^2*b^2 + 2*(a^3*b + 3*a^2*b^2 + 2*a*b^3)*e^(-2*d*x - 2*c) + (a^3*b + a^2*b^2)*e^(-4*d*x - 4*c))*d) - 3/8*((a + 2*b)*e^(-2*d*x - 2*c) + a)/((a^2*b + a*b^2 + 2*(a^2*b + 3*a*b^2 + 2*b^3)*e^(-2*d*x - 2*c) + (a^2*b + a*b^2)*e^(-4*d*x - 4*c))*d) + 1/4*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^2*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d)","B",0
150,1,108,0,0.375331," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a + b\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{3} e^{\left(-4 \, d x - 4 \, c\right)} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} e^{\left(-2 \, d x - 2 \, c\right)}\right)} d} + \frac{d x + c}{a^{2} d} + \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{2} d}"," ",0,"2*(a + b)*e^(-2*d*x - 2*c)/((a^3*e^(-4*d*x - 4*c) + a^3 + 2*(a^3 + 2*a^2*b)*e^(-2*d*x - 2*c))*d) + (d*x + c)/(a^2*d) + 1/2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d)","B",0
151,1,597,0,0.546793," ","integrate(tanh(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} + 6 \, a b + 4 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a^{2} + 6 \, a b + 4 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{a^{2} + 2 \, a b + {\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\left(a^{4} + a^{3} b + {\left(a^{4} + a^{3} b\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{2} + 2 \, a b + {\left(a^{2} + 8 \, a b + 8 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} - \frac{{\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a}{2 \, {\left(a^{3} + a^{2} b + 2 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{3} + a^{2} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{\log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, \sqrt{{\left(a + b\right)} b} {\left(a + b\right)} d} + \frac{\log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{2} d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{2} d}"," ",0,"-1/16*(a^2 + 6*a*b + 4*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)*d) + 1/16*(a^2 + 6*a*b + 4*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)*d) + 1/4*(a^2 + 2*a*b + (a^2 + 8*a*b + 8*b^2)*e^(2*d*x + 2*c))/((a^4 + a^3*b + (a^4 + a^3*b)*e^(4*d*x + 4*c) + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(2*d*x + 2*c))*d) - 1/4*(a^2 + 2*a*b + (a^2 + 8*a*b + 8*b^2)*e^(-2*d*x - 2*c))/((a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c) + (a^4 + a^3*b)*e^(-4*d*x - 4*c))*d) - 1/2*((a + 2*b)*e^(-2*d*x - 2*c) + a)/((a^3 + a^2*b + 2*(a^3 + 3*a^2*b + 2*a*b^2)*e^(-2*d*x - 2*c) + (a^3 + a^2*b)*e^(-4*d*x - 4*c))*d) + 1/8*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/(sqrt((a + b)*b)*(a + b)*d) + 1/4*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^2*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d)","B",0
152,1,106,0,0.423069," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, b e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{3} e^{\left(-4 \, d x - 4 \, c\right)} + a^{3} + 2 \, {\left(a^{3} + 2 \, a^{2} b\right)} e^{\left(-2 \, d x - 2 \, c\right)}\right)} d} + \frac{d x + c}{a^{2} d} + \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{2} d}"," ",0,"2*b*e^(-2*d*x - 2*c)/((a^3*e^(-4*d*x - 4*c) + a^3 + 2*(a^3 + 2*a^2*b)*e^(-2*d*x - 2*c))*d) + (d*x + c)/(a^2*d) + 1/2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^2*d)","B",0
153,1,187,0,0.693835," ","integrate(1/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a b + 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{4 \, {\left(a^{3} + a^{2} b\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{a b + {\left(a b + 2 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{d x + c}{a^{2} d}"," ",0,"1/4*(3*a*b + 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + a^2*b)*sqrt((a + b)*b)*d) - (a*b + (a*b + 2*b^2)*e^(-2*d*x - 2*c))/((a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c) + (a^4 + a^3*b)*e^(-4*d*x - 4*c))*d) + (d*x + c)/(a^2*d)","B",0
154,1,209,0,0.350996," ","integrate(coth(d*x+c)/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} e^{\left(-2 \, d x - 2 \, c\right)}}{{\left(a^{4} + a^{3} b + 2 \, {\left(a^{4} + 3 \, a^{3} b + 2 \, a^{2} b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{4} + a^{3} b\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)} d} + \frac{{\left(2 \, a b + b^{2}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{{\left(a^{2} + 2 \, a b + b^{2}\right)} d} + \frac{d x + c}{a^{2} d}"," ",0,"2*b^2*e^(-2*d*x - 2*c)/((a^4 + a^3*b + 2*(a^4 + 3*a^3*b + 2*a^2*b^2)*e^(-2*d*x - 2*c) + (a^4 + a^3*b)*e^(-4*d*x - 4*c))*d) + 1/2*(2*a*b + b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^4 + 2*a^3*b + a^2*b^2)*d) + log(e^(-d*x - c) + 1)/((a^2 + 2*a*b + b^2)*d) + log(e^(-d*x - c) - 1)/((a^2 + 2*a*b + b^2)*d) + (d*x + c)/(a^2*d)","B",0
155,1,1070,0,0.917381," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(2 \, a b + b^{2}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\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 + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d} - \frac{{\left(3 \, a^{2} b + 10 \, a b^{2} + 4 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a^{2} b + 10 \, a b^{2} + 4 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{2 \, a^{3} + a^{2} b + 2 \, a b^{2} + {\left(2 \, a^{3} - a^{2} b - 8 \, a b^{2} - 8 \, b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + 4 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{4 \, {\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(6 \, d x + 6 \, c\right)} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{2 \, a^{3} + a^{2} b + 2 \, a b^{2} + 2 \, {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + 4 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a^{3} - a^{2} b - 8 \, a b^{2} - 8 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)}}{4 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{5} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} - \frac{2 \, a^{2} - a b + 2 \, {\left(2 \, a^{2} + 4 \, a b - b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(2 \, a^{2} + a b + 2 \, 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} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{4} + 6 \, a^{3} b + 9 \, a^{2} b^{2} + 4 \, a b^{3}\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{\log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d}"," ",0,"1/4*(2*a*b + b^2)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^4 + 2*a^3*b + a^2*b^2)*d) - 1/4*(2*a*b + b^2)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^4 + 2*a^3*b + a^2*b^2)*d) - 1/16*(3*a^2*b + 10*a*b^2 + 4*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt((a + b)*b)*d) + 1/16*(3*a^2*b + 10*a*b^2 + 4*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + 2*a^3*b + a^2*b^2)*sqrt((a + b)*b)*d) - 3/8*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) + 1/4*(2*a^3 + a^2*b + 2*a*b^2 + (2*a^3 - a^2*b - 8*a*b^2 - 8*b^3)*e^(4*d*x + 4*c) + 2*(2*a^3 + 4*a^2*b + 3*a*b^2 + 4*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^(6*d*x + 6*c) - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*e^(4*d*x + 4*c) + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*e^(2*d*x + 2*c))*d) - 1/4*(2*a^3 + a^2*b + 2*a*b^2 + 2*(2*a^3 + 4*a^2*b + 3*a*b^2 + 4*b^3)*e^(-2*d*x - 2*c) + (2*a^3 - a^2*b - 8*a*b^2 - 8*b^3)*e^(-4*d*x - 4*c))/((a^5 + 2*a^4*b + a^3*b^2 + (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*e^(-2*d*x - 2*c) - (a^5 + 6*a^4*b + 9*a^3*b^2 + 4*a^2*b^3)*e^(-4*d*x - 4*c) - (a^5 + 2*a^4*b + a^3*b^2)*e^(-6*d*x - 6*c))*d) - 1/2*(2*a^2 - a*b + 2*(2*a^2 + 4*a*b - b^2)*e^(-2*d*x - 2*c) + (2*a^2 + a*b + 2*b^2)*e^(-4*d*x - 4*c))/((a^4 + 2*a^3*b + a^2*b^2 + (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*e^(-2*d*x - 2*c) - (a^4 + 6*a^3*b + 9*a^2*b^2 + 4*a*b^3)*e^(-4*d*x - 4*c) - (a^4 + 2*a^3*b + a^2*b^2)*e^(-6*d*x - 6*c))*d) + 1/2*log(e^(2*d*x + 2*c) - 1)/((a^2 + 2*a*b + b^2)*d) - 1/2*log(e^(-2*d*x - 2*c) - 1)/((a^2 + 2*a*b + b^2)*d)","B",0
156,1,384,0,0.472768," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a b^{2} + b^{3}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d} + \frac{{\left(a + 3 \, b\right)} \log\left(e^{\left(-d x - c\right)} + 1\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(a + 3 \, b\right)} \log\left(e^{\left(-d x - c\right)} - 1\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{2 \, {\left({\left(a^{3} - b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{3} + 2 \, a^{2} b + b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} - b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2} + 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} + 6 \, a^{4} b + 9 \, a^{3} b^{2} + 4 \, 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} + 2 \, a^{4} b + a^{3} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{d x + c}{a^{2} d}"," ",0,"1/2*(3*a*b^2 + b^3)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d) + (a + 3*b)*log(e^(-d*x - c) + 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + (a + 3*b)*log(e^(-d*x - c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 2*((a^3 - b^3)*e^(-2*d*x - 2*c) + 2*(a^3 + 2*a^2*b + b^3)*e^(-4*d*x - 4*c) + (a^3 - b^3)*e^(-6*d*x - 6*c))/((a^5 + 2*a^4*b + a^3*b^2 + 4*(a^4*b + 2*a^3*b^2 + a^2*b^3)*e^(-2*d*x - 2*c) - 2*(a^5 + 6*a^4*b + 9*a^3*b^2 + 4*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 + 2*a^4*b + a^3*b^2)*e^(-8*d*x - 8*c))*d) + (d*x + c)/(a^2*d)","B",0
157,1,2961,0,1.413979," ","integrate(coth(d*x+c)^4/(a+b*sech(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d} - \frac{b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{{\left(a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d} + \frac{b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{{\left(a + 2 \, b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{b \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{{\left(a + 2 \, b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{b \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{{\left(3 \, a^{3} b + 38 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a b + 8 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a^{3} b + 38 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(3 \, a b + 8 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{44 \, a^{4} + 59 \, a^{3} b + 24 \, a^{2} b^{2} + 24 \, a b^{3} + 3 \, {\left(24 \, a^{4} + 27 \, a^{3} b - 18 \, a^{2} b^{2} - 48 \, a b^{3} - 32 \, b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 6 \, {\left(6 \, a^{4} + 55 \, a^{3} b + 79 \, a^{2} b^{2} + 68 \, a b^{3} + 48 \, b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(50 \, a^{4} + 278 \, a^{3} b + 309 \, a^{2} b^{2} + 180 \, a b^{3} + 144 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(10 \, a^{4} - 75 \, a^{3} b - 103 \, a^{2} b^{2} - 36 \, a b^{3} - 48 \, 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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{44 \, a^{4} + 59 \, a^{3} b + 24 \, a^{2} b^{2} + 24 \, a b^{3} - 2 \, {\left(10 \, a^{4} - 75 \, a^{3} b - 103 \, a^{2} b^{2} - 36 \, a b^{3} - 48 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(50 \, a^{4} + 278 \, a^{3} b + 309 \, a^{2} b^{2} + 180 \, a b^{3} + 144 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 6 \, {\left(6 \, a^{4} + 55 \, a^{3} b + 79 \, a^{2} b^{2} + 68 \, a b^{3} + 48 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(24 \, a^{4} + 27 \, a^{3} b - 18 \, a^{2} b^{2} - 48 \, a b^{3} - 32 \, 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} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{6} + 9 \, a^{5} b + 21 \, a^{4} b^{2} + 19 \, a^{3} b^{3} + 6 \, a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} - a^{5} b - 9 \, a^{4} b^{2} - 11 \, a^{3} b^{3} - 4 \, a^{2} b^{4}\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} + 17 \, a^{2} b - 6 \, a b^{2} + 3 \, {\left(8 \, a^{3} + 13 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 6 \, {\left(4 \, a^{3} + 19 \, a^{2} b + 13 \, a b^{2} - 12 \, b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(8 \, a^{3} + 68 \, a^{2} b + 69 \, a b^{2} - 36 \, b^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(4 \, a^{3} - 15 \, a^{2} b - 37 \, a b^{2} + 12 \, b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{12 \, {\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(10 \, d x + 10 \, c\right)} + {\left(a^{5} - a^{4} b - 9 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 4 \, a b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(a^{5} + 9 \, a^{4} b + 21 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 6 \, a b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(a^{5} + 9 \, a^{4} b + 21 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 6 \, a b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(a^{5} - a^{4} b - 9 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 4 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{8 \, a^{3} + 17 \, a^{2} b - 6 \, a b^{2} - 2 \, {\left(4 \, a^{3} - 15 \, a^{2} b - 37 \, a b^{2} + 12 \, b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(8 \, a^{3} + 68 \, a^{2} b + 69 \, a b^{2} - 36 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 6 \, {\left(4 \, a^{3} + 19 \, a^{2} b + 13 \, a b^{2} - 12 \, b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(8 \, a^{3} + 13 \, a^{2} b + 8 \, a b^{2} + 8 \, b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{12 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} - {\left(a^{5} - a^{4} b - 9 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 4 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{5} + 9 \, a^{4} b + 21 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 6 \, a b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{5} + 9 \, a^{4} b + 21 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 6 \, a b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} - a^{4} b - 9 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 4 \, a b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{4 \, a^{2} - 11 \, a b - 2 \, {\left(2 \, a^{2} - 9 \, a b + 19 \, b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(10 \, a^{2} + 22 \, a b - 33 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 6 \, {\left(2 \, a^{2} + 3 \, a b + 11 \, b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - 3 \, {\left(3 \, a b - 2 \, b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{8 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} - {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(a^{4} + 9 \, a^{3} b + 21 \, a^{2} b^{2} + 19 \, a b^{3} + 6 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{4} - a^{3} b - 9 \, a^{2} b^{2} - 11 \, a b^{3} - 4 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d}"," ",0,"1/4*(a^2*b + 3*a*b^2 + b^3)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d) - 1/2*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/4*(a^2*b + 3*a*b^2 + b^3)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d) + 1/2*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + 1/2*(a + 2*b)*log(e^(2*d*x + 2*c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + b*log(e^(2*d*x + 2*c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/2*(a + 2*b)*log(e^(-2*d*x - 2*c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - b*log(e^(-2*d*x - 2*c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/64*(3*a^3*b + 38*a^2*b^2 + 56*a*b^3 + 16*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sqrt((a + b)*b)*d) + 1/16*(3*a*b + 8*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)*d) + 1/64*(3*a^3*b + 38*a^2*b^2 + 56*a*b^3 + 16*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sqrt((a + b)*b)*d) - 1/16*(3*a*b + 8*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)*d) + 3/32*(3*a*b - 2*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)*d) + 1/48*(44*a^4 + 59*a^3*b + 24*a^2*b^2 + 24*a*b^3 + 3*(24*a^4 + 27*a^3*b - 18*a^2*b^2 - 48*a*b^3 - 32*b^4)*e^(8*d*x + 8*c) + 6*(6*a^4 + 55*a^3*b + 79*a^2*b^2 + 68*a*b^3 + 48*b^4)*e^(6*d*x + 6*c) - 2*(50*a^4 + 278*a^3*b + 309*a^2*b^2 + 180*a*b^3 + 144*b^4)*e^(4*d*x + 4*c) - 2*(10*a^4 - 75*a^3*b - 103*a^2*b^2 - 36*a*b^3 - 48*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*e^(8*d*x + 8*c) + 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*e^(6*d*x + 6*c) - 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*e^(4*d*x + 4*c) - (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*e^(2*d*x + 2*c))*d) - 1/48*(44*a^4 + 59*a^3*b + 24*a^2*b^2 + 24*a*b^3 - 2*(10*a^4 - 75*a^3*b - 103*a^2*b^2 - 36*a*b^3 - 48*b^4)*e^(-2*d*x - 2*c) - 2*(50*a^4 + 278*a^3*b + 309*a^2*b^2 + 180*a*b^3 + 144*b^4)*e^(-4*d*x - 4*c) + 6*(6*a^4 + 55*a^3*b + 79*a^2*b^2 + 68*a*b^3 + 48*b^4)*e^(-6*d*x - 6*c) + 3*(24*a^4 + 27*a^3*b - 18*a^2*b^2 - 48*a*b^3 - 32*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 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*e^(-2*d*x - 2*c) - 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*e^(-4*d*x - 4*c) + 2*(a^6 + 9*a^5*b + 21*a^4*b^2 + 19*a^3*b^3 + 6*a^2*b^4)*e^(-6*d*x - 6*c) + (a^6 - a^5*b - 9*a^4*b^2 - 11*a^3*b^3 - 4*a^2*b^4)*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 + 17*a^2*b - 6*a*b^2 + 3*(8*a^3 + 13*a^2*b + 8*a*b^2 + 8*b^3)*e^(8*d*x + 8*c) + 6*(4*a^3 + 19*a^2*b + 13*a*b^2 - 12*b^3)*e^(6*d*x + 6*c) - 2*(8*a^3 + 68*a^2*b + 69*a*b^2 - 36*b^3)*e^(4*d*x + 4*c) - 2*(4*a^3 - 15*a^2*b - 37*a*b^2 + 12*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^(10*d*x + 10*c) + (a^5 - a^4*b - 9*a^3*b^2 - 11*a^2*b^3 - 4*a*b^4)*e^(8*d*x + 8*c) + 2*(a^5 + 9*a^4*b + 21*a^3*b^2 + 19*a^2*b^3 + 6*a*b^4)*e^(6*d*x + 6*c) - 2*(a^5 + 9*a^4*b + 21*a^3*b^2 + 19*a^2*b^3 + 6*a*b^4)*e^(4*d*x + 4*c) - (a^5 - a^4*b - 9*a^3*b^2 - 11*a^2*b^3 - 4*a*b^4)*e^(2*d*x + 2*c))*d) - 1/12*(8*a^3 + 17*a^2*b - 6*a*b^2 - 2*(4*a^3 - 15*a^2*b - 37*a*b^2 + 12*b^3)*e^(-2*d*x - 2*c) - 2*(8*a^3 + 68*a^2*b + 69*a*b^2 - 36*b^3)*e^(-4*d*x - 4*c) + 6*(4*a^3 + 19*a^2*b + 13*a*b^2 - 12*b^3)*e^(-6*d*x - 6*c) + 3*(8*a^3 + 13*a^2*b + 8*a*b^2 + 8*b^3)*e^(-8*d*x - 8*c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 - (a^5 - a^4*b - 9*a^3*b^2 - 11*a^2*b^3 - 4*a*b^4)*e^(-2*d*x - 2*c) - 2*(a^5 + 9*a^4*b + 21*a^3*b^2 + 19*a^2*b^3 + 6*a*b^4)*e^(-4*d*x - 4*c) + 2*(a^5 + 9*a^4*b + 21*a^3*b^2 + 19*a^2*b^3 + 6*a*b^4)*e^(-6*d*x - 6*c) + (a^5 - a^4*b - 9*a^3*b^2 - 11*a^2*b^3 - 4*a*b^4)*e^(-8*d*x - 8*c) - (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*e^(-10*d*x - 10*c))*d) + 1/8*(4*a^2 - 11*a*b - 2*(2*a^2 - 9*a*b + 19*b^2)*e^(-2*d*x - 2*c) - 2*(10*a^2 + 22*a*b - 33*b^2)*e^(-4*d*x - 4*c) - 6*(2*a^2 + 3*a*b + 11*b^2)*e^(-6*d*x - 6*c) - 3*(3*a*b - 2*b^2)*e^(-8*d*x - 8*c))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 - (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*e^(-2*d*x - 2*c) - 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*e^(-4*d*x - 4*c) + 2*(a^4 + 9*a^3*b + 21*a^2*b^2 + 19*a*b^3 + 6*b^4)*e^(-6*d*x - 6*c) + (a^4 - a^3*b - 9*a^2*b^2 - 11*a*b^3 - 4*b^4)*e^(-8*d*x - 8*c) - (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*e^(-10*d*x - 10*c))*d)","B",0
158,1,3239,0,1.992707," ","integrate(tanh(d*x+c)^6/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{45 \, {\left(a + 2 \, b\right)} a \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{1024 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{9 \, a^{2} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{512 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{45 \, {\left(a + 2 \, b\right)} a \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{1024 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{9 \, a^{2} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{512 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(3 \, a^{5} - 10 \, a^{4} b + 80 \, a^{3} b^{2} + 480 \, a^{2} b^{3} + 640 \, a b^{4} + 256 \, b^{5}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{1024 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a^{5} - 10 \, a^{4} b + 80 \, a^{3} b^{2} + 480 \, a^{2} b^{3} + 640 \, a b^{4} + 256 \, b^{5}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{1024 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{5 \, {\left(3 \, a^{2} + 8 \, a b + 8 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, a^{6} - 12 \, a^{5} b - 204 \, a^{4} b^{2} - 384 \, a^{3} b^{3} - 192 \, a^{2} b^{4} + {\left(3 \, a^{6} - 10 \, a^{5} b - 560 \, a^{4} b^{2} - 2080 \, a^{3} b^{3} - 2560 \, a^{2} b^{4} - 1024 \, a b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(9 \, a^{6} - 12 \, a^{5} b - 1100 \, a^{4} b^{2} - 5248 \, a^{3} b^{3} - 10304 \, a^{2} b^{4} - 9216 \, a b^{5} - 3072 \, b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(9 \, a^{6} - 14 \, a^{5} b - 864 \, a^{4} b^{2} - 3136 \, a^{3} b^{3} - 3840 \, a^{2} b^{4} - 1536 \, a b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{256 \, {\left(a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} + {\left(a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{7} b^{2} + 4 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + 2 \, a^{4} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{7} b^{2} + 14 \, a^{6} b^{3} + 27 \, a^{5} b^{4} + 24 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{7} b^{2} + 4 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + 2 \, a^{4} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{3 \, a^{6} - 12 \, a^{5} b - 204 \, a^{4} b^{2} - 384 \, a^{3} b^{3} - 192 \, a^{2} b^{4} + {\left(9 \, a^{6} - 14 \, a^{5} b - 864 \, a^{4} b^{2} - 3136 \, a^{3} b^{3} - 3840 \, a^{2} b^{4} - 1536 \, a b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(9 \, a^{6} - 12 \, a^{5} b - 1100 \, a^{4} b^{2} - 5248 \, a^{3} b^{3} - 10304 \, a^{2} b^{4} - 9216 \, a b^{5} - 3072 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{6} - 10 \, a^{5} b - 560 \, a^{4} b^{2} - 2080 \, a^{3} b^{3} - 2560 \, a^{2} b^{4} - 1024 \, a b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{256 \, {\left(a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4} + 4 \, {\left(a^{7} b^{2} + 4 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + 2 \, a^{4} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} b^{2} + 14 \, a^{6} b^{3} + 27 \, a^{5} b^{4} + 24 \, a^{4} b^{5} + 8 \, a^{3} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} b^{2} + 4 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + 2 \, a^{4} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} b^{2} + 2 \, a^{6} b^{3} + a^{5} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{3 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 24 \, a^{3} b^{2} - 16 \, a^{2} b^{3} + {\left(3 \, a^{5} - 128 \, a^{3} b^{2} - 256 \, a^{2} b^{3} - 128 \, a b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(9 \, a^{5} + 18 \, a^{4} b - 128 \, a^{3} b^{2} - 512 \, a^{2} b^{3} - 640 \, a b^{4} - 256 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(9 \, a^{5} + 16 \, a^{4} b - 112 \, a^{3} b^{2} - 256 \, a^{2} b^{3} - 128 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{128 \, {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} + a^{4} b^{4} + {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} + a^{4} b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{6} b^{2} + 14 \, a^{5} b^{3} + 27 \, a^{4} b^{4} + 24 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{3 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 24 \, a^{3} b^{2} - 16 \, a^{2} b^{3} + {\left(9 \, a^{5} + 16 \, a^{4} b - 112 \, a^{3} b^{2} - 256 \, a^{2} b^{3} - 128 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(9 \, a^{5} + 18 \, a^{4} b - 128 \, a^{3} b^{2} - 512 \, a^{2} b^{3} - 640 \, a b^{4} - 256 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{5} - 128 \, a^{3} b^{2} - 256 \, a^{2} b^{3} - 128 \, a b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{128 \, {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} + a^{4} b^{4} + 4 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} b^{2} + 14 \, a^{5} b^{3} + 27 \, a^{4} b^{4} + 24 \, a^{3} b^{5} + 8 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} b^{2} + 4 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + 2 \, a^{3} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} b^{2} + 2 \, a^{5} b^{3} + a^{4} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{15 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(9 \, a^{4} + 36 \, a^{3} b + 100 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(9 \, a^{4} + 34 \, a^{3} b + 48 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}{256 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{5} b^{2} + 4 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + 2 \, a^{2} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 27 \, a^{3} b^{4} + 24 \, a^{2} b^{5} + 8 \, a b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{5} b^{2} + 4 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + 2 \, a^{2} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} + \frac{15 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 4 \, a^{2} b^{2} + {\left(9 \, a^{4} + 34 \, a^{3} b + 48 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(9 \, a^{4} + 36 \, a^{3} b + 100 \, a^{2} b^{2} + 128 \, a b^{3} + 64 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 3 \, {\left(a^{4} + 2 \, a^{3} b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{256 \, {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4} + 4 \, {\left(a^{5} b^{2} + 4 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + 2 \, a^{2} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} b^{2} + 14 \, a^{4} b^{3} + 27 \, a^{3} b^{4} + 24 \, a^{2} b^{5} + 8 \, a b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} b^{2} + 4 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + 2 \, a^{2} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} b^{2} + 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{5 \, {\left(3 \, a^{3} + 6 \, a^{2} b + {\left(9 \, a^{3} + 40 \, a^{2} b + 40 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(3 \, a^{3} + 14 \, a^{2} b + 24 \, a b^{2} + 16 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{3} + 8 \, a^{2} b + 8 \, a b^{2}\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} + 4 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + 2 \, a b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 27 \, a^{2} b^{4} + 24 \, a b^{5} + 8 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{4} b^{2} + 4 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + 2 \, a b^{5}\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(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{3} d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{3} d}"," ",0,"-45/1024*(a + 2*b)*a*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)*d) - 9/512*a^2*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)*d) + 45/1024*(a + 2*b)*a*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)*d) + 9/512*a^2*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)*d) - 1/1024*(3*a^5 - 10*a^4*b + 80*a^3*b^2 + 480*a^2*b^3 + 640*a*b^4 + 256*b^5)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5*b^2 + 2*a^4*b^3 + a^3*b^4)*sqrt((a + b)*b)*d) + 1/1024*(3*a^5 - 10*a^4*b + 80*a^3*b^2 + 480*a^2*b^3 + 640*a*b^4 + 256*b^5)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5*b^2 + 2*a^4*b^3 + a^3*b^4)*sqrt((a + b)*b)*d) + 5/256*(3*a^2 + 8*a*b + 8*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b^2 + 2*a*b^3 + b^4)*sqrt((a + b)*b)*d) - 1/256*(3*a^6 - 12*a^5*b - 204*a^4*b^2 - 384*a^3*b^3 - 192*a^2*b^4 + (3*a^6 - 10*a^5*b - 560*a^4*b^2 - 2080*a^3*b^3 - 2560*a^2*b^4 - 1024*a*b^5)*e^(6*d*x + 6*c) + (9*a^6 - 12*a^5*b - 1100*a^4*b^2 - 5248*a^3*b^3 - 10304*a^2*b^4 - 9216*a*b^5 - 3072*b^6)*e^(4*d*x + 4*c) + (9*a^6 - 14*a^5*b - 864*a^4*b^2 - 3136*a^3*b^3 - 3840*a^2*b^4 - 1536*a*b^5)*e^(2*d*x + 2*c))/((a^7*b^2 + 2*a^6*b^3 + a^5*b^4 + (a^7*b^2 + 2*a^6*b^3 + a^5*b^4)*e^(8*d*x + 8*c) + 4*(a^7*b^2 + 4*a^6*b^3 + 5*a^5*b^4 + 2*a^4*b^5)*e^(6*d*x + 6*c) + 2*(3*a^7*b^2 + 14*a^6*b^3 + 27*a^5*b^4 + 24*a^4*b^5 + 8*a^3*b^6)*e^(4*d*x + 4*c) + 4*(a^7*b^2 + 4*a^6*b^3 + 5*a^5*b^4 + 2*a^4*b^5)*e^(2*d*x + 2*c))*d) + 1/256*(3*a^6 - 12*a^5*b - 204*a^4*b^2 - 384*a^3*b^3 - 192*a^2*b^4 + (9*a^6 - 14*a^5*b - 864*a^4*b^2 - 3136*a^3*b^3 - 3840*a^2*b^4 - 1536*a*b^5)*e^(-2*d*x - 2*c) + (9*a^6 - 12*a^5*b - 1100*a^4*b^2 - 5248*a^3*b^3 - 10304*a^2*b^4 - 9216*a*b^5 - 3072*b^6)*e^(-4*d*x - 4*c) + (3*a^6 - 10*a^5*b - 560*a^4*b^2 - 2080*a^3*b^3 - 2560*a^2*b^4 - 1024*a*b^5)*e^(-6*d*x - 6*c))/((a^7*b^2 + 2*a^6*b^3 + a^5*b^4 + 4*(a^7*b^2 + 4*a^6*b^3 + 5*a^5*b^4 + 2*a^4*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^7*b^2 + 14*a^6*b^3 + 27*a^5*b^4 + 24*a^4*b^5 + 8*a^3*b^6)*e^(-4*d*x - 4*c) + 4*(a^7*b^2 + 4*a^6*b^3 + 5*a^5*b^4 + 2*a^4*b^5)*e^(-6*d*x - 6*c) + (a^7*b^2 + 2*a^6*b^3 + a^5*b^4)*e^(-8*d*x - 8*c))*d) - 3/128*(3*a^5 - 2*a^4*b - 24*a^3*b^2 - 16*a^2*b^3 + (3*a^5 - 128*a^3*b^2 - 256*a^2*b^3 - 128*a*b^4)*e^(6*d*x + 6*c) + (9*a^5 + 18*a^4*b - 128*a^3*b^2 - 512*a^2*b^3 - 640*a*b^4 - 256*b^5)*e^(4*d*x + 4*c) + (9*a^5 + 16*a^4*b - 112*a^3*b^2 - 256*a^2*b^3 - 128*a*b^4)*e^(2*d*x + 2*c))/((a^6*b^2 + 2*a^5*b^3 + a^4*b^4 + (a^6*b^2 + 2*a^5*b^3 + a^4*b^4)*e^(8*d*x + 8*c) + 4*(a^6*b^2 + 4*a^5*b^3 + 5*a^4*b^4 + 2*a^3*b^5)*e^(6*d*x + 6*c) + 2*(3*a^6*b^2 + 14*a^5*b^3 + 27*a^4*b^4 + 24*a^3*b^5 + 8*a^2*b^6)*e^(4*d*x + 4*c) + 4*(a^6*b^2 + 4*a^5*b^3 + 5*a^4*b^4 + 2*a^3*b^5)*e^(2*d*x + 2*c))*d) + 3/128*(3*a^5 - 2*a^4*b - 24*a^3*b^2 - 16*a^2*b^3 + (9*a^5 + 16*a^4*b - 112*a^3*b^2 - 256*a^2*b^3 - 128*a*b^4)*e^(-2*d*x - 2*c) + (9*a^5 + 18*a^4*b - 128*a^3*b^2 - 512*a^2*b^3 - 640*a*b^4 - 256*b^5)*e^(-4*d*x - 4*c) + (3*a^5 - 128*a^3*b^2 - 256*a^2*b^3 - 128*a*b^4)*e^(-6*d*x - 6*c))/((a^6*b^2 + 2*a^5*b^3 + a^4*b^4 + 4*(a^6*b^2 + 4*a^5*b^3 + 5*a^4*b^4 + 2*a^3*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^6*b^2 + 14*a^5*b^3 + 27*a^4*b^4 + 24*a^3*b^5 + 8*a^2*b^6)*e^(-4*d*x - 4*c) + 4*(a^6*b^2 + 4*a^5*b^3 + 5*a^4*b^4 + 2*a^3*b^5)*e^(-6*d*x - 6*c) + (a^6*b^2 + 2*a^5*b^3 + a^4*b^4)*e^(-8*d*x - 8*c))*d) - 15/256*(3*a^4 + 4*a^3*b + 4*a^2*b^2 + 3*(a^4 + 2*a^3*b)*e^(6*d*x + 6*c) + (9*a^4 + 36*a^3*b + 100*a^2*b^2 + 128*a*b^3 + 64*b^4)*e^(4*d*x + 4*c) + (9*a^4 + 34*a^3*b + 48*a^2*b^2 + 32*a*b^3)*e^(2*d*x + 2*c))/((a^5*b^2 + 2*a^4*b^3 + a^3*b^4 + (a^5*b^2 + 2*a^4*b^3 + a^3*b^4)*e^(8*d*x + 8*c) + 4*(a^5*b^2 + 4*a^4*b^3 + 5*a^3*b^4 + 2*a^2*b^5)*e^(6*d*x + 6*c) + 2*(3*a^5*b^2 + 14*a^4*b^3 + 27*a^3*b^4 + 24*a^2*b^5 + 8*a*b^6)*e^(4*d*x + 4*c) + 4*(a^5*b^2 + 4*a^4*b^3 + 5*a^3*b^4 + 2*a^2*b^5)*e^(2*d*x + 2*c))*d) + 15/256*(3*a^4 + 4*a^3*b + 4*a^2*b^2 + (9*a^4 + 34*a^3*b + 48*a^2*b^2 + 32*a*b^3)*e^(-2*d*x - 2*c) + (9*a^4 + 36*a^3*b + 100*a^2*b^2 + 128*a*b^3 + 64*b^4)*e^(-4*d*x - 4*c) + 3*(a^4 + 2*a^3*b)*e^(-6*d*x - 6*c))/((a^5*b^2 + 2*a^4*b^3 + a^3*b^4 + 4*(a^5*b^2 + 4*a^4*b^3 + 5*a^3*b^4 + 2*a^2*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^5*b^2 + 14*a^4*b^3 + 27*a^3*b^4 + 24*a^2*b^5 + 8*a*b^6)*e^(-4*d*x - 4*c) + 4*(a^5*b^2 + 4*a^4*b^3 + 5*a^3*b^4 + 2*a^2*b^5)*e^(-6*d*x - 6*c) + (a^5*b^2 + 2*a^4*b^3 + a^3*b^4)*e^(-8*d*x - 8*c))*d) + 5/64*(3*a^3 + 6*a^2*b + (9*a^3 + 40*a^2*b + 40*a*b^2)*e^(-2*d*x - 2*c) + 3*(3*a^3 + 14*a^2*b + 24*a*b^2 + 16*b^3)*e^(-4*d*x - 4*c) + (3*a^3 + 8*a^2*b + 8*a*b^2)*e^(-6*d*x - 6*c))/((a^4*b^2 + 2*a^3*b^3 + a^2*b^4 + 4*(a^4*b^2 + 4*a^3*b^3 + 5*a^2*b^4 + 2*a*b^5)*e^(-2*d*x - 2*c) + 2*(3*a^4*b^2 + 14*a^3*b^3 + 27*a^2*b^4 + 24*a*b^5 + 8*b^6)*e^(-4*d*x - 4*c) + 4*(a^4*b^2 + 4*a^3*b^3 + 5*a^2*b^4 + 2*a*b^5)*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*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^3*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
159,1,206,0,0.420213," ","integrate(tanh(d*x+c)^5/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{4 \, {\left({\left(a^{2} + a b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(a^{2} + 4 \, a b + 3 \, b^{2}\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} e^{\left(-8 \, d x - 8 \, c\right)} + a^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{d x + c}{a^{3} d} + \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{3} d}"," ",0,"4*((a^2 + a*b)*e^(-2*d*x - 2*c) + (a^2 + 4*a*b + 3*b^2)*e^(-4*d*x - 4*c) + (a^2 + a*b)*e^(-6*d*x - 6*c))/((a^5*e^(-8*d*x - 8*c) + a^5 + 4*(a^5 + 2*a^4*b)*e^(-2*d*x - 2*c) + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*e^(-4*d*x - 4*c) + 4*(a^5 + 2*a^4*b)*e^(-6*d*x - 6*c))*d) + (d*x + c)/(a^3*d) + 1/2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
160,1,2201,0,1.020320," ","integrate(tanh(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(a^{4} - 20 \, a^{3} b - 120 \, a^{2} b^{2} - 160 \, a b^{3} - 64 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(a - 2 \, b\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(a^{4} - 20 \, a^{3} b - 120 \, a^{2} b^{2} - 160 \, a b^{3} - 64 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{3 \, {\left(a + 4 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{128 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{{\left(a - 2 \, b\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{a^{5} + 38 \, a^{4} b + 88 \, a^{3} b^{2} + 48 \, a^{2} b^{3} + {\left(a^{5} + 76 \, a^{4} b + 392 \, a^{3} b^{2} + 576 \, a^{2} b^{3} + 256 \, a b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(3 \, a^{5} + 186 \, a^{4} b + 1024 \, a^{3} b^{2} + 2240 \, a^{2} b^{3} + 2176 \, a b^{4} + 768 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(3 \, a^{5} + 148 \, a^{4} b + 648 \, a^{3} b^{2} + 896 \, a^{2} b^{3} + 384 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{64 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3} + {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{5} + 38 \, a^{4} b + 88 \, a^{3} b^{2} + 48 \, a^{2} b^{3} + {\left(3 \, a^{5} + 148 \, a^{4} b + 648 \, a^{3} b^{2} + 896 \, a^{2} b^{3} + 384 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{5} + 186 \, a^{4} b + 1024 \, a^{3} b^{2} + 2240 \, a^{2} b^{3} + 2176 \, a b^{4} + 768 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{5} + 76 \, a^{4} b + 392 \, a^{3} b^{2} + 576 \, a^{2} b^{3} + 256 \, a b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{64 \, {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} b + 14 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 24 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 5 \, a^{5} b^{3} + 2 \, a^{4} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} b + 2 \, a^{6} b^{2} + a^{5} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{a^{4} + 8 \, a^{3} b + 4 \, a^{2} b^{2} + {\left(a^{4} + 30 \, a^{3} b + 64 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(3 \, a^{4} + 64 \, a^{3} b + 180 \, a^{2} b^{2} + 192 \, a b^{3} + 64 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(3 \, a^{4} + 42 \, a^{3} b + 80 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{6} b + 2 \, a^{5} b^{2} + a^{4} b^{3} + {\left(a^{6} b + 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 5 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{6} b + 14 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 24 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 5 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{a^{4} + 8 \, a^{3} b + 4 \, a^{2} b^{2} + {\left(3 \, a^{4} + 42 \, a^{3} b + 80 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{4} + 64 \, a^{3} b + 180 \, a^{2} b^{2} + 192 \, a b^{3} + 64 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{4} + 30 \, a^{3} b + 64 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{6} b + 2 \, a^{5} b^{2} + a^{4} b^{3} + 4 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 5 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} b + 14 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 24 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} b + 4 \, a^{5} b^{2} + 5 \, a^{4} b^{3} + 2 \, a^{3} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} b + 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{3 \, {\left(a^{3} - 2 \, a^{2} b + {\left(3 \, a^{3} - 4 \, a^{2} b - 16 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(3 \, a^{3} + 2 \, a^{2} b - 8 \, a b^{2} - 16 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{3} + 4 \, a^{2} b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{32 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3} + 4 \, {\left(a^{5} b + 4 \, a^{4} b^{2} + 5 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} b + 14 \, a^{4} b^{2} + 27 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 8 \, a b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} b + 4 \, a^{4} b^{2} + 5 \, a^{3} b^{3} + 2 \, a^{2} b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{3} d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{3} d}"," ",0,"1/256*(a^4 - 20*a^3*b - 120*a^2*b^2 - 160*a*b^3 - 64*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5*b + 2*a^4*b^2 + a^3*b^3)*sqrt((a + b)*b)*d) + 1/64*(a - 2*b)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b + 2*a*b^2 + b^3)*sqrt((a + b)*b)*d) - 1/256*(a^4 - 20*a^3*b - 120*a^2*b^2 - 160*a*b^3 - 64*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5*b + 2*a^4*b^2 + a^3*b^3)*sqrt((a + b)*b)*d) - 3/128*(a + 4*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b + 2*a*b^2 + b^3)*sqrt((a + b)*b)*d) - 1/64*(a - 2*b)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2*b + 2*a*b^2 + b^3)*sqrt((a + b)*b)*d) + 1/64*(a^5 + 38*a^4*b + 88*a^3*b^2 + 48*a^2*b^3 + (a^5 + 76*a^4*b + 392*a^3*b^2 + 576*a^2*b^3 + 256*a*b^4)*e^(6*d*x + 6*c) + (3*a^5 + 186*a^4*b + 1024*a^3*b^2 + 2240*a^2*b^3 + 2176*a*b^4 + 768*b^5)*e^(4*d*x + 4*c) + (3*a^5 + 148*a^4*b + 648*a^3*b^2 + 896*a^2*b^3 + 384*a*b^4)*e^(2*d*x + 2*c))/((a^7*b + 2*a^6*b^2 + a^5*b^3 + (a^7*b + 2*a^6*b^2 + a^5*b^3)*e^(8*d*x + 8*c) + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*e^(6*d*x + 6*c) + 2*(3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*e^(4*d*x + 4*c) + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*e^(2*d*x + 2*c))*d) - 1/64*(a^5 + 38*a^4*b + 88*a^3*b^2 + 48*a^2*b^3 + (3*a^5 + 148*a^4*b + 648*a^3*b^2 + 896*a^2*b^3 + 384*a*b^4)*e^(-2*d*x - 2*c) + (3*a^5 + 186*a^4*b + 1024*a^3*b^2 + 2240*a^2*b^3 + 2176*a*b^4 + 768*b^5)*e^(-4*d*x - 4*c) + (a^5 + 76*a^4*b + 392*a^3*b^2 + 576*a^2*b^3 + 256*a*b^4)*e^(-6*d*x - 6*c))/((a^7*b + 2*a^6*b^2 + a^5*b^3 + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^7*b + 14*a^6*b^2 + 27*a^5*b^3 + 24*a^4*b^4 + 8*a^3*b^5)*e^(-4*d*x - 4*c) + 4*(a^7*b + 4*a^6*b^2 + 5*a^5*b^3 + 2*a^4*b^4)*e^(-6*d*x - 6*c) + (a^7*b + 2*a^6*b^2 + a^5*b^3)*e^(-8*d*x - 8*c))*d) + 1/16*(a^4 + 8*a^3*b + 4*a^2*b^2 + (a^4 + 30*a^3*b + 64*a^2*b^2 + 32*a*b^3)*e^(6*d*x + 6*c) + (3*a^4 + 64*a^3*b + 180*a^2*b^2 + 192*a*b^3 + 64*b^4)*e^(4*d*x + 4*c) + (3*a^4 + 42*a^3*b + 80*a^2*b^2 + 32*a*b^3)*e^(2*d*x + 2*c))/((a^6*b + 2*a^5*b^2 + a^4*b^3 + (a^6*b + 2*a^5*b^2 + a^4*b^3)*e^(8*d*x + 8*c) + 4*(a^6*b + 4*a^5*b^2 + 5*a^4*b^3 + 2*a^3*b^4)*e^(6*d*x + 6*c) + 2*(3*a^6*b + 14*a^5*b^2 + 27*a^4*b^3 + 24*a^3*b^4 + 8*a^2*b^5)*e^(4*d*x + 4*c) + 4*(a^6*b + 4*a^5*b^2 + 5*a^4*b^3 + 2*a^3*b^4)*e^(2*d*x + 2*c))*d) - 1/16*(a^4 + 8*a^3*b + 4*a^2*b^2 + (3*a^4 + 42*a^3*b + 80*a^2*b^2 + 32*a*b^3)*e^(-2*d*x - 2*c) + (3*a^4 + 64*a^3*b + 180*a^2*b^2 + 192*a*b^3 + 64*b^4)*e^(-4*d*x - 4*c) + (a^4 + 30*a^3*b + 64*a^2*b^2 + 32*a*b^3)*e^(-6*d*x - 6*c))/((a^6*b + 2*a^5*b^2 + a^4*b^3 + 4*(a^6*b + 4*a^5*b^2 + 5*a^4*b^3 + 2*a^3*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^6*b + 14*a^5*b^2 + 27*a^4*b^3 + 24*a^3*b^4 + 8*a^2*b^5)*e^(-4*d*x - 4*c) + 4*(a^6*b + 4*a^5*b^2 + 5*a^4*b^3 + 2*a^3*b^4)*e^(-6*d*x - 6*c) + (a^6*b + 2*a^5*b^2 + a^4*b^3)*e^(-8*d*x - 8*c))*d) - 3/32*(a^3 - 2*a^2*b + (3*a^3 - 4*a^2*b - 16*a*b^2)*e^(-2*d*x - 2*c) + (3*a^3 + 2*a^2*b - 8*a*b^2 - 16*b^3)*e^(-4*d*x - 4*c) + (a^3 + 4*a^2*b)*e^(-6*d*x - 6*c))/((a^5*b + 2*a^4*b^2 + a^3*b^3 + 4*(a^5*b + 4*a^4*b^2 + 5*a^3*b^3 + 2*a^2*b^4)*e^(-2*d*x - 2*c) + 2*(3*a^5*b + 14*a^4*b^2 + 27*a^3*b^3 + 24*a^2*b^4 + 8*a*b^5)*e^(-4*d*x - 4*c) + 4*(a^5*b + 4*a^4*b^2 + 5*a^3*b^3 + 2*a^2*b^4)*e^(-6*d*x - 6*c) + (a^5*b + 2*a^4*b^2 + a^3*b^3)*e^(-8*d*x - 8*c))*d) + 1/4*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^3*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
161,1,209,0,0.336298," ","integrate(tanh(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{2 \, {\left({\left(a^{2} + 2 \, a b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{2} + 3 \, a b + 3 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(a^{2} + 2 \, a b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{5} e^{\left(-8 \, d x - 8 \, c\right)} + a^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{d x + c}{a^{3} d} + \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{3} d}"," ",0,"2*((a^2 + 2*a*b)*e^(-2*d*x - 2*c) + 2*(a^2 + 3*a*b + 3*b^2)*e^(-4*d*x - 4*c) + (a^2 + 2*a*b)*e^(-6*d*x - 6*c))/((a^5*e^(-8*d*x - 8*c) + a^5 + 4*(a^5 + 2*a^4*b)*e^(-2*d*x - 2*c) + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*e^(-4*d*x - 4*c) + 4*(a^5 + 2*a^4*b)*e^(-6*d*x - 6*c))*d) + (d*x + c)/(a^3*d) + 1/2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
162,1,1255,0,0.926795," ","integrate(tanh(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{3} + 30 \, a^{2} b + 40 \, a b^{2} + 16 \, b^{3}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(3 \, a^{3} + 30 \, a^{2} b + 40 \, a b^{2} + 16 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{5 \, a^{4} + 20 \, a^{3} b + 12 \, a^{2} b^{2} + {\left(5 \, a^{4} + 66 \, a^{3} b + 128 \, a^{2} b^{2} + 64 \, a b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + {\left(15 \, a^{4} + 164 \, a^{3} b + 460 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(15 \, a^{4} + 118 \, a^{3} b + 208 \, a^{2} b^{2} + 96 \, a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{5 \, a^{4} + 20 \, a^{3} b + 12 \, a^{2} b^{2} + {\left(15 \, a^{4} + 118 \, a^{3} b + 208 \, a^{2} b^{2} + 96 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(15 \, a^{4} + 164 \, a^{3} b + 460 \, a^{2} b^{2} + 512 \, a b^{3} + 192 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(5 \, a^{4} + 66 \, a^{3} b + 128 \, a^{2} b^{2} + 64 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{16 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} - \frac{5 \, a^{3} + 2 \, a^{2} b + {\left(15 \, a^{3} + 32 \, a^{2} b + 8 \, a b^{2}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + {\left(15 \, a^{3} + 46 \, a^{2} b + 56 \, a b^{2} + 16 \, b^{3}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(5 \, a^{3} + 16 \, a^{2} b + 8 \, a b^{2}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{8 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2} + 4 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{6} + 14 \, a^{5} b + 27 \, a^{4} b^{2} + 24 \, a^{3} b^{3} + 8 \, a^{2} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{6} + 4 \, a^{5} b + 5 \, a^{4} b^{2} + 2 \, a^{3} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{3 \, \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{\log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, a^{3} d} - \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, a^{3} d}"," ",0,"-1/64*(3*a^3 + 30*a^2*b + 40*a*b^2 + 16*b^3)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)*d) + 1/64*(3*a^3 + 30*a^2*b + 40*a*b^2 + 16*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)*d) + 1/16*(5*a^4 + 20*a^3*b + 12*a^2*b^2 + (5*a^4 + 66*a^3*b + 128*a^2*b^2 + 64*a*b^3)*e^(6*d*x + 6*c) + (15*a^4 + 164*a^3*b + 460*a^2*b^2 + 512*a*b^3 + 192*b^4)*e^(4*d*x + 4*c) + (15*a^4 + 118*a^3*b + 208*a^2*b^2 + 96*a*b^3)*e^(2*d*x + 2*c))/((a^7 + 2*a^6*b + a^5*b^2 + (a^7 + 2*a^6*b + a^5*b^2)*e^(8*d*x + 8*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(6*d*x + 6*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(4*d*x + 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(2*d*x + 2*c))*d) - 1/16*(5*a^4 + 20*a^3*b + 12*a^2*b^2 + (15*a^4 + 118*a^3*b + 208*a^2*b^2 + 96*a*b^3)*e^(-2*d*x - 2*c) + (15*a^4 + 164*a^3*b + 460*a^2*b^2 + 512*a*b^3 + 192*b^4)*e^(-4*d*x - 4*c) + (5*a^4 + 66*a^3*b + 128*a^2*b^2 + 64*a*b^3)*e^(-6*d*x - 6*c))/((a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(-4*d*x - 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-6*d*x - 6*c) + (a^7 + 2*a^6*b + a^5*b^2)*e^(-8*d*x - 8*c))*d) - 1/8*(5*a^3 + 2*a^2*b + (15*a^3 + 32*a^2*b + 8*a*b^2)*e^(-2*d*x - 2*c) + (15*a^3 + 46*a^2*b + 56*a*b^2 + 16*b^3)*e^(-4*d*x - 4*c) + (5*a^3 + 16*a^2*b + 8*a*b^2)*e^(-6*d*x - 6*c))/((a^6 + 2*a^5*b + a^4*b^2 + 4*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^6 + 14*a^5*b + 27*a^4*b^2 + 24*a^3*b^3 + 8*a^2*b^4)*e^(-4*d*x - 4*c) + 4*(a^6 + 4*a^5*b + 5*a^4*b^2 + 2*a^3*b^3)*e^(-6*d*x - 6*c) + (a^6 + 2*a^5*b + a^4*b^2)*e^(-8*d*x - 8*c))*d) + 3/32*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^2 + 2*a*b + b^2)*sqrt((a + b)*b)*d) + 1/4*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/(a^3*d) - 1/4*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
163,1,193,0,0.420335," ","integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(a b e^{\left(-2 \, d x - 2 \, c\right)} + a b e^{\left(-6 \, d x - 6 \, c\right)} + {\left(2 \, a b + 3 \, b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)}\right)}}{{\left(a^{5} e^{\left(-8 \, d x - 8 \, c\right)} + a^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{5} + 2 \, a^{4} b\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)} d} + \frac{d x + c}{a^{3} d} + \frac{\log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, a^{3} d}"," ",0,"4*(a*b*e^(-2*d*x - 2*c) + a*b*e^(-6*d*x - 6*c) + (2*a*b + 3*b^2)*e^(-4*d*x - 4*c))/((a^5*e^(-8*d*x - 8*c) + a^5 + 4*(a^5 + 2*a^4*b)*e^(-2*d*x - 2*c) + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2)*e^(-4*d*x - 4*c) + 4*(a^5 + 2*a^4*b)*e^(-6*d*x - 6*c))*d) + (d*x + c)/(a^3*d) + 1/2*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/(a^3*d)","B",0
164,1,402,0,0.528183," ","integrate(1/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{16 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{9 \, a^{3} b + 6 \, a^{2} b^{2} + {\left(27 \, a^{3} b + 68 \, a^{2} b^{2} + 32 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(9 \, a^{3} b + 30 \, a^{2} b^{2} + 40 \, a b^{3} + 16 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(9 \, a^{3} b + 28 \, a^{2} b^{2} + 16 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}}{4 \, {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{d x + c}{a^{3} d}"," ",0,"1/16*(15*a^2*b + 20*a*b^2 + 8*b^3)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt((a + b)*b)*d) - 1/4*(9*a^3*b + 6*a^2*b^2 + (27*a^3*b + 68*a^2*b^2 + 32*a*b^3)*e^(-2*d*x - 2*c) + 3*(9*a^3*b + 30*a^2*b^2 + 40*a*b^3 + 16*b^4)*e^(-4*d*x - 4*c) + (9*a^3*b + 28*a^2*b^2 + 16*a*b^3)*e^(-6*d*x - 6*c))/((a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(-4*d*x - 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-6*d*x - 6*c) + (a^7 + 2*a^6*b + a^5*b^2)*e^(-8*d*x - 8*c))*d) + (d*x + c)/(a^3*d)","B",0
165,1,419,0,0.721140," ","integrate(coth(d*x+c)/(a+b*sech(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 + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d} + \frac{2 \, {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{2} b^{2} + 7 \, a b^{3} + 3 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + {\left(3 \, a^{2} b^{2} + 2 \, a b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)}\right)}}{{\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(3 \, a^{7} + 14 \, a^{6} b + 27 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} + 2 \, a^{4} b^{3}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(a^{7} + 2 \, a^{6} b + a^{5} b^{2}\right)} e^{\left(-8 \, d x - 8 \, c\right)}\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} + 1\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{\log\left(e^{\left(-d x - c\right)} - 1\right)}{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} + \frac{d x + c}{a^{3} d}"," ",0,"1/2*(3*a^2*b + 3*a*b^2 + b^3)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d) + 2*((3*a^2*b^2 + 2*a*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^2*b^2 + 7*a*b^3 + 3*b^4)*e^(-4*d*x - 4*c) + (3*a^2*b^2 + 2*a*b^3)*e^(-6*d*x - 6*c))/((a^7 + 2*a^6*b + a^5*b^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-2*d*x - 2*c) + 2*(3*a^7 + 14*a^6*b + 27*a^5*b^2 + 24*a^4*b^3 + 8*a^3*b^4)*e^(-4*d*x - 4*c) + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 + 2*a^4*b^3)*e^(-6*d*x - 6*c) + (a^7 + 2*a^6*b + a^5*b^2)*e^(-8*d*x - 8*c))*d) + log(e^(-d*x - c) + 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + log(e^(-d*x - c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) + (d*x + c)/(a^3*d)","B",0
166,1,1971,0,0.940760," ","integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\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 + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\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 + 70 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(15 \, a^{3} b + 70 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{15 \, b \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{8 \, a^{5} + 9 \, a^{4} b + 28 \, a^{3} b^{2} + 12 \, a^{2} b^{3} + {\left(8 \, a^{5} - 9 \, a^{4} b - 98 \, a^{3} b^{2} - 160 \, a^{2} b^{3} - 64 \, a b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} + 2 \, {\left(16 \, a^{5} + 23 \, a^{4} b - 77 \, a^{3} b^{2} - 246 \, a^{2} b^{3} - 288 \, a b^{4} - 96 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 99 \, a^{3} b^{2} + 190 \, a^{2} b^{3} + 272 \, a b^{4} + 96 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(16 \, a^{5} + 41 \, a^{4} b + 77 \, a^{3} b^{2} + 130 \, a^{2} b^{3} + 48 \, a b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{16 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3} - {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} e^{\left(10 \, d x + 10 \, c\right)} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(8 \, d x + 8 \, c\right)} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{8 \, a^{5} + 9 \, a^{4} b + 28 \, a^{3} b^{2} + 12 \, a^{2} b^{3} + 2 \, {\left(16 \, a^{5} + 41 \, a^{4} b + 77 \, a^{3} b^{2} + 130 \, a^{2} b^{3} + 48 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(24 \, a^{5} + 64 \, a^{4} b + 99 \, a^{3} b^{2} + 190 \, a^{2} b^{3} + 272 \, a b^{4} + 96 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(16 \, a^{5} + 23 \, a^{4} b - 77 \, a^{3} b^{2} - 246 \, a^{2} b^{3} - 288 \, a b^{4} - 96 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(8 \, a^{5} - 9 \, a^{4} b - 98 \, a^{3} b^{2} - 160 \, a^{2} b^{3} - 64 \, a b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{16 \, {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3} + {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(3 \, a^{8} + 17 \, a^{7} b + 33 \, a^{6} b^{2} + 27 \, a^{5} b^{3} + 8 \, a^{4} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} - \frac{8 \, a^{4} - 9 \, a^{3} b - 2 \, a^{2} b^{2} + 2 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 27 \, a^{2} b^{2} - 4 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(24 \, a^{4} + 64 \, a^{3} b + 53 \, a^{2} b^{2} - 40 \, a b^{3} - 8 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(16 \, a^{4} + 41 \, a^{3} b + 27 \, a^{2} b^{2} + 40 \, a b^{3} + 8 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(8 \, a^{4} + 9 \, a^{3} b + 24 \, a^{2} b^{2} + 8 \, a b^{3}\right)} e^{\left(-8 \, d x - 8 \, c\right)}}{8 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3} + {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 2 \, {\left(a^{7} + 7 \, a^{6} b + 23 \, a^{5} b^{2} + 37 \, a^{4} b^{3} + 28 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(3 \, a^{7} + 17 \, a^{6} b + 33 \, a^{5} b^{2} + 27 \, a^{4} b^{3} + 8 \, a^{3} b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)} d} + \frac{\log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d} - \frac{\log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d}"," ",0,"1/4*(3*a^2*b + 3*a*b^2 + b^3)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((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 + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d) - 1/64*(15*a^3*b + 70*a^2*b^2 + 56*a*b^3 + 16*b^4)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt((a + b)*b)*d) + 1/64*(15*a^3*b + 70*a^2*b^2 + 56*a*b^3 + 16*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sqrt((a + b)*b)*d) - 15/32*b*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sqrt((a + b)*b)*d) + 1/16*(8*a^5 + 9*a^4*b + 28*a^3*b^2 + 12*a^2*b^3 + (8*a^5 - 9*a^4*b - 98*a^3*b^2 - 160*a^2*b^3 - 64*a*b^4)*e^(8*d*x + 8*c) + 2*(16*a^5 + 23*a^4*b - 77*a^3*b^2 - 246*a^2*b^3 - 288*a*b^4 - 96*b^5)*e^(6*d*x + 6*c) + 2*(24*a^5 + 64*a^4*b + 99*a^3*b^2 + 190*a^2*b^3 + 272*a*b^4 + 96*b^5)*e^(4*d*x + 4*c) + 2*(16*a^5 + 41*a^4*b + 77*a^3*b^2 + 130*a^2*b^3 + 48*a*b^4)*e^(2*d*x + 2*c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3 - (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*e^(10*d*x + 10*c) - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*e^(8*d*x + 8*c) - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*e^(6*d*x + 6*c) + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*e^(4*d*x + 4*c) + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*e^(2*d*x + 2*c))*d) - 1/16*(8*a^5 + 9*a^4*b + 28*a^3*b^2 + 12*a^2*b^3 + 2*(16*a^5 + 41*a^4*b + 77*a^3*b^2 + 130*a^2*b^3 + 48*a*b^4)*e^(-2*d*x - 2*c) + 2*(24*a^5 + 64*a^4*b + 99*a^3*b^2 + 190*a^2*b^3 + 272*a*b^4 + 96*b^5)*e^(-4*d*x - 4*c) + 2*(16*a^5 + 23*a^4*b - 77*a^3*b^2 - 246*a^2*b^3 - 288*a*b^4 - 96*b^5)*e^(-6*d*x - 6*c) + (8*a^5 - 9*a^4*b - 98*a^3*b^2 - 160*a^2*b^3 - 64*a*b^4)*e^(-8*d*x - 8*c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3 + (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*e^(-2*d*x - 2*c) + 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*e^(-4*d*x - 4*c) - 2*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*e^(-6*d*x - 6*c) - (3*a^8 + 17*a^7*b + 33*a^6*b^2 + 27*a^5*b^3 + 8*a^4*b^4)*e^(-8*d*x - 8*c) - (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*e^(-10*d*x - 10*c))*d) - 1/8*(8*a^4 - 9*a^3*b - 2*a^2*b^2 + 2*(16*a^4 + 23*a^3*b - 27*a^2*b^2 - 4*a*b^3)*e^(-2*d*x - 2*c) + 2*(24*a^4 + 64*a^3*b + 53*a^2*b^2 - 40*a*b^3 - 8*b^4)*e^(-4*d*x - 4*c) + 2*(16*a^4 + 41*a^3*b + 27*a^2*b^2 + 40*a*b^3 + 8*b^4)*e^(-6*d*x - 6*c) + (8*a^4 + 9*a^3*b + 24*a^2*b^2 + 8*a*b^3)*e^(-8*d*x - 8*c))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3 + (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*e^(-2*d*x - 2*c) + 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*e^(-4*d*x - 4*c) - 2*(a^7 + 7*a^6*b + 23*a^5*b^2 + 37*a^4*b^3 + 28*a^3*b^4 + 8*a^2*b^5)*e^(-6*d*x - 6*c) - (3*a^7 + 17*a^6*b + 33*a^5*b^2 + 27*a^4*b^3 + 8*a^3*b^4)*e^(-8*d*x - 8*c) - (a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*e^(-10*d*x - 10*c))*d) + 1/2*log(e^(2*d*x + 2*c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d) - 1/2*log(e^(-2*d*x - 2*c) - 1)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d)","B",0
167,1,692,0,0.538347," ","integrate(coth(d*x+c)^3/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{2 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d} + \frac{{\left(a + 4 \, b\right)} \log\left(e^{\left(-d x - c\right)} + 1\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} + \frac{{\left(a + 4 \, b\right)} \log\left(e^{\left(-d x - c\right)} - 1\right)}{{\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{2 \, {\left({\left(a^{5} - 4 \, a^{2} b^{3} - 2 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, {\left(2 \, a^{5} + 4 \, a^{4} b - 7 \, a b^{4} - 3 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(3 \, a^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 16 \, a b^{4} + 6 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 2 \, {\left(2 \, a^{5} + 4 \, a^{4} b - 7 \, a b^{4} - 3 \, b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(a^{5} - 4 \, a^{2} b^{3} - 2 \, a b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)}\right)}}{{\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 15 \, a^{6} b^{2} + 13 \, a^{5} b^{3} + 4 \, a^{4} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(a^{8} + 3 \, a^{7} b - 13 \, a^{6} b^{2} - 47 \, a^{5} b^{3} - 48 \, a^{4} b^{4} - 16 \, a^{3} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(a^{8} + 7 \, a^{7} b + 23 \, a^{6} b^{2} + 37 \, a^{5} b^{3} + 28 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(a^{8} + 3 \, a^{7} b - 13 \, a^{6} b^{2} - 47 \, a^{5} b^{3} - 48 \, a^{4} b^{4} - 16 \, a^{3} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 2 \, {\left(a^{8} + 7 \, a^{7} b + 15 \, a^{6} b^{2} + 13 \, a^{5} b^{3} + 4 \, a^{4} b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + {\left(a^{8} + 3 \, a^{7} b + 3 \, a^{6} b^{2} + a^{5} b^{3}\right)} e^{\left(-12 \, d x - 12 \, c\right)}\right)} d} + \frac{d x + c}{a^{3} d}"," ",0,"1/2*(6*a^2*b^2 + 4*a*b^3 + b^4)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d) + (a + 4*b)*log(e^(-d*x - c) + 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) + (a + 4*b)*log(e^(-d*x - c) - 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 2*((a^5 - 4*a^2*b^3 - 2*a*b^4)*e^(-2*d*x - 2*c) + 2*(2*a^5 + 4*a^4*b - 7*a*b^4 - 3*b^5)*e^(-4*d*x - 4*c) + 2*(3*a^5 + 8*a^4*b + 8*a^3*b^2 + 4*a^2*b^3 + 16*a*b^4 + 6*b^5)*e^(-6*d*x - 6*c) + 2*(2*a^5 + 4*a^4*b - 7*a*b^4 - 3*b^5)*e^(-8*d*x - 8*c) + (a^5 - 4*a^2*b^3 - 2*a*b^4)*e^(-10*d*x - 10*c))/((a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3 + 2*(a^8 + 7*a^7*b + 15*a^6*b^2 + 13*a^5*b^3 + 4*a^4*b^4)*e^(-2*d*x - 2*c) - (a^8 + 3*a^7*b - 13*a^6*b^2 - 47*a^5*b^3 - 48*a^4*b^4 - 16*a^3*b^5)*e^(-4*d*x - 4*c) - 4*(a^8 + 7*a^7*b + 23*a^6*b^2 + 37*a^5*b^3 + 28*a^4*b^4 + 8*a^3*b^5)*e^(-6*d*x - 6*c) - (a^8 + 3*a^7*b - 13*a^6*b^2 - 47*a^5*b^3 - 48*a^4*b^4 - 16*a^3*b^5)*e^(-8*d*x - 8*c) + 2*(a^8 + 7*a^7*b + 15*a^6*b^2 + 13*a^5*b^3 + 4*a^4*b^4)*e^(-10*d*x - 10*c) + (a^8 + 3*a^7*b + 3*a^6*b^2 + a^5*b^3)*e^(-12*d*x - 12*c))*d) + (d*x + c)/(a^3*d)","B",0
168,1,4920,0,1.837728," ","integrate(coth(d*x+c)^4/(a+b*sech(d*x+c)^2)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, a^{3} b + 12 \, a^{2} b^{2} + 8 \, a b^{3} + 2 \, b^{4}\right)} \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d} - \frac{3 \, b \log\left(a e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a + 2 \, b\right)} e^{\left(2 \, d x + 2 \, c\right)} + a\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{{\left(3 \, a^{3} b + 12 \, a^{2} b^{2} + 8 \, a b^{3} + 2 \, b^{4}\right)} \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d} + \frac{3 \, b \log\left(2 \, {\left(a + 2 \, b\right)} e^{\left(-2 \, d x - 2 \, c\right)} + a e^{\left(-4 \, d x - 4 \, c\right)} + a\right)}{4 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} + \frac{{\left(2 \, a + 5 \, b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\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(e^{\left(2 \, d x + 2 \, c\right)} - 1\right)}{2 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{{\left(2 \, a + 5 \, b\right)} \log\left(e^{\left(-2 \, d x - 2 \, c\right)} - 1\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(e^{\left(-2 \, d x - 2 \, c\right)} - 1\right)}{2 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d} - \frac{{\left(15 \, a^{4} b + 260 \, a^{3} b^{2} + 504 \, a^{2} b^{3} + 288 \, a b^{4} + 64 \, b^{5}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{5 \, {\left(3 \, a b + 10 \, b^{2}\right)} \log\left(\frac{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(2 \, d x + 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{{\left(15 \, a^{4} b + 260 \, a^{3} b^{2} + 504 \, a^{2} b^{3} + 288 \, a b^{4} + 64 \, b^{5}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{256 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{5 \, {\left(3 \, a b + 10 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{64 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{15 \, {\left(3 \, a b - 4 \, b^{2}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{128 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sqrt{{\left(a + b\right)} b} d} + \frac{176 \, a^{6} + 275 \, a^{5} b + 306 \, a^{4} b^{2} + 456 \, a^{3} b^{3} + 144 \, a^{2} b^{4} + 3 \, {\left(96 \, a^{6} + 111 \, a^{5} b - 220 \, a^{4} b^{2} - 776 \, a^{3} b^{3} - 832 \, a^{2} b^{4} - 256 \, a b^{5}\right)} e^{\left(12 \, d x + 12 \, c\right)} + 6 \, {\left(120 \, a^{6} + 528 \, a^{5} b + 525 \, a^{4} b^{2} - 52 \, a^{3} b^{3} - 896 \, a^{2} b^{4} - 1216 \, a b^{5} - 384 \, b^{6}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(176 \, a^{6} + 1337 \, a^{5} b + 7554 \, a^{4} b^{2} + 16416 \, a^{3} b^{3} + 26880 \, a^{2} b^{4} + 25344 \, a b^{5} + 6912 \, b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} - 4 \, {\left(184 \, a^{6} + 1056 \, a^{5} b + 2993 \, a^{4} b^{2} + 4122 \, a^{3} b^{3} + 5892 \, a^{2} b^{4} + 6144 \, a b^{5} + 1728 \, b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(384 \, a^{6} + 1177 \, a^{5} b - 736 \, a^{4} b^{2} + 112 \, a^{3} b^{3} - 624 \, a^{2} b^{4} - 6144 \, a b^{5} - 2304 \, b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(136 \, a^{6} + 912 \, a^{5} b + 1211 \, a^{4} b^{2} + 1440 \, a^{3} b^{3} + 1896 \, a^{2} b^{4} + 576 \, a b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}}{192 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4} - {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} e^{\left(14 \, d x + 14 \, c\right)} - {\left(a^{9} + 12 \, a^{8} b + 38 \, a^{7} b^{2} + 52 \, a^{6} b^{3} + 33 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} e^{\left(12 \, d x + 12 \, c\right)} + {\left(3 \, a^{9} + 20 \, a^{8} b + 34 \, a^{7} b^{2} - 4 \, a^{6} b^{3} - 61 \, a^{5} b^{4} - 56 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(3 \, a^{9} + 28 \, a^{8} b + 130 \, a^{7} b^{2} + 300 \, a^{6} b^{3} + 355 \, a^{5} b^{4} + 208 \, a^{4} b^{5} + 48 \, a^{3} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} - {\left(3 \, a^{9} + 28 \, a^{8} b + 130 \, a^{7} b^{2} + 300 \, a^{6} b^{3} + 355 \, a^{5} b^{4} + 208 \, a^{4} b^{5} + 48 \, a^{3} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(3 \, a^{9} + 20 \, a^{8} b + 34 \, a^{7} b^{2} - 4 \, a^{6} b^{3} - 61 \, a^{5} b^{4} - 56 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{9} + 12 \, a^{8} b + 38 \, a^{7} b^{2} + 52 \, a^{6} b^{3} + 33 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{176 \, a^{6} + 275 \, a^{5} b + 306 \, a^{4} b^{2} + 456 \, a^{3} b^{3} + 144 \, a^{2} b^{4} + 2 \, {\left(136 \, a^{6} + 912 \, a^{5} b + 1211 \, a^{4} b^{2} + 1440 \, a^{3} b^{3} + 1896 \, a^{2} b^{4} + 576 \, a b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(384 \, a^{6} + 1177 \, a^{5} b - 736 \, a^{4} b^{2} + 112 \, a^{3} b^{3} - 624 \, a^{2} b^{4} - 6144 \, a b^{5} - 2304 \, b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(184 \, a^{6} + 1056 \, a^{5} b + 2993 \, a^{4} b^{2} + 4122 \, a^{3} b^{3} + 5892 \, a^{2} b^{4} + 6144 \, a b^{5} + 1728 \, b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(176 \, a^{6} + 1337 \, a^{5} b + 7554 \, a^{4} b^{2} + 16416 \, a^{3} b^{3} + 26880 \, a^{2} b^{4} + 25344 \, a b^{5} + 6912 \, b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, {\left(120 \, a^{6} + 528 \, a^{5} b + 525 \, a^{4} b^{2} - 52 \, a^{3} b^{3} - 896 \, a^{2} b^{4} - 1216 \, a b^{5} - 384 \, b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + 3 \, {\left(96 \, a^{6} + 111 \, a^{5} b - 220 \, a^{4} b^{2} - 776 \, a^{3} b^{3} - 832 \, a^{2} b^{4} - 256 \, a b^{5}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{192 \, {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4} + {\left(a^{9} + 12 \, a^{8} b + 38 \, a^{7} b^{2} + 52 \, a^{6} b^{3} + 33 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{9} + 20 \, a^{8} b + 34 \, a^{7} b^{2} - 4 \, a^{6} b^{3} - 61 \, a^{5} b^{4} - 56 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{9} + 28 \, a^{8} b + 130 \, a^{7} b^{2} + 300 \, a^{6} b^{3} + 355 \, a^{5} b^{4} + 208 \, a^{4} b^{5} + 48 \, a^{3} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{9} + 28 \, a^{8} b + 130 \, a^{7} b^{2} + 300 \, a^{6} b^{3} + 355 \, a^{5} b^{4} + 208 \, a^{4} b^{5} + 48 \, a^{3} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{9} + 20 \, a^{8} b + 34 \, a^{7} b^{2} - 4 \, a^{6} b^{3} - 61 \, a^{5} b^{4} - 56 \, a^{4} b^{5} - 16 \, a^{3} b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{9} + 12 \, a^{8} b + 38 \, a^{7} b^{2} + 52 \, a^{6} b^{3} + 33 \, a^{5} b^{4} + 8 \, a^{4} b^{5}\right)} e^{\left(-12 \, d x - 12 \, c\right)} - {\left(a^{9} + 4 \, a^{8} b + 6 \, a^{7} b^{2} + 4 \, a^{6} b^{3} + a^{5} b^{4}\right)} e^{\left(-14 \, d x - 14 \, c\right)}\right)} d} + \frac{32 \, a^{5} + 77 \, a^{4} b - 72 \, a^{3} b^{2} - 12 \, a^{2} b^{3} + 3 \, {\left(32 \, a^{5} + 65 \, a^{4} b + 94 \, a^{3} b^{2} + 128 \, a^{2} b^{3} + 32 \, a b^{4}\right)} e^{\left(12 \, d x + 12 \, c\right)} + 6 \, {\left(48 \, a^{5} + 200 \, a^{4} b + 203 \, a^{3} b^{2} + 90 \, a^{2} b^{3} + 176 \, a b^{4} + 32 \, b^{5}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(224 \, a^{5} + 839 \, a^{4} b + 1500 \, a^{3} b^{2} - 612 \, a^{2} b^{3} - 3648 \, a b^{4} - 576 \, b^{5}\right)} e^{\left(8 \, d x + 8 \, c\right)} - 4 \, {\left(16 \, a^{5} + 216 \, a^{4} b + 695 \, a^{3} b^{2} + 252 \, a^{2} b^{3} - 912 \, a b^{4} - 144 \, b^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(96 \, a^{5} + 343 \, a^{4} b - 850 \, a^{3} b^{2} - 1808 \, a^{2} b^{3} + 1056 \, a b^{4} + 192 \, b^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(16 \, a^{5} + 216 \, a^{4} b + 269 \, a^{3} b^{2} - 294 \, a^{2} b^{3} - 48 \, a b^{4}\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} + 12 \, a^{7} b + 38 \, a^{6} b^{2} + 52 \, a^{5} b^{3} + 33 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(12 \, d x + 12 \, c\right)} + {\left(3 \, a^{8} + 20 \, a^{7} b + 34 \, a^{6} b^{2} - 4 \, a^{5} b^{3} - 61 \, a^{4} b^{4} - 56 \, a^{3} b^{5} - 16 \, a^{2} b^{6}\right)} e^{\left(10 \, d x + 10 \, c\right)} + {\left(3 \, a^{8} + 28 \, a^{7} b + 130 \, a^{6} b^{2} + 300 \, a^{5} b^{3} + 355 \, a^{4} b^{4} + 208 \, a^{3} b^{5} + 48 \, a^{2} b^{6}\right)} e^{\left(8 \, d x + 8 \, c\right)} - {\left(3 \, a^{8} + 28 \, a^{7} b + 130 \, a^{6} b^{2} + 300 \, a^{5} b^{3} + 355 \, a^{4} b^{4} + 208 \, a^{3} b^{5} + 48 \, a^{2} b^{6}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(3 \, a^{8} + 20 \, a^{7} b + 34 \, a^{6} b^{2} - 4 \, a^{5} b^{3} - 61 \, a^{4} b^{4} - 56 \, a^{3} b^{5} - 16 \, a^{2} b^{6}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(a^{8} + 12 \, a^{7} b + 38 \, a^{6} b^{2} + 52 \, a^{5} b^{3} + 33 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} d} - \frac{32 \, a^{5} + 77 \, a^{4} b - 72 \, a^{3} b^{2} - 12 \, a^{2} b^{3} + 2 \, {\left(16 \, a^{5} + 216 \, a^{4} b + 269 \, a^{3} b^{2} - 294 \, a^{2} b^{3} - 48 \, a b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(96 \, a^{5} + 343 \, a^{4} b - 850 \, a^{3} b^{2} - 1808 \, a^{2} b^{3} + 1056 \, a b^{4} + 192 \, b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(16 \, a^{5} + 216 \, a^{4} b + 695 \, a^{3} b^{2} + 252 \, a^{2} b^{3} - 912 \, a b^{4} - 144 \, b^{5}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(224 \, a^{5} + 839 \, a^{4} b + 1500 \, a^{3} b^{2} - 612 \, a^{2} b^{3} - 3648 \, a b^{4} - 576 \, b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, {\left(48 \, a^{5} + 200 \, a^{4} b + 203 \, a^{3} b^{2} + 90 \, a^{2} b^{3} + 176 \, a b^{4} + 32 \, b^{5}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + 3 \, {\left(32 \, a^{5} + 65 \, a^{4} b + 94 \, a^{3} b^{2} + 128 \, a^{2} b^{3} + 32 \, a b^{4}\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} + 12 \, a^{7} b + 38 \, a^{6} b^{2} + 52 \, a^{5} b^{3} + 33 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{8} + 20 \, a^{7} b + 34 \, a^{6} b^{2} - 4 \, a^{5} b^{3} - 61 \, a^{4} b^{4} - 56 \, a^{3} b^{5} - 16 \, a^{2} b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{8} + 28 \, a^{7} b + 130 \, a^{6} b^{2} + 300 \, a^{5} b^{3} + 355 \, a^{4} b^{4} + 208 \, a^{3} b^{5} + 48 \, a^{2} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{8} + 28 \, a^{7} b + 130 \, a^{6} b^{2} + 300 \, a^{5} b^{3} + 355 \, a^{4} b^{4} + 208 \, a^{3} b^{5} + 48 \, a^{2} b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{8} + 20 \, a^{7} b + 34 \, a^{6} b^{2} - 4 \, a^{5} b^{3} - 61 \, a^{4} b^{4} - 56 \, a^{3} b^{5} - 16 \, a^{2} b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{8} + 12 \, a^{7} b + 38 \, a^{6} b^{2} + 52 \, a^{5} b^{3} + 33 \, a^{4} b^{4} + 8 \, a^{3} b^{5}\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} - 83 \, a^{3} b + 6 \, a^{2} b^{2} + 2 \, {\left(8 \, a^{4} - 299 \, a^{2} b^{2} + 24 \, a b^{3}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(96 \, a^{4} + 71 \, a^{3} b - 344 \, a^{2} b^{2} + 1208 \, a b^{3} - 48 \, b^{4}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - 4 \, {\left(56 \, a^{4} + 144 \, a^{3} b + 31 \, a^{2} b^{2} - 546 \, a b^{3} + 36 \, b^{4}\right)} e^{\left(-6 \, d x - 6 \, c\right)} - {\left(176 \, a^{4} + 569 \, a^{3} b + 666 \, a^{2} b^{2} + 1704 \, a b^{3} - 144 \, b^{4}\right)} e^{\left(-8 \, d x - 8 \, c\right)} - 6 \, {\left(8 \, a^{4} + 32 \, a^{3} b + 93 \, a^{2} b^{2} - 28 \, a b^{3} + 8 \, b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - 15 \, {\left(3 \, a^{3} b - 4 \, a^{2} b^{2}\right)} e^{\left(-12 \, d x - 12 \, c\right)}}{32 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4} + {\left(a^{7} + 12 \, a^{6} b + 38 \, a^{5} b^{2} + 52 \, a^{4} b^{3} + 33 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-2 \, d x - 2 \, c\right)} - {\left(3 \, a^{7} + 20 \, a^{6} b + 34 \, a^{5} b^{2} - 4 \, a^{4} b^{3} - 61 \, a^{3} b^{4} - 56 \, a^{2} b^{5} - 16 \, a b^{6}\right)} e^{\left(-4 \, d x - 4 \, c\right)} - {\left(3 \, a^{7} + 28 \, a^{6} b + 130 \, a^{5} b^{2} + 300 \, a^{4} b^{3} + 355 \, a^{3} b^{4} + 208 \, a^{2} b^{5} + 48 \, a b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + {\left(3 \, a^{7} + 28 \, a^{6} b + 130 \, a^{5} b^{2} + 300 \, a^{4} b^{3} + 355 \, a^{3} b^{4} + 208 \, a^{2} b^{5} + 48 \, a b^{6}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + {\left(3 \, a^{7} + 20 \, a^{6} b + 34 \, a^{5} b^{2} - 4 \, a^{4} b^{3} - 61 \, a^{3} b^{4} - 56 \, a^{2} b^{5} - 16 \, a b^{6}\right)} e^{\left(-10 \, d x - 10 \, c\right)} - {\left(a^{7} + 12 \, a^{6} b + 38 \, a^{5} b^{2} + 52 \, a^{4} b^{3} + 33 \, a^{3} b^{4} + 8 \, a^{2} b^{5}\right)} e^{\left(-12 \, d x - 12 \, 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(-14 \, d x - 14 \, c\right)}\right)} d}"," ",0,"1/8*(3*a^3*b + 12*a^2*b^2 + 8*a*b^3 + 2*b^4)*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d) - 3/4*b*log(a*e^(4*d*x + 4*c) + 2*(a + 2*b)*e^(2*d*x + 2*c) + a)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 1/8*(3*a^3*b + 12*a^2*b^2 + 8*a*b^3 + 2*b^4)*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d) + 3/4*b*log(2*(a + 2*b)*e^(-2*d*x - 2*c) + a*e^(-4*d*x - 4*c) + a)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) + 1/4*(2*a + 5*b)*log(e^(2*d*x + 2*c) - 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) + 3/2*b*log(e^(2*d*x + 2*c) - 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 1/4*(2*a + 5*b)*log(e^(-2*d*x - 2*c) - 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 3/2*b*log(e^(-2*d*x - 2*c) - 1)/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d) - 1/256*(15*a^4*b + 260*a^3*b^2 + 504*a^2*b^3 + 288*a*b^4 + 64*b^5)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*sqrt((a + b)*b)*d) + 5/64*(3*a*b + 10*b^2)*log((a*e^(2*d*x + 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(2*d*x + 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*b)*d) + 1/256*(15*a^4*b + 260*a^3*b^2 + 504*a^2*b^3 + 288*a*b^4 + 64*b^5)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*sqrt((a + b)*b)*d) - 5/64*(3*a*b + 10*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*b)*d) + 15/128*(3*a*b - 4*b^2)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sqrt((a + b)*b)*d) + 1/192*(176*a^6 + 275*a^5*b + 306*a^4*b^2 + 456*a^3*b^3 + 144*a^2*b^4 + 3*(96*a^6 + 111*a^5*b - 220*a^4*b^2 - 776*a^3*b^3 - 832*a^2*b^4 - 256*a*b^5)*e^(12*d*x + 12*c) + 6*(120*a^6 + 528*a^5*b + 525*a^4*b^2 - 52*a^3*b^3 - 896*a^2*b^4 - 1216*a*b^5 - 384*b^6)*e^(10*d*x + 10*c) + (176*a^6 + 1337*a^5*b + 7554*a^4*b^2 + 16416*a^3*b^3 + 26880*a^2*b^4 + 25344*a*b^5 + 6912*b^6)*e^(8*d*x + 8*c) - 4*(184*a^6 + 1056*a^5*b + 2993*a^4*b^2 + 4122*a^3*b^3 + 5892*a^2*b^4 + 6144*a*b^5 + 1728*b^6)*e^(6*d*x + 6*c) - (384*a^6 + 1177*a^5*b - 736*a^4*b^2 + 112*a^3*b^3 - 624*a^2*b^4 - 6144*a*b^5 - 2304*b^6)*e^(4*d*x + 4*c) + 2*(136*a^6 + 912*a^5*b + 1211*a^4*b^2 + 1440*a^3*b^3 + 1896*a^2*b^4 + 576*a*b^5)*e^(2*d*x + 2*c))/((a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4 - (a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*e^(14*d*x + 14*c) - (a^9 + 12*a^8*b + 38*a^7*b^2 + 52*a^6*b^3 + 33*a^5*b^4 + 8*a^4*b^5)*e^(12*d*x + 12*c) + (3*a^9 + 20*a^8*b + 34*a^7*b^2 - 4*a^6*b^3 - 61*a^5*b^4 - 56*a^4*b^5 - 16*a^3*b^6)*e^(10*d*x + 10*c) + (3*a^9 + 28*a^8*b + 130*a^7*b^2 + 300*a^6*b^3 + 355*a^5*b^4 + 208*a^4*b^5 + 48*a^3*b^6)*e^(8*d*x + 8*c) - (3*a^9 + 28*a^8*b + 130*a^7*b^2 + 300*a^6*b^3 + 355*a^5*b^4 + 208*a^4*b^5 + 48*a^3*b^6)*e^(6*d*x + 6*c) - (3*a^9 + 20*a^8*b + 34*a^7*b^2 - 4*a^6*b^3 - 61*a^5*b^4 - 56*a^4*b^5 - 16*a^3*b^6)*e^(4*d*x + 4*c) + (a^9 + 12*a^8*b + 38*a^7*b^2 + 52*a^6*b^3 + 33*a^5*b^4 + 8*a^4*b^5)*e^(2*d*x + 2*c))*d) - 1/192*(176*a^6 + 275*a^5*b + 306*a^4*b^2 + 456*a^3*b^3 + 144*a^2*b^4 + 2*(136*a^6 + 912*a^5*b + 1211*a^4*b^2 + 1440*a^3*b^3 + 1896*a^2*b^4 + 576*a*b^5)*e^(-2*d*x - 2*c) - (384*a^6 + 1177*a^5*b - 736*a^4*b^2 + 112*a^3*b^3 - 624*a^2*b^4 - 6144*a*b^5 - 2304*b^6)*e^(-4*d*x - 4*c) - 4*(184*a^6 + 1056*a^5*b + 2993*a^4*b^2 + 4122*a^3*b^3 + 5892*a^2*b^4 + 6144*a*b^5 + 1728*b^6)*e^(-6*d*x - 6*c) + (176*a^6 + 1337*a^5*b + 7554*a^4*b^2 + 16416*a^3*b^3 + 26880*a^2*b^4 + 25344*a*b^5 + 6912*b^6)*e^(-8*d*x - 8*c) + 6*(120*a^6 + 528*a^5*b + 525*a^4*b^2 - 52*a^3*b^3 - 896*a^2*b^4 - 1216*a*b^5 - 384*b^6)*e^(-10*d*x - 10*c) + 3*(96*a^6 + 111*a^5*b - 220*a^4*b^2 - 776*a^3*b^3 - 832*a^2*b^4 - 256*a*b^5)*e^(-12*d*x - 12*c))/((a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4 + (a^9 + 12*a^8*b + 38*a^7*b^2 + 52*a^6*b^3 + 33*a^5*b^4 + 8*a^4*b^5)*e^(-2*d*x - 2*c) - (3*a^9 + 20*a^8*b + 34*a^7*b^2 - 4*a^6*b^3 - 61*a^5*b^4 - 56*a^4*b^5 - 16*a^3*b^6)*e^(-4*d*x - 4*c) - (3*a^9 + 28*a^8*b + 130*a^7*b^2 + 300*a^6*b^3 + 355*a^5*b^4 + 208*a^4*b^5 + 48*a^3*b^6)*e^(-6*d*x - 6*c) + (3*a^9 + 28*a^8*b + 130*a^7*b^2 + 300*a^6*b^3 + 355*a^5*b^4 + 208*a^4*b^5 + 48*a^3*b^6)*e^(-8*d*x - 8*c) + (3*a^9 + 20*a^8*b + 34*a^7*b^2 - 4*a^6*b^3 - 61*a^5*b^4 - 56*a^4*b^5 - 16*a^3*b^6)*e^(-10*d*x - 10*c) - (a^9 + 12*a^8*b + 38*a^7*b^2 + 52*a^6*b^3 + 33*a^5*b^4 + 8*a^4*b^5)*e^(-12*d*x - 12*c) - (a^9 + 4*a^8*b + 6*a^7*b^2 + 4*a^6*b^3 + a^5*b^4)*e^(-14*d*x - 14*c))*d) + 1/48*(32*a^5 + 77*a^4*b - 72*a^3*b^2 - 12*a^2*b^3 + 3*(32*a^5 + 65*a^4*b + 94*a^3*b^2 + 128*a^2*b^3 + 32*a*b^4)*e^(12*d*x + 12*c) + 6*(48*a^5 + 200*a^4*b + 203*a^3*b^2 + 90*a^2*b^3 + 176*a*b^4 + 32*b^5)*e^(10*d*x + 10*c) + (224*a^5 + 839*a^4*b + 1500*a^3*b^2 - 612*a^2*b^3 - 3648*a*b^4 - 576*b^5)*e^(8*d*x + 8*c) - 4*(16*a^5 + 216*a^4*b + 695*a^3*b^2 + 252*a^2*b^3 - 912*a*b^4 - 144*b^5)*e^(6*d*x + 6*c) - (96*a^5 + 343*a^4*b - 850*a^3*b^2 - 1808*a^2*b^3 + 1056*a*b^4 + 192*b^5)*e^(4*d*x + 4*c) + 2*(16*a^5 + 216*a^4*b + 269*a^3*b^2 - 294*a^2*b^3 - 48*a*b^4)*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 + 12*a^7*b + 38*a^6*b^2 + 52*a^5*b^3 + 33*a^4*b^4 + 8*a^3*b^5)*e^(12*d*x + 12*c) + (3*a^8 + 20*a^7*b + 34*a^6*b^2 - 4*a^5*b^3 - 61*a^4*b^4 - 56*a^3*b^5 - 16*a^2*b^6)*e^(10*d*x + 10*c) + (3*a^8 + 28*a^7*b + 130*a^6*b^2 + 300*a^5*b^3 + 355*a^4*b^4 + 208*a^3*b^5 + 48*a^2*b^6)*e^(8*d*x + 8*c) - (3*a^8 + 28*a^7*b + 130*a^6*b^2 + 300*a^5*b^3 + 355*a^4*b^4 + 208*a^3*b^5 + 48*a^2*b^6)*e^(6*d*x + 6*c) - (3*a^8 + 20*a^7*b + 34*a^6*b^2 - 4*a^5*b^3 - 61*a^4*b^4 - 56*a^3*b^5 - 16*a^2*b^6)*e^(4*d*x + 4*c) + (a^8 + 12*a^7*b + 38*a^6*b^2 + 52*a^5*b^3 + 33*a^4*b^4 + 8*a^3*b^5)*e^(2*d*x + 2*c))*d) - 1/48*(32*a^5 + 77*a^4*b - 72*a^3*b^2 - 12*a^2*b^3 + 2*(16*a^5 + 216*a^4*b + 269*a^3*b^2 - 294*a^2*b^3 - 48*a*b^4)*e^(-2*d*x - 2*c) - (96*a^5 + 343*a^4*b - 850*a^3*b^2 - 1808*a^2*b^3 + 1056*a*b^4 + 192*b^5)*e^(-4*d*x - 4*c) - 4*(16*a^5 + 216*a^4*b + 695*a^3*b^2 + 252*a^2*b^3 - 912*a*b^4 - 144*b^5)*e^(-6*d*x - 6*c) + (224*a^5 + 839*a^4*b + 1500*a^3*b^2 - 612*a^2*b^3 - 3648*a*b^4 - 576*b^5)*e^(-8*d*x - 8*c) + 6*(48*a^5 + 200*a^4*b + 203*a^3*b^2 + 90*a^2*b^3 + 176*a*b^4 + 32*b^5)*e^(-10*d*x - 10*c) + 3*(32*a^5 + 65*a^4*b + 94*a^3*b^2 + 128*a^2*b^3 + 32*a*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 + (a^8 + 12*a^7*b + 38*a^6*b^2 + 52*a^5*b^3 + 33*a^4*b^4 + 8*a^3*b^5)*e^(-2*d*x - 2*c) - (3*a^8 + 20*a^7*b + 34*a^6*b^2 - 4*a^5*b^3 - 61*a^4*b^4 - 56*a^3*b^5 - 16*a^2*b^6)*e^(-4*d*x - 4*c) - (3*a^8 + 28*a^7*b + 130*a^6*b^2 + 300*a^5*b^3 + 355*a^4*b^4 + 208*a^3*b^5 + 48*a^2*b^6)*e^(-6*d*x - 6*c) + (3*a^8 + 28*a^7*b + 130*a^6*b^2 + 300*a^5*b^3 + 355*a^4*b^4 + 208*a^3*b^5 + 48*a^2*b^6)*e^(-8*d*x - 8*c) + (3*a^8 + 20*a^7*b + 34*a^6*b^2 - 4*a^5*b^3 - 61*a^4*b^4 - 56*a^3*b^5 - 16*a^2*b^6)*e^(-10*d*x - 10*c) - (a^8 + 12*a^7*b + 38*a^6*b^2 + 52*a^5*b^3 + 33*a^4*b^4 + 8*a^3*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)*e^(-14*d*x - 14*c))*d) + 1/32*(16*a^4 - 83*a^3*b + 6*a^2*b^2 + 2*(8*a^4 - 299*a^2*b^2 + 24*a*b^3)*e^(-2*d*x - 2*c) - (96*a^4 + 71*a^3*b - 344*a^2*b^2 + 1208*a*b^3 - 48*b^4)*e^(-4*d*x - 4*c) - 4*(56*a^4 + 144*a^3*b + 31*a^2*b^2 - 546*a*b^3 + 36*b^4)*e^(-6*d*x - 6*c) - (176*a^4 + 569*a^3*b + 666*a^2*b^2 + 1704*a*b^3 - 144*b^4)*e^(-8*d*x - 8*c) - 6*(8*a^4 + 32*a^3*b + 93*a^2*b^2 - 28*a*b^3 + 8*b^4)*e^(-10*d*x - 10*c) - 15*(3*a^3*b - 4*a^2*b^2)*e^(-12*d*x - 12*c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4 + (a^7 + 12*a^6*b + 38*a^5*b^2 + 52*a^4*b^3 + 33*a^3*b^4 + 8*a^2*b^5)*e^(-2*d*x - 2*c) - (3*a^7 + 20*a^6*b + 34*a^5*b^2 - 4*a^4*b^3 - 61*a^3*b^4 - 56*a^2*b^5 - 16*a*b^6)*e^(-4*d*x - 4*c) - (3*a^7 + 28*a^6*b + 130*a^5*b^2 + 300*a^4*b^3 + 355*a^3*b^4 + 208*a^2*b^5 + 48*a*b^6)*e^(-6*d*x - 6*c) + (3*a^7 + 28*a^6*b + 130*a^5*b^2 + 300*a^4*b^3 + 355*a^3*b^4 + 208*a^2*b^5 + 48*a*b^6)*e^(-8*d*x - 8*c) + (3*a^7 + 20*a^6*b + 34*a^5*b^2 - 4*a^4*b^3 - 61*a^3*b^4 - 56*a^2*b^5 - 16*a*b^6)*e^(-10*d*x - 10*c) - (a^7 + 12*a^6*b + 38*a^5*b^2 + 52*a^4*b^3 + 33*a^3*b^4 + 8*a^2*b^5)*e^(-12*d*x - 12*c) - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*e^(-14*d*x - 14*c))*d)","B",0
169,1,718,0,0.839948," ","integrate(1/(a+b*sech(d*x+c)^2)^4,x, algorithm=""maxima"")","\frac{{\left(35 \, a^{3} b + 70 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} \log\left(\frac{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b - 2 \, \sqrt{{\left(a + b\right)} b}}{a e^{\left(-2 \, d x - 2 \, c\right)} + a + 2 \, b + 2 \, \sqrt{{\left(a + b\right)} b}}\right)}{32 \, {\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{{\left(a + b\right)} b} d} - \frac{87 \, a^{5} b + 116 \, a^{4} b^{2} + 44 \, a^{3} b^{3} + 3 \, {\left(145 \, a^{5} b + 458 \, a^{4} b^{2} + 416 \, a^{3} b^{3} + 128 \, a^{2} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 6 \, {\left(145 \, a^{5} b + 632 \, a^{4} b^{2} + 1072 \, a^{3} b^{3} + 768 \, a^{2} b^{4} + 208 \, a b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 2 \, {\left(435 \, a^{5} b + 2146 \, a^{4} b^{2} + 4396 \, a^{3} b^{3} + 4968 \, a^{2} b^{4} + 2912 \, a b^{5} + 704 \, b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(145 \, a^{5} b + 708 \, a^{4} b^{2} + 1324 \, a^{3} b^{3} + 1024 \, a^{2} b^{4} + 288 \, a b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 3 \, {\left(29 \, a^{5} b + 122 \, a^{4} b^{2} + 136 \, a^{3} b^{3} + 48 \, a^{2} b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)}}{24 \, {\left(a^{10} + 3 \, a^{9} b + 3 \, a^{8} b^{2} + a^{7} b^{3} + 6 \, {\left(a^{10} + 5 \, a^{9} b + 9 \, a^{8} b^{2} + 7 \, a^{7} b^{3} + 2 \, a^{6} b^{4}\right)} e^{\left(-2 \, d x - 2 \, c\right)} + 3 \, {\left(5 \, a^{10} + 31 \, a^{9} b + 79 \, a^{8} b^{2} + 101 \, a^{7} b^{3} + 64 \, a^{6} b^{4} + 16 \, a^{5} b^{5}\right)} e^{\left(-4 \, d x - 4 \, c\right)} + 4 \, {\left(5 \, a^{10} + 33 \, a^{9} b + 93 \, a^{8} b^{2} + 147 \, a^{7} b^{3} + 138 \, a^{6} b^{4} + 72 \, a^{5} b^{5} + 16 \, a^{4} b^{6}\right)} e^{\left(-6 \, d x - 6 \, c\right)} + 3 \, {\left(5 \, a^{10} + 31 \, a^{9} b + 79 \, a^{8} b^{2} + 101 \, a^{7} b^{3} + 64 \, a^{6} b^{4} + 16 \, a^{5} b^{5}\right)} e^{\left(-8 \, d x - 8 \, c\right)} + 6 \, {\left(a^{10} + 5 \, a^{9} b + 9 \, a^{8} b^{2} + 7 \, a^{7} b^{3} + 2 \, a^{6} b^{4}\right)} e^{\left(-10 \, d x - 10 \, c\right)} + {\left(a^{10} + 3 \, a^{9} b + 3 \, a^{8} b^{2} + a^{7} b^{3}\right)} e^{\left(-12 \, d x - 12 \, c\right)}\right)} d} + \frac{d x + c}{a^{4} d}"," ",0,"1/32*(35*a^3*b + 70*a^2*b^2 + 56*a*b^3 + 16*b^4)*log((a*e^(-2*d*x - 2*c) + a + 2*b - 2*sqrt((a + b)*b))/(a*e^(-2*d*x - 2*c) + a + 2*b + 2*sqrt((a + b)*b)))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt((a + b)*b)*d) - 1/24*(87*a^5*b + 116*a^4*b^2 + 44*a^3*b^3 + 3*(145*a^5*b + 458*a^4*b^2 + 416*a^3*b^3 + 128*a^2*b^4)*e^(-2*d*x - 2*c) + 6*(145*a^5*b + 632*a^4*b^2 + 1072*a^3*b^3 + 768*a^2*b^4 + 208*a*b^5)*e^(-4*d*x - 4*c) + 2*(435*a^5*b + 2146*a^4*b^2 + 4396*a^3*b^3 + 4968*a^2*b^4 + 2912*a*b^5 + 704*b^6)*e^(-6*d*x - 6*c) + 3*(145*a^5*b + 708*a^4*b^2 + 1324*a^3*b^3 + 1024*a^2*b^4 + 288*a*b^5)*e^(-8*d*x - 8*c) + 3*(29*a^5*b + 122*a^4*b^2 + 136*a^3*b^3 + 48*a^2*b^4)*e^(-10*d*x - 10*c))/((a^10 + 3*a^9*b + 3*a^8*b^2 + a^7*b^3 + 6*(a^10 + 5*a^9*b + 9*a^8*b^2 + 7*a^7*b^3 + 2*a^6*b^4)*e^(-2*d*x - 2*c) + 3*(5*a^10 + 31*a^9*b + 79*a^8*b^2 + 101*a^7*b^3 + 64*a^6*b^4 + 16*a^5*b^5)*e^(-4*d*x - 4*c) + 4*(5*a^10 + 33*a^9*b + 93*a^8*b^2 + 147*a^7*b^3 + 138*a^6*b^4 + 72*a^5*b^5 + 16*a^4*b^6)*e^(-6*d*x - 6*c) + 3*(5*a^10 + 31*a^9*b + 79*a^8*b^2 + 101*a^7*b^3 + 64*a^6*b^4 + 16*a^5*b^5)*e^(-8*d*x - 8*c) + 6*(a^10 + 5*a^9*b + 9*a^8*b^2 + 7*a^7*b^3 + 2*a^6*b^4)*e^(-10*d*x - 10*c) + (a^10 + 3*a^9*b + 3*a^8*b^2 + a^7*b^3)*e^(-12*d*x - 12*c))*d) + (d*x + c)/(a^4*d)","B",0
170,1,33,0,0.459634," ","integrate((1-sech(x)^2)^(3/2),x, algorithm=""maxima"")","-x - \frac{2 \, e^{\left(-2 \, x\right)}}{2 \, e^{\left(-2 \, x\right)} + e^{\left(-4 \, x\right)} + 1} - \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-x - 2*e^(-2*x)/(2*e^(-2*x) + e^(-4*x) + 1) - log(e^(-2*x) + 1)","A",0
171,1,13,0,0.606334," ","integrate((1-sech(x)^2)^(1/2),x, algorithm=""maxima"")","-x - \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-x - log(e^(-2*x) + 1)","A",0
172,1,22,0,0.669718," ","integrate(1/(1-sech(x)^2)^(1/2),x, algorithm=""maxima"")","-x - \log\left(e^{\left(-x\right)} + 1\right) - \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"-x - log(e^(-x) + 1) - log(e^(-x) - 1)","A",0
173,1,33,0,0.488973," ","integrate((-1+sech(x)^2)^(3/2),x, algorithm=""maxima"")","i \, x + \frac{2 i \, e^{\left(-2 \, x\right)}}{2 \, e^{\left(-2 \, x\right)} + e^{\left(-4 \, x\right)} + 1} + i \, \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"I*x + 2*I*e^(-2*x)/(2*e^(-2*x) + e^(-4*x) + 1) + I*log(e^(-2*x) + 1)","C",0
174,1,13,0,0.545297," ","integrate((-1+sech(x)^2)^(1/2),x, algorithm=""maxima"")","-i \, x - i \, \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-I*x - I*log(e^(-2*x) + 1)","C",0
175,1,22,0,0.439430," ","integrate(1/(-1+sech(x)^2)^(1/2),x, algorithm=""maxima"")","i \, x + i \, \log\left(e^{\left(-x\right)} + 1\right) + i \, \log\left(e^{\left(-x\right)} - 1\right)"," ",0,"I*x + I*log(e^(-x) + 1) + I*log(e^(-x) - 1)","C",0
176,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(1/2)*tanh(x)^5,x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \tanh\left(x\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*tanh(x)^5, x)","F",0
177,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(1/2)*tanh(x)^4,x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \tanh\left(x\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*tanh(x)^4, x)","F",0
178,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(1/2)*tanh(x)^3,x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \tanh\left(x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*tanh(x)^3, x)","F",0
179,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(1/2)*tanh(x)^2,x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \tanh\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*tanh(x)^2, x)","F",0
180,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(1/2)*tanh(x),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \tanh\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*tanh(x), x)","F",0
181,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a), x)","F",0
182,0,0,0,0.000000," ","integrate(coth(x)*(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \coth\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*coth(x), x)","F",0
183,0,0,0,0.000000," ","integrate(coth(x)^2*(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \coth\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*coth(x)^2, x)","F",0
184,0,0,0,0.000000," ","integrate(coth(x)^3*(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \coth\left(x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*coth(x)^3, x)","F",0
185,0,0,0,0.000000," ","integrate(coth(x)^4*(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \coth\left(x\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*coth(x)^4, x)","F",0
186,0,0,0,0.000000," ","integrate(coth(x)^5*(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{sech}\left(x\right)^{2} + a} \coth\left(x\right)^{5}\,{d x}"," ",0,"integrate(sqrt(b*sech(x)^2 + a)*coth(x)^5, x)","F",0
187,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(3/2)*tanh(x)^3,x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)^{3}\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(3/2)*tanh(x)^3, x)","F",0
188,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(3/2)*tanh(x)^2,x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(3/2)*tanh(x)^2, x)","F",0
189,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(3/2)*tanh(x),x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(x\right)\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(3/2)*tanh(x), x)","F",0
190,0,0,0,0.000000," ","integrate((a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate(coth(x)*(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(3/2)*coth(x), x)","F",0
192,0,0,0,0.000000," ","integrate(coth(x)^2*(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \coth\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(3/2)*coth(x)^2, x)","F",0
193,0,0,0,0.000000," ","integrate((a+b*sech(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{sech}\left(d x + c\right)^{2} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*sech(d*x + c)^2 + a)^(5/2), x)","F",0
194,0,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{5}}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^5/sqrt(b*sech(x)^2 + a), x)","F",0
195,0,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{4}}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^4/sqrt(b*sech(x)^2 + a), x)","F",0
196,0,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{3}}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^3/sqrt(b*sech(x)^2 + a), x)","F",0
197,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)^2/sqrt(b*sech(x)^2 + a), x)","F",0
198,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tanh(x)/sqrt(b*sech(x)^2 + a), x)","F",0
199,0,0,0,0.000000," ","integrate(1/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*sech(x)^2 + a), x)","F",0
200,0,0,0,0.000000," ","integrate(coth(x)/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)/sqrt(b*sech(x)^2 + a), x)","F",0
201,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)^2/sqrt(b*sech(x)^2 + a), x)","F",0
202,0,0,0,0.000000," ","integrate(coth(x)^3/(a+b*sech(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{3}}{\sqrt{b \operatorname{sech}\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(coth(x)^3/sqrt(b*sech(x)^2 + a), x)","F",0
203,0,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{5}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^5/(b*sech(x)^2 + a)^(3/2), x)","F",0
204,0,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{4}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^4/(b*sech(x)^2 + a)^(3/2), x)","F",0
205,0,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{3}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^3/(b*sech(x)^2 + a)^(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^2/(b*sech(x)^2 + a)^(3/2), x)","F",0
207,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*sech(x)^2 + a)^(3/2), x)","F",0
208,0,0,0,0.000000," ","integrate(1/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(-3/2), x)","F",0
209,0,0,0,0.000000," ","integrate(coth(x)/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*sech(x)^2 + a)^(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*sech(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(coth(x)^2/(b*sech(x)^2 + a)^(3/2), x)","F",0
211,0,0,0,0.000000," ","integrate(tanh(x)^6/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{6}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^6/(b*sech(x)^2 + a)^(5/2), x)","F",0
212,0,0,0,0.000000," ","integrate(tanh(x)^5/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{5}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^5/(b*sech(x)^2 + a)^(5/2), x)","F",0
213,0,0,0,0.000000," ","integrate(tanh(x)^4/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{4}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^4/(b*sech(x)^2 + a)^(5/2), x)","F",0
214,0,0,0,0.000000," ","integrate(tanh(x)^3/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{3}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^3/(b*sech(x)^2 + a)^(5/2), x)","F",0
215,0,0,0,0.000000," ","integrate(tanh(x)^2/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)^{2}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)^2/(b*sech(x)^2 + a)^(5/2), x)","F",0
216,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tanh\left(x\right)}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tanh(x)/(b*sech(x)^2 + a)^(5/2), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*sech(x)^2 + a)^(-5/2), x)","F",0
218,0,0,0,0.000000," ","integrate(coth(x)/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)/(b*sech(x)^2 + a)^(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate(coth(x)^2/(a+b*sech(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\coth\left(x\right)^{2}}{{\left(b \operatorname{sech}\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(coth(x)^2/(b*sech(x)^2 + a)^(5/2), x)","F",0
220,0,0,0,0.000000," ","integrate(1/(a+b*sech(d*x+c)^2)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{sech}\left(d x + c\right)^{2} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*sech(d*x + c)^2 + a)^(-7/2), x)","F",0
